A deterministic finite automaton for faster protein hit detection in BLAST

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第三章有穷自动机

例：将图示的DFA M最小化。
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1、将M状态分为两个子集： P0=({1,2,3,4},{5,6,7})
2、{1,2,3,4}读入a后划为： P1=({1,2},{3,4},{5,6,7})
3、进一步划分： P2=({1,2},{3},{4},{5,6,7})
对M的状态集S进行划分的步骤：
①把S的终态与非终态分开，分成两个子集，形成基本划分，属于这两个不同子集的状态是可区别的。
②假定某个时候已含m个子集，记={I(1) , I(2) , …,I(m) }且属于不同子集的状态是可区别的，再检查中的每个I能否进一步划分，对于某个I(i) ，令I(i) ={S1,S2,…,Sk}，若存在一个输入字符使得move(I(i) ,a)不包含在现行的某一子集I(i)中，则将I(i)一分为二。
若M的某些结既是初态结，又是终态结，
或者存在一条从某个初态结到某个终态结的道路，则空字可为M所接受。
例： NFA M=({0,1,2,3,4},{a,b},f,{0},{2,4})
f(0,a)={0,3} f(2,b)={2} f(0,b)={0,1}
f(3,a)={4} f(1,b)={2} f(4,a)={4}
M’=(K, ,f,S,Z)
一个含有m个状态和n个输入字符的NFA 可表示为一张状态转换图，该图含有m个状态结，每个结可射出若干条箭弧与别的结点相连接，每条弧用*中的一个字（不一定要不同的字，且可以为空字）作标记（称输入字），整个图至少含有一个初态结以及若干个终态结。

正则表达式转换成nfa

正则表达式（Regular Expression）是一种用于匹配字符串的强大工具，而NFA（Non-deterministic Finite Automaton，非确定性有限自动机）是一种可以用于匹配正则表达式的模型。

下面是将正则表达式转换为NFA的一般步骤：1. 将正则表达式转换为Brzozowski标准形式。

Brzozowski标准形式是一种将正则表达式转换为后缀形式的方法。

在Brzozowski标准形式中，每个操作符都被放在括号中，例如(ab)*c表示匹配零个或多个ab，后面跟着一个c。

2. 将Brzozowski标准形式转换为Thompson构造法。

Thompson构造法是一种通过构建一组字符串来模拟正则表达式的匹配过程的方法。

在Thompson构造法中，每个操作符都被表示为一个特定的字符串，例如星号(*)表示重复零个或多个次数的字符串，括号()表示匹配括号内字符串的重复次数。

3. 将Thompson构造法转换为NFA。

在Thompson构造法中，每个字符串都表示一个状态转换。

因此，可以将每个字符串转换为一个状态，并根据字符串之间的顺序将这些状态连接起来。

在NFA中，每个状态都表示一个可能的输入序列，而状态之间的转换则表示输入序列的下一个可能的输入。

4. 确定NFA的起始状态和终止状态。

在NFA中，起始状态是开始匹配正则表达式的状态，而终止状态是匹配结束的状态。

可以根据Thompson构造法中每个字符串的顺序来确定起始状态和终止状态。

例如，如果最后一个字符串是正则表达式的结尾，那么它对应的状态就是终止状态。

5. 确定NFA的转换函数和接受集。

转换函数是将一个状态和一个输入字符映射到下一个状态的函数。

接受集是一个状态集合，当自动机达到这个状态集合时，它就匹配成功。

可以根据NFA中的状态转换来确定转换函数和接受集。

通过以上步骤，可以将正则表达式转换为NFA，以便进行字符串匹配。

[生活]计算机专业英语词汇缩写大全

[生活]计算机专业英语词汇缩写大全计算机专业英语词汇缩写大全计算机专业英语词汇缩写大全(J-Z)2010年01月06日星期三 12:47J J2EE — Java 2 Enterprise Edition J2ME — Java 2 Micro Edition J2SE — Java 2 Standard Edition JAXB — Java Architecture for XML Binding JAX-RPC — Java XML for Remote Procedure Calls JAXP — Java API for XML Processing JBOD — Just a Bunch of Disks JCE — Java Cryptography Extension JCL — Job Control Language JCP — Java Community Process JDBC — Java Database Connectivity JDK — Java Development KitJES — Job Entry SubsystemJDS — Java Desktop SystemJFC — Java Foundation Classes JFET — Junction Field-Effect Transistor JFS — IBM Journaling File System JINI — Jini Is Not InitialsJIT — Just-In-TimeJMX — Java Management Extensions JMS — Java Message Service JNDI — Java Naming and Directory Interface JNI — Java Native InterfaceJPEG — Joint Photographic Experts Group JRE — Java Runtime Environment JS — JavaScriptJSON — JavaScript Object NotationJSP — Jackson Structured Programming JSP — JavaServer PagesJTAG — Joint Test Action Group JUG — Java Users Group JVM — Java Virtual Machine jwz — Jamie ZawinskiKK&R — Kernighan and Ritchie KB — KeyboardKb — KilobitKB — KilobyteKB — Knowledge BaseKDE — K Desktop Environment kHz — KilohertzKISS — Keep It Simple, Stupid KVM — Keyboard, Video, Mouse LL10N — LocalizationL2TP — Layer 2 Tunneling Protocol LAMP — Linux Apache MySQL Perl LAMP — Linux Apache MySQL PHP LAMP — Linux Apache MySQL Python LAN —Local Area Network LBA — Logical Block Addressing LCD — Liquid Crystal Display LCOS — Liquid Crystal On Silicon LDAP — Lightweight Directory Access ProtocolLE — Logical ExtentsLED — Light-Emitting Diode LF — Line FeedLF — Low FrequencyLFS — Linux From Scratch lib — libraryLIF — Low Insertion Force LIFO — Last In First Out LILO — Linux LoaderLKML — Linux Kernel Mailing List LM — Lan ManagerLGPL — Lesser General Public License LOC — Lines of CodeLPI — Linux Professional Institute LPT — Line Print Terminal LSB — Least Significant Bit LSB — Linux Standard Base LSI — Large-Scale IntegrationLTL — Linear Temporal Logic LTR — Left-to-RightLUG — Linux User Group LUN — Logical Unit Number LV — Logical VolumeLVD — Low Voltage Differential LVM — Logical Volume Management LZW — Lempel-Ziv-Welch MMAC — Mandatory Access Control MAC — Media Access Control MAN —Metropolitan Area Network MANET — Mobile Ad-Hoc Network MAPI —Messaging Application Programming InterfaceMb — MegabitMB — MegabyteMBCS — Multi Byte Character Set MBR — Master Boot RecordMCA — Micro Channel Architecture MCSA — Microsoft Certified Systems AdministratorMCSD — Microsoft Certified Solution DeveloperMCSE — Microsoft Certified Systems Engineer MDA — Mail Delivery AgentMDA — Model-Driven Architecture MDA — Monochrome Display Adapter MDF — Main Distribution FrameMDI — Multiple Document Interface ME — [Windows] Millennium Edition MF — Medium FrequencyMFC — Microsoft Foundation Classes MFM — Modified Frequency Modulation MGCP — Media Gateway Control Protocol MHz — Megahertz MIB — Management Information Base MICR — Magnetic Ink Character Recognition MIDI — Musical Instrument Digital Interface MIMD —Multiple Instruction, Multiple Data MIMO — Multiple-Input Multiple-Output MIPS — Million Instructions Per Second MIPS — Microprocessor without Interlocked Pipeline StagesMIS — Management Information Systems MISD — Multiple Instruction, Single Data MIT — Massachusetts Institute of Technology MIME —Multipurpose Internet Mail ExtensionsMMDS — Mortality Medical Data System MMI — Man Machine Interface. MMIO — Memory-Mapped I/OMMORPG — Massively Multiplayer Online Role-Playing GameMMU — Memory Management Unit MMX — Multi-Media Extensions MNG —Multiple-image Network Graphics MoBo — MotherboardMOM — Message-Oriented Middleware MOO — MUD Object OrientedMOSFET — Metal-Oxide Semiconductor FET MOTD — Message Of The Day MPAA — Motion Picture Association of America MPEG — Motion Pictures Experts Group MPL — Mozilla Public License MPLS —Multiprotocol Label Switching MPU — Microprocessor Unit MS — Memory StickMS — MicrosoftMSB — Most Significant Bit MS-DOS — Microsoft DOSMT — Machine TranslationMTA — Mail Transfer AgentMTU — Maximum Transmission Unit MSA — Mail Submission Agent MSDN — Microsoft Developer Network MSI — Medium-Scale Integration MSI — Microsoft InstallerMUA — Mail User AgentMUD — Multi-User DungeonMVC — Model-View-ControllerMVP — Most Valuable Professional MVS — Multiple Virtual Storage MX — Mail exchangeMXF — Material Exchange Format NNACK — Negative ACKnowledgement NAK — Negative AcKnowledge Character NAS — Network-Attached Storage NAT — Network Address Translation NCP — NetWare Core ProtocolNCQ — Native Command Queuing NCSA — National Center for Supercomputing ApplicationsNDPS — Novell Distributed Print Services NDS — Novell Directory Services NEP — Network Equipment Provider NEXT — Near-End CrossTalk NFA — Nondeterministic Finite Automaton GNSCB — Next-Generation Secure Computing BaseNFS — Network File SystemNI — National InstrumentsNIC — Network Interface Controller NIM — No Internal Message NIO — New I/ONIST — National Institute of Standards and TechnologyNLP — Natural Language Processing NLS — Native Language Support NP — Non-Deterministic Polynomial-TimeNPL — Netscape Public License NPU — Network Processing Unit NS —NetscapeNSA — National Security Agency NSPR — Netscape Portable Runtime NMI — Non-Maskable Interrupt NNTP — Network News Transfer Protocol NOC — Network Operations Center NOP — No OPerationNOS — Network Operating System NPTL — Native POSIX Thread Library NSS — Novell Storage Service NSS — Network Security Services NSS —Name Service SwitchNT — New TechnologyNTFS — NT FilesystemNTLM — NT Lan ManagerNTP — Network Time Protocol NUMA — Non-Uniform Memory Access NURBS — Non-Uniform Rational B-Spline NVR - Network Video Recorder NVRAM — Non-Volatile Random Access Memory OOASIS — Organization for the Advancement of StructuredInformation StandardsOAT — Operational Acceptance Testing OBSAI — Open Base Station Architecture InitiativeODBC — Open Database Connectivity OEM — Original Equipment Manufacturer OES — Open Enterprise ServerOFTC — Open and Free Technology Community OLAP — Online Analytical Processing OLE — Object Linking and Embedding OLED — Organic LightEmitting Diode OLPC — One Laptop per Child OLTP — Online Transaction Processing OMG — Object Management Group OO — Object-Oriented OO — Open OfficeOOM — Out of memoryOOo — OOP — Object-Oriented Programming OPML — Outline Processor Markup Language ORB — Object Request Broker ORM — Oject-Relational Mapping OS — Open SourceOS — Operating SystemOSCON — O'Reilly Open Source Convention OSDN — Open Source Developer Network OSI — Open Source Initiative OSI — Open Systems Interconnection OSPF — Open Shortest Path First OSS — Open Sound SystemOSS — Open-Source SoftwareOSS — Operations Support System OSTG — Open Source Technology Group OUI — Organizationally Unique Identifier PP2P — Peer-To-PeerPAN — Personal Area Network PAP — Password Authentication Protocol PARC — Palo Alto Research Center PATA — Parallel ATAPC — Personal ComputerPCB — Printed Circuit BoardPCB — Process Control BlockPCI — Peripheral Component Interconnect PCIe — PCI ExpressPCL — Printer Command Language PCMCIA — Personal Computer Memory Card InternationalAssociationPCM — Pulse-Code ModulationPCRE — Perl Compatible Regular Expressions PD — Public Domain PDA — Personal Digital Assistant PDF — Portable Document Format PDP — Programmed Data Processor PE — Physical ExtentsPEBKAC — Problem Exists Between Keyboard And ChairPERL — Practical Extraction and Reporting LanguagePGA — Pin Grid ArrayPGO — Profile-Guided Optimization PGP — Pretty Good PrivacyPHP — PHP: Hypertext Preprocessor PIC — Peripheral Interface Controller PIC — Programmable Interrupt Controller PID — Proportional-Integral-Derivative PID — Process IDPIM — Personal Information Manager PINE — Program for Internet News & EmailPIO — Programmed Input/Output PKCS — Public Key Cryptography Standards PKI — Public Key Infrastructure PLC — Power Line Communication PLC — Programmable Logic Controller PLD — Programmable Logic Device PL/I — Programming Language One PL/M — Programming Language for MicrocomputersPL/P — Programming Language for Prime PLT — Power Line Telecoms PMM — POST Memory ManagerPNG — Portable Network Graphics PnP — Plug-and-PlayPoE — Power over EthernetPOP — Point of PresencePOP3 — Post Office Protocol v3 POSIX — Portable Operating System Interface POST — Power-On Self TestPPC — PowerPCPPI — Pixels Per InchPPP — Point-to-Point Protocol PPPoA — PPP over ATMPPPoE — PPP over EthernetPPTP — Point-to-Point Tunneling Protocol PS — PostScriptPS/2 — Personal System/2PSU — Power Supply UnitPSVI — Post-Schema-Validation Infoset PV — Physical VolumePVG — Physical Volume GroupPVR — Personal Video RecorderPXE — Preboot Execution Environment PXI — PCI eXtensions for Instrumentation QQDR — Quad Data RateQA — Quality AssuranceQFP — Quad Flat PackageQoS — Quality of ServiceQOTD — Quote of the DayQt — Quasar ToolkitQTAM — Queued Teleprocessing Access Method RRACF — Resource Access Control Facility RAD — Rapid Application Development RADIUS — Remote Authentication Dial In User Service RAID — Redundant Array of Independent Disks RAID — Redundant Array of Inexpensive Disks RAIT — Redundant Array of Inexpensive Tapes RAM —Random Access MemoryRARP — Reverse Address Resolution Protocol RAS — Remote Access ServiceRC — Region CodeRC — Release CandidateRC — Run CommandsRCS — Revision Control SystemRDBMS — Relational Database Management SystemRDF — Resource Description Framework RDM — Relational Data Model RDS — Remote Data ServicesREFAL — REcursive Functions Algorithmic LanguageREST — Representational State Transfer regex — Regular Expression regexp — Regular Expression RF — Radio FrequencyRFC — Request For CommentsRFI — Radio Frequency Interference RFID — Radio Frequency Identification RGB — Red, Green, BlueRGBA — Red, Green, Blue, Alpha RHL — Red Hat LinuxRHEL — Red Hat Enterprise Linux RIA — Rich Internet Application RIAA — Recording Industry Association of AmericaRIP — Raster Image Processor RIP — Routing Information Protocol RISC — Reduced Instruction Set Computer RLE — Run-Length Encoding RLL — Run-Length LimitedRMI — Remote Method Invocation RMS — Richard Matthew Stallman ROM — Read Only MemoryROMB — Read-Out Motherboard RPC — Remote Procedure Call RPG —Report Program Generator RPM — RPM Package ManagerRSA — Rivest Shamir Adleman RSI — Repetitive Strain Injury RSS —Rich Site Summary, RDF Site Summary, or Really SimpleSyndicationRTC — Real-Time ClockRTE — Real-Time EnterpriseRTL — Right-to-LeftRTOS — Real Time Operating System RTP — Real-time Transport Protocol RTS — Ready To SendRTSP — Real Time Streaming Protocol SSaaS — Software as a Service SAN — Storage Area NetworkSAR — Search And Replace[1]SATA — Serial ATASAX — Simple API for XMLSBOD — Spinning Beachball of Death SBP-2 — Serial Bus Protocol 2 sbin — superuser binarySBU — Standard Build UnitSCADA — Supervisory Control And Data AcquisitionSCID — Source Code in Database SCM — Software Configuration Management SCM — Source Code Management SCP — Secure Copy SCPI — Standard Commands for Programmable Instrumentation SCSI — Small Computer System Interface SCTP — Stream Control Transmission Protocol SD — Secure DigitalSDDL — Security Descriptor Definition LanguageSDI — Single Document InterfaceSDIO — Secure Digital Input OutputSDK — Software Development KitSDL — Simple DirectMedia LayerSDN — Service Delivery NetworkSDP — Session Description ProtocolSDR — Software-Defined RadioSDRAM — Synchronous Dynamic Random Access MemorySDSL — Symmetric DSLSE — Single EndedSEAL — Semantics-directed Environment Adaptation Language SEI — Software Engineering InstituteSEO — Search Engine OptimizationSFTP — Secure FTPSFTP — Simple File Transfer ProtocolSFTP — SSH File Transfer ProtocolSGI — Silicon Graphics, IncorporatedSGML — Standard Generalized Markup LanguageSHA — Secure Hash AlgorithmSHDSL — Single-pair High-speed Digital Subscriber LineSIGCAT — Special Interest Group on CD-ROM Applications andTechnologySIGGRAPH — Special Interest Group on GraphicsSIMD — Single Instruction, Multiple DataSIMM — Single Inline Memory ModuleSIP — Session Initiation ProtocolSIP — Supplementary Ideographic PlaneSISD — Single Instruction, Single Data SLED — SUSE LinuxEnterprise Desktop SLES — SUSE Linux Enterprise Server SLI — Scalable Link Interface SLIP — Serial Line Internet Protocol SLM — Service Level Management SLOC — Source Lines of Code SPMD — Single Program, Multiple Data SMA — SubMiniature version A SMB — Server Message Block SMBIOS — System Management BIOS SMIL — Synchronized Multimedia Integration LanguageS/MIME — Secure/Multipurpose Internet Mail ExtensionsSMP — Supplementary Multilingual Plane SMP — Symmetric Multi-Processing SMS — Short Message Service SMS — System Management Server SMT — Simultaneous Multithreading SMTP — Simple Mail Transfer Protocol SNA — Systems Network Architecture SNMP — Simple Network Management Protocol SOA — Service-Oriented Architecture SOE — Standard Operating Environment SOAP — Simple Object Access Protocol SoC — System-on-a-ChipSO-DIMM — Small Outline DIMM SOHO — Small Office/Home OfficeSOI — Silicon On InsulatorSP — Service PackSPA — Single Page Application SPF — Sender Policy Framework SPI —Serial Peripheral Interface SPI — Stateful Packet Inspection SPARC —Scalable Processor Architecture SQL — Structured Query Language SRAM —Static Random Access Memory SSD — Software Specification Document SSD - Solid-State DriveSSE — Streaming SIMD Extensions SSH — Secure ShellSSI — Server Side Includes SSI — Single-System Image SSI — Small-Scale Integration SSID — Service Set Identifier SSL — Secure Socket Layer SSP — Supplementary Special-purpose Plane SSSE — Supplementary Streaming SIMD Extensionssu — superuserSUS — Single UNIX Specification SUSE — Software und System-Entwicklung SVC — Scalable Video Coding SVG — Scalable Vector Graphics SVGA — Super Video Graphics Array SVD — Structured VLSI Design SWF —Shock Wave FlashSWT — Standard Widget Toolkit Sysop — System operatorTTAO — Track-At-OnceTB — TerabyteTcl — Tool Command Language TCP — Transmission Control Protocol TCP/IP — Transmission Control Protocol/Internet ProtocolTCU — Telecommunication Control Unit TDMA — Time Division Multiple Access TFT — Thin Film Transistor TI — Texas Instruments TLA — Three-Letter Acronym TLD — Top-Level DomainTLS — Thread-Local Storage TLS — Transport Layer Security tmp —temporaryTNC — Terminal Node Controller TNC — Threaded Neill-Concelman connector TSO — Time Sharing OptionTSP — Traveling Salesman Problem TSR — Terminate and Stay Resident TTA — True Tap AudioTTF — TrueType FontTTL — Transistor-Transistor Logic TTL — Time To LiveTTS — Text-to-SpeechTTY — TeletypeTUCOWS — The Ultimate Collection of Winsock SoftwareTUG — TeX Users GroupTWAIN - Technology Without An Interesting NameUUAAG — User Agent Accessibility Guidelines UAC — User Account Control UART — Universal Asynchronous Receiver/Transmitter UAT — User Acceptance Testing UCS — Universal Character SetUDDI — Universal Description, Discovery, and Integration UDMA — Ultra DMAUDP — User Datagram Protocol UE — User ExperienceUEFI — Unified Extensible Firmware Interface UHF — Ultra High Frequency UI — User InterfaceUL — UploadULA — Uncommitted Logic Array UMA — Upper Memory AreaUMB — Upper Memory BlockUML — Unified Modeling Language UML — User-Mode LinuxUMPC — Ultra-Mobile Personal Computer UNC — Universal Naming Convention UPS — Uninterruptible Power Supply URI — Uniform Resource Identifier URL — Uniform Resource Locator URN — Uniform Resource Name USB — Universal Serial Bus usr — userUSR — U.S. RoboticsUTC — Coordinated Universal Time UTF — Unicode Transformation FormatUTP — Unshielded Twisted Pair UUCP — Unix to Unix CopyUUID — Universally Unique Identifier UVC — Universal Virtual Computer Vvar — variableVAX — Virtual Address eXtension VCPI — Virtual Control Program Interface VR — Virtual RealityVRML — Virtual Reality Modeling Language VB — Visual BasicVBA — Visual Basic for Applications VBS — Visual Basic Script VDSL — Very High Bitrate Digital Subscriber LineVESA — Video Electronics Standards AssociationVFAT — Virtual FATVFS — Virtual File SystemVG — Volume GroupVGA — Video Graphics ArrayVHF — Very High FrequencyVLAN — Virtual Local Area Network VLSM — Variable Length Subnet Mask VLB — Vesa Local BusVLF — Very Low FrequencyVLIW - Very Long Instruction Word— uinvac VLSI — Very-Large-Scale Integration VM — Virtual MachineVM — Virtual MemoryVOD — Video On DemandVoIP — Voice over Internet Protocol VPN — Virtual Private Network VPU — Visual Processing Unit VSAM — Virtual Storage Access Method VSAT — Very Small Aperture Terminal VT — Video Terminal?VTAM — Virtual Telecommunications Access MethodWW3C — World Wide Web Consortium WAFS — Wide Area File ServicesWAI — Web Accessibility Initiative WAIS — Wide Area Information Server WAN — Wide Area NetworkWAP — Wireless Access Point WAP — Wireless Application Protocol WAV — WAVEform audio format WBEM — Web-Based Enterprise Management WCAG — Web Content Accessibility Guidelines WCF — Windows Communication Foundation WDM — Wavelength-Division Multiplexing WebDAV — WWW Distributed Authoring and VersioningWEP — Wired Equivalent Privacy Wi-Fi — Wireless FidelityWiMAX — Worldwide Interoperability for Microwave AccessWinFS — Windows Future Storage WINS- Windows Internet Name Service WLAN — Wireless Local Area Network WMA — Windows Media Audio WMV — Windows Media VideoWOL — Wake-on-LANWOM — Wake-on-ModemWOR — Wake-on-RingWPA — Wi-Fi Protected Access WPAN — Wireless Personal Area Network WPF — Windows Presentation Foundation WSDL — Web Services Description Language WSFL — Web Services Flow Language WUSB — Wireless Universal Serial Bus WWAN — Wireless Wide Area Network WWID — World Wide Identifier WWN — World Wide NameWWW — World Wide WebWYSIWYG — What You See Is What You Get WZC — Wireless Zero Configuration WFI — Wait For InterruptXXAG — XML Accessibility Guidelines XAML — eXtensible Application Markup LanguageXDM — X Window Display Manager XDMCP — X Display Manager Control Protocol XCBL — XML Common Business Library XHTML — eXtensible Hypertext Markup Language XILP — X Interactive ListProc XML —eXtensible Markup Language XMMS — X Multimedia SystemXMPP — eXtensible Messaging and Presence ProtocolXMS — Extended Memory SpecificationXNS — Xerox Network Systems XP — Cross-PlatformXP — Extreme ProgrammingXPCOM — Cross Platform Component Object ModelXPI — XPInstallXPIDL — Cross-Platform IDLXSD — XML Schema Definition XSL — eXtensible Stylesheet Language XSL-FO — eXtensible Stylesheet Language Formatting Objects XSLT — eXtensible Stylesheet Language TransformationsXSS — Cross-Site ScriptingXTF — eXtensible Tag Framework XTF — eXtended Triton Format XUL —XML User Interface Language YY2K — Year Two ThousandYACC — Yet Another Compiler Compiler YAML — YAML Ain't Markup Language YAST — Yet Another Setup Tool ZZCAV — Zone Constant Angular Velocity ZCS — Zero Code Suppression ZIF — Zero Insertion ForceZIFS — Zero Insertion Force Socket ZISC — Zero Instruction Set Computer ZOPE — Z Object Publishing Environment ZMA — Zone Multicast Address。

dfa算法原理

dfa算法原理
DFA算法全称为DeterministicFiniteAutomaton，即确定有限状态自动机。

该算法是一种基于有限状态机的模式匹配算法，常用于字符串匹配、编译器、正则表达式等领域中。

DFA算法的基本原理是将模式串和文本串视为有限状态自动机的输入，通过状态转换的方式匹配模式串和文本串之间的关系。

具体来说，可以将匹配过程表示为从初始状态开始，经过状态转移，最终到达接受状态的过程。

为了实现这一过程，我们需要对模式串和文本串进行预处理。

首先，将模式串转化为DFA图，确定初始状态和接受状态，并标记每个状态对应的字符。

然后，在匹配文本串时，根据当前状态和下一个字符，进行状态转移，直至到达接受状态，或者匹配失败。

DFA算法的优点在于其匹配效率高、空间复杂度低。

但是，对于一些复杂的模式串，如带有通配符的，DFA算法可能无法实现精确匹配。

总的来说，DFA算法是一种常用的模式匹配算法，具有高效、简便等特点，值得我们深入学习和掌握。

- 1 -。

编译原理实验NFA确定化为DFA

编译原理实验NFA确定化为DFA编译原理中的NFA（Non-deterministic Finite Automaton，非确定性有限自动机）是一种能够识别正则语言的形式化模型。

它的设计简单，但效率较低。

为了提高识别效率，需要将NFA转化为DFA（Deterministic Finite Automaton，确定性有限自动机）。

本文将介绍NFA确定化为DFA的一般方法，并以一个具体例子来说明该过程。

首先，我们来了解一下NFA和DFA的差异。

NFA可以有多个转移路径，每个输入符号可以对应多个状态转移，而DFA每个输入符号只能对应唯一的状态转移。

这使得NFA在识别过程中具有非确定性，无法确定下一个状态。

而DFA则能够准确地根据当前状态和输入符号确定下一个状态。

NFA确定化为DFA的一般方法如下：1.创建DFA的初始状态。

该状态对应NFA的起始状态以及从起始状态经过ε（空）转移可以到达的所有状态。

2.对DFA的每个状态进行如下处理：a)对当前状态的每个输入符号进行处理。

b)根据当前状态和输入符号，确定下一个状态。

如果有多个状态，需要将它们合并为一个DFA状态。

c)重复上述步骤，直到处理完所有输入符号。

3.对于合并的DFA状态，需要重复执行第2步的处理过程，直到没有新的合并状态产生为止。

4.最终得到的DFA包含的状态即为NFA确定化的结果。

下面以一个具体的例子来说明NFA确定化为DFA的过程。

考虑以下NFA：（状态）（输入符号）（转移状态）1a,ε1,22a33b44a5首先，创建DFA的初始状态，根据NFA的起始状态和通过ε转移可以到达的状态。

在该例子中，起始状态为1，通过ε转移可以到达状态1和2、因此，初始状态为{1,2}。

接下来，对初始状态{1,2}进行处理。

对于输入符号a，根据NFA的状态转移表可以得到DFA的下一个状态为{1,2,3}，因为NFA的状态1通过a和ε可以到达状态3、对于输入符号b，当前状态没有转移。

第三章名词解释

第三章名词解释1.最小化（minimize）指DFA M状态数的最小化，是指构造一个等价的DFA M'，而后者有最小的状态。

2.标示符（IDentifier）是指用来标识某个实体的一个符号。

在不同的应用环境下有不同的含义。

3.正规表达式（regular expression）是说明单词的模式(pattern)的一种重要的表示法（记号），是定义正规集的工具。

4.正规式（Normal form）正规式也称正则表达式，也是表示正规集的数学工具。

5.正规集（Normal set）如果把每类单词视作一种语言，那么每一类单词的全体单词组成了相应的正规集。

6. 有限状态自动机（finite state automaton）有限状态自动机拥有有限数量的状态，每个状态可以迁移到零个或多个状态，输入字串决定执行哪个状态的迁移。

有限状态自动机可以表示为一个有向图。

有限状态自动机是自动机理论的研究对象。

7.词法分析器（Lexical analyzer）词法分析是指将我们编写的文本代码流解析为一个一个的记号，分析得到的记号以供后续语法分析使用。

8.确定的有限自动机（DFA: Deterministic Finite Automata）自动机的每个状态都有对字母表中所有符号的转移。

9.五元式（Five element type）由五个要素组成的式子K：由有限个状态组成的集合∑：由有限个输入字符组成的字母表f：从K到∑的单值映射，q),(，指明当前态为p，输入字符a，下一个状态为qf=pas：一个属于K的特定状态，称之为初始状态Z：若干个属于K的特定状态，它们组成的集合称之为终态集，记为Z。

10.非确定的有限自动机(NFA：Non deterministic finite automaton)自动机的状态对字母表中的每个符号可以有也可以没有转移，对一个符号甚至可以有多个转移。

自动机接受一个字，如果存在至少一个从q0 到 F 中标记(label)著这个输入字的一个状态的路径。

简述有限状态机的分类和区别

简述有限状态机的分类和区别
有限状态机是计算机科学中的一种数学模型，用于描述系统的状态转换行为。

根据状态转换的规则和方式，可以将有限状态机分为两类：确定性有限状态机和非确定性有限状态机。

确定性有限状态机（Deterministic Finite Automaton，DFA）
指的是状态转换是唯一的，即在任何时候，从任何状态出发，只要读入相同的输入符号，都会到达同一个状态。

这种状态机的状态转换图是一个有向无环图，每个状态只有一个后继状态。

非确定性有限状态机（Nondeterministic Finite Automaton，NFA）指的是状态转换不唯一，即在某些情况下，从同一状态出发，
读入相同的输入符号，可能会到达不同的状态。

这种状态机的状态转换图是一个有向图，每个状态可能有多个后继状态。

在实际应用中，有限状态机还可以根据状态的数量、输入符号的类型、输出符号的类型等进行分类。

例如，根据状态数量的不同，可以将有限状态机分为有限自动机和无限自动机；根据输入符号的类型，可以将有限状态机分为确定性和非确定性的输入符号型有限状态机等。

总之，有限状态机是一种非常重要的计算机模型，能够描述许多复杂的系统行为。

了解有限状态机的分类和区别，可以更好地理解和应用它们。

- 1 -。

举例说明正则文法与dfa之间的转换关系

举例说明正则文法与dfa之间的转换关系正则文法（Regular Grammar）和确定有限状态自动机（DFA，Deterministic Finite Automaton）是形式语言理论中的两个重要概念，它们之间存在一定的转换关系。

下面将通过一个例子来说明这种转换关系。

假设我们有一个正则文法 G，它由两个产生式A → aBb 和B → b 组成。

这个文法描述的语言是所有以一个 'a' 开头，后跟一个或多个 'b' 的字符串，即 L(G) = {a^n b^n n >= 1}。

我们可以将这个正则文法转换为确定有限状态自动机。

首先，我们需要为文法中的每个非终结符（A 和 B）创建一个状态。

对于产生式A → aBb，我们将创建一个状态 s_1，并将转移函数δ(s_0, a) = s_1 和δ(s_1, b) = s_2，其中 s_0 是初始状态。

对于产生式B → b，我们将创建一个状态 s_3，并将转移函数δ(s_1, b) = s_3。

终止状态集合将包括所有产生式右边的状态，即{s_2, s_3}。

这样，我们就可以得到一个确定有限状态自动机，它的初始状态是 s_0，终止状态集合是 {s_2, s_3}，转移函数是δ(s_0, a) = s_1, δ(s_1, b) = s_2, 和δ(s_1, b) = s_3。

这个自动机接受的语言就是由正则文法 G 描述的语言L(G)。

总的来说，正则文法转换为 DFA 的过程可以概括为：对于文法中的每个非终结符，创建一个状态；对于每个产生式，定义转移函数；将所有产生式右边的状态标记为终止状态。

通过这种方式，我们可以将正则文法转换为确定有限状态自动机，从而实现对正则语言的有效识别和匹配。

编译原理课程设计--NFA转化为DFA的转换算法及实现

编译原理课程实践报告设计名称：NFA转化为DFA的转换算法及实现二级学院：数学与计算机科学学院专业：计算机科学与技术班级：计科本091班*名：***学号： ********** 指导老师：***日期： 2012年6月摘要确定有限自动机确定的含义是在某种状态，面临一个特定的符号只有一个转换，进入唯一的一个状态。

不确定的有限自动机则相反，在某种状态下，面临一个特定的符号是存在不止一个转换，即是可以允许进入一个状态集合。

在非确定的有限自动机NFA中,由于某些状态的转移需从若干个可能的后续状态中进行选择，故一个NFA对符号串的识别就必然是一个试探的过程。

这种不确定性给识别过程带来的反复，无疑会影响到FA的工作效率。

而DFA则是确定的,将NFA转化为DFA将大大提高工作效率,因此将NFA转化为DFA是有其一定必要的。

对于任意的一个不确定有限自动机（NFA）都会存在一个等价的确定的有限自动机（DFA），即L(N)=L(M)。

本文主要是介绍如何将NFA转换为与之等价的简化的DFA，通过具体实例，结合图形，详细说明转换的算法原理。

关键词：有限自动机；确定有限自动机（DFA），不确定有限自动机（NFA）AbstractFinite automata is determinate and indeterminate two class. Determine the meaning is in a certain state, faces a particular symbol only one conversion, enter only one state. Not deterministic finite automata is the opposite, in a certain state, faces a particular symbol is the presence of more than one conversion, that is to be allowed to enter a state set.Non deterministic finite state automata NFA, because of some state are transferred from a number of possible follow-up state are chosen, so a NFA symbol string recognition must be a trial process. This uncertainty to the recognition process brought about by repeated, will undoubtedly affect the efficiency of the FA. While the DFA is determined, converting NFA to DFA will greatly improve the working efficiency, thus converting NFA to DFA is its necessary.For any a nondeterministic finite automaton ( NFA ) can be an equivalent deterministic finite automaton ( DFA ), L ( N ) =L ( M ). This paper mainly introduces how to convert NFA to equivalent simplified DFA, through concrete examples, combined with graphics, a detailed description of the algorithm principle of conversion.Keywords:：finite automata; deterministic finite automaton ( DFA ), nondeterministic finite automaton ( NFA目录1.前言： (1)1.1背景 (1)1.2实践目的 (1)1.2课程实践的意义 (1)2.NFA和DFA的概念 (2)2.1 不确定有限自动机NFA (2)2.2确定有限自动机DFA (3)3．从NDF到DFA的等价变化步骤 (5)3.1转换思路 (5)3.2.消除空转移 (5)3.3子集构造法 (7)4程序实现 (9)4.1程序框架图 (9)4.2 数据流程图 (9)4.3实现代码 (10)4.4运行环境 (10)4.5程序实现结果 (10)5.用户手册 (12)6.课程总结： (12)7.参考文献 (12)8. 附录 (13)1.前言：1.1背景有限自动机作为一种识别装置，它能准确地识别正规集，即识别正规文法所定义的语言和正规式所表示的集合，引入有穷自动机这个理论，正是为词法分析程序的自动构造寻找特殊的方法和工具。

dfa最小化填表算法

dfa最小化填表算法DFA minimization is a critical technique in automata theory that seeks to reduce the number of states in a deterministic finite automaton while maintaining the same language recognition capabilities. By minimizing a DFA, we can simplify its structure, making it easier to understand and potentially more efficient to use in practical applications. The process of DFA minimization typically involves identifying equivalent states and merging them to create a smaller automaton.DFA最小化是自动机理论中的一项重要技术，旨在减少确定性有限自动机中的状态数，同时保持相同的语言识别能力。

通过最小化DFA，我们可以简化其结构，使其更易于理解，并在实际应用中可能更有效。

DFA最小化的过程通常涉及识别等价状态并将它们合并以创建一个较小的自动机。

The table-filling algorithm is a common method used to minimize DFAs by constructing an equivalence table and merging equivalent states. This algorithm is based on the idea that states are equivalent if they produce the same output for every possible input string. By systematically comparing states and merging equivalent ones, thetable-filling algorithm can efficiently minimize a DFA while preserving its language recognition properties.填表算法是一种常用的方法，通过构建等价表和合并等价状态来最小化DFA。

面向装配的设计dfa案例

面向装配的设计dfa案例
面向装配的设计DFA（Deterministic Finite Automaton）案例是指根据装配过程中的需求和约束，设计出一个能够自动识别组装过程中正确和错误操作的有限状态机。

以下是一个面向装配的DFA案例：
假设有一个装配产品的过程，其中需要按照以下步骤进行操作：
1. 将零件A放入装配台，然后连接零件B。

2. 连接好的零件AB放入装配台，然后连接零件C。

3. 连接好的零件ABC放入装配台，然后连接零件D。

4. 连接好的零件ABCD放入装配台，并完成组装。

根据以上需求，我们可以设计一个DFA来检测装配过程中的错误操作。

状态机可以包括以下几个状态：
- 初始状态：未开始组装。

- 状态A：已放入零件A。

- 状态AB：已连接零件A和B。

- 状态ABC：已连接零件A、B和C。

- 状态ABCD：已连接零件A、B、C和D。

- 终止状态：组装完成。

根据以上状态，我们可以定义状态转移条件：
- 从初始状态到状态A需要满足条件：放入零件A。

- 从状态A到状态AB需要满足条件：连接零件B。

- 从状态AB到状态ABC需要满足条件：连接零件C。

- 从状态ABC到状态ABCD需要满足条件：连接零件D。

- 从状态ABCD到终止状态需要满足条件：完成组装。

通过以上定义的状态和状态转移条件，我们可以设计一个DFA，用于判断装配过程中的正确和错误操作。

当DFA检测到错误操作时，它可以发出警告或停止组装过程，以避免产生不合格的产品。

hutool-dfa java用法

hutool-dfa java用法Hutool- DFA是一个基于DFA（Deterministic Finite Automaton）算法的Java工具库，用于进行敏感词过滤和敏感词替换。

它提供了一种高效的方式来检测和过滤文本中的敏感词，并且可以根据需要进行替换。

使用Hutool-DFA非常简单，以下是一些常见的用法示例：1. 导入Hutool-DFA库首先，你需要在你的Java项目中导入Hutool-DFA库。

你可以通过在你的项目中添加以下依赖项来实现：```xml\n<dependency>\n<groupId>cn.hutool</groupId>\n<artifactId>hutool-dfa</artifactId>\n<version>5.7.10</version>\n</dependency>\n```2. 创建DFA对象接下来，你需要创建一个DFA对象。

你可以使用`DFA.create()`方法来创建一个默认配置的DFA对象，也可以使用`DFA.create(Config config)`方法来创建一个自定义配置的DFA对象。

```java\n// 创建默认配置的DFA 对象\nDFA dfa = DFA.create();// 创建自定义配置的DFA 对象\nConfig config = newConfig();\nconfig.setMatchType(MatchType.MIN_MATCH) ;\nconfig.setIgnoreCase(true);\nconfig.setSkipPatte rn(\"[\\\\w]+\");\ndfa = DFA.create(config);\n```3. 添加敏感词一旦你创建了一个DFA对象，你就可以使用`addKeyword(String keyword)`方法来添加敏感词。

dfa原理

dfa原理
DFA（Deterministic Finite Automaton）是一种有限状态自动机，用于识别正则语言。

它由五个元素组成：一个有限的状态集合、一个有限的输入符号集合、一个转移函数、一个初始状态和一组接受状态。

它的原理是在给定输入的情况下，从初始状态开始，根据输入符号和状态转移函数的规则，自动地向前转移到下一个状态，直到达到接受状态或无法继续转移。

DFA具有确定性，即对于每个状态和输入符号对，只存在一
个唯一的下一个状态。

这使得DFA的行为是可预测和确定的。

DFA还具有有限状态空间，因为状态数量是有限的，所以它
可以在有限的时间内处理任何输入字符串。

DFA的转移函数定义了从一个状态到另一个状态的转移规则。

可以根据当前状态和输入符号来确定下一个状态。

一旦到达某个接受状态，DFA就会停止并接受输入字符串，否则它会继
续转移状态。

DFA可以用来识别正则表达式中的模式。

例如，在文本中搜
索特定的单词或字符串。

它可以较快地进行模式匹配，因为它的状态转移是直接和确定的。

总之，DFA是一种用于识别正则语言的自动机。

它通过从初
始状态开始，根据输入符号和状态转移函数的规则，自动地向前转移状态，直到达到接受状态或无法继续转移。

它的主要特点是确定性和有限状态空间。

自动机正则表达式

自动机正则表达式自动机（automaton）是一种数学模型，用于表示计算系统的运行行为。

正则表达式（regular expression）是一种语言，用于描述一类字符串的集合。

自动机和正则表达式之间存在着密切的关系。

一方面，自动机可以接受一个正则表达式所描述的字符串集合；另一方面，正则表达式可以通过构造一个对应的自动机来进行匹配。

自动机可以被看作是一种抽象的计算机，它可以根据一些预定义的规则对输入的序列进行处理。

自动机的行为通常是基于当前状态和输入字符所确定的。

根据状态的不同，自动机可以有不同的行为。

自动机通常可以分为有限自动机（finite automaton）和不确定自动机（nondeterministic automaton）。

有限自动机只有有限个状态，并且在每个状态下，只能有一个对应的输出动作。

而不确定自动机则可以在每个状态下有多个对应的输出动作。

正则表达式是用于描述字符模式的一种语法。

它由一系列的字符和特殊符号组成，用于匹配一类字符串的集合。

正则表达式中可以使用的特殊符号包括点号（.）、问号（?）、星号（*）、加号（+）、竖线（）等。

这些特殊符号可以用来描述字符的重复次数、匹配任意字符等。

正则表达式可以通过自动机进行匹配。

对于每个正则表达式，可以构建一个对应的自动机，然后使用这个自动机来匹配输入的字符串。

匹配的过程通常从自动机的起始状态开始，不断根据输入字符和当前状态进行转移，直到到达自动机的终止状态。

在正则表达式中，使用星号（*）表示前一个字符可以重复任意次数，使用加号（+）表示前一个字符可以重复一次或多次，使用问号（?）表示前一个字符可以出现零次或一次。

通过使用这些特殊符号，可以描述重复的字符模式。

正则表达式还支持字符类（character class）的概念，可以用方括号（[...]）来表示一个字符集合。

方括号中可以列举出字符的取值范围，也可以使用特殊符号来表示某些常见的字符集合，例如\d表示数字字符集合，\w表示字母、数字和下划线字符集合，\s表示空白字符集合等。

nfa转正则表达式

nfa转正则表达式
这里的NFA指的是有限状态自动机（Nondeterministic Finite Automaton），而不是题目中提供的互联网知识链接。

将一个有限状态自动机转换成正则表达式需要使用“状态消除法”（State Elimination Method）。

具体步骤如下：
1. 添加一个新的起始状态S，并将其与原来的起始状态相连，边上的标记为ε，表示空串。

2. 添加一个新的接受状态F，并将原来的接受状态与其相连，边上的标记为ε。

3. 对于每一对状态p、q，将它们之间的所有路径上的标记组合成一个正则表达式
R(p,q)。

4. 对于每一对状态p、q，找到一条从p 到q 的路径，标记上的正则表达式为R(p,q)；如果不存在这样的路径，则将R(p,q) 设为空串ε。

5. 对于每一对状态p、q 和中间状态r，计算出连接p 与q 时，经过r 的正则表达式R(p,r)R(r,r)*R(r,q)，其中* 表示Kleene 闭包，即重复0 次或多次。

6. 最终得到的正则表达式就是从S 到F 的正则表达式，也就是R(S,F)。

需要注意的是，如果原始的有限状态自动机存在ε-转移（即边的标记为空串ε），则需要先将其转化为不含ε-转移的形式，这个过程被称为ε-消除。

五元组构造dfa代码

五元组构造dfa代码在计算机科学中，确定有限状态自动机（Deterministic Finite Automaton，简称DFA）是一种用来识别和处理特定类型文本模式的机器模型。

DFA是一种能够判断给定字符串是否属于某种特定语言的模型，也是计算机科学中非常重要的概念之一。

在DFA的构造过程中，五元组构造方式是最为常用的。

本文将详细介绍五元组构造DFA的过程以及相关的代码实现。

一、什么是五元组构造法五元组法是指将DFA用五个元素（五元组）来描述的构造方法，五元组法常用于表示DFA，用来表达DFA的最基本的信息。

五元组法包含了五个元素：Q、Σ、δ、q0、F。

下面将详细介绍这五个元素的含义：1. Q ：Q表示一组有限的状态集合。

状态集合是指某个状态转移中出现的所有状态所组成的集合。

2. Σ ：Σ表示字母表，也就是说一个有限个字符的集合。

3. δ ：δ表示状态转移函数，它是从Q×Σ到Q的映射函数。

也就是说，对于DFA的一个状态q和一个输入符号a，它总有一个确定的下一状态p=δ(q,a)。

4. q0 ：q0表示DFA的初始状态，它必须属于状态集合Q。

5. F ：F表示一组终结符集合，是状态集合Q的子集。

∀q∈F，则状态q是DFA的终态。

五元组构造法是一种从给定的正则表达式，构造DFA模型的方法。

根据正则表达式可以得到NFA（非确定有限状态自动机），然后通过子集构造法，将NFA转化为DFA。

DFA的构造过程能够帮助我们更好地理解DFA的工作原理，并进一步优化DFA的性能，提高程序的运行效率和速度。

二、代码实现在实现五元组构造法时，我们需要编写相应的代码实现。

下面是基于Python语言的五元组构造DFA代码实现：``` python class DFA: def __init__(self, Q, Sigma, delta, q0, F): self.Q = Qself.Sigma = Sigma self.delta = delta self.q0 = q0 self.F = Fdef transition_function(self, state,input_symbol): if input_symbol inself.Sigma: returnself.delta[state][input_symbol] else: raise ValueError("Invalid Input Symbol")def simulate(self, input_string):current_state = self.q0 for symbol ininput_string: current_state =self.transition_function(current_state, symbol)return current_state in self.Fdef from_nfa(nfa): states = set()alphabet = set(nfa.alphabet) delta = {}start_state = frozenset([nfa.start]) end_states= set()def dfs(state): if state in states: return states.add(state) ifnfa.start in state: start_state =frozenset(state) if nfa.accepts(state): end_states.add(frozenset(state))transitions = {} for symbol inalphabet: next_states =set(nfa.move(state, symbol)) fornext_state in next_states:dfs(next_state) if next_states !=set(): transitions[symbol] =frozenset(next_states)delta[frozenset(state)] = transitionsdfs(nfa.start) return DFA(states,alphabet, delta, start_state, end_states) ```上述代码中，我们定义了DFA类，其中包括有限状态集合Q，字母表Σ，状态转移函数δ，初始状态q0和终结符集合F。

dfsa 算法

dfsa 算法DFSA（Deterministic Finite-State Automaton）算法，也被称为确定有穷自动机算法，是一种基于有限状态机的算法。

它由一个有穷个状态组成，接受一个输入序列，并按照预先定义好的规则进行状态转移，最终输出一个确定的结果。

DFSA 算法在计算机科学领域中被广泛运用，特别在图形处理、自然语言处理、网络安全等领域中有着重要的作用。

I. 算法原理DFSA 算法的核心原理是有限状态机，它通过定义状态和状态之间的转移函数来描述一个系统。

在 DFSA 算法中，有限状态机由以下几个要素构成：1. 输入字母表：指的是输入序列中可能出现的符号集合。

2. 状态集合：表示有限状态机中可能的状态集合。

3. 转移函数：将当前状态和输入序列中的符号映射到下一个状态，描述了从一个状态转移到另一个状态的条件。

4. 初始状态：有限状态机开始处理输入序列时的初始状态。

5. 接受状态集合：当有限状态机结束处理输入序列时，处于接受状态集合中的状态表明已经接受了输入序列，并输出了对应的结果。

DFSA 算法按照预先定义的转移函数依次处理输入序列中的符号，根据输入序列中的符号和当前状态，在状态集合中进行状态转移，直到处理完整个输入序列。

最终，当算法结束时，根据最终的状态是否处于接受状态集合中，决定最终的输出结果。

II. 算法应用DFSA 算法具有广泛的应用领域，以下是其中几个常见的应用场景：1. 图形处理：在图像识别、图像分类、图像分割等领域中，DFSA算法可以用于描述图像的状态转移过程，从而对图像进行处理和分析。

2. 自然语言处理：在自然语言处理、文本挖掘等领域中，DFSA 算法可以用于分析文本的语义和语法结构，进行词性标注、关键词提取、句法分析等任务。

3. 网络安全：在网络入侵检测、恶意代码识别等领域中，DFSA 算法可以根据网络流量中的特征，建立状态机并进行实时的流量分析，识别潜在的威胁。

4. 编译原理：在编译器的实现中，DFSA 算法可以用于词法分析，根据预定义的词法规则对源代码进行词法单位的划分和分类。

最小dfa的状态转换矩阵

最小化DFA（Deterministic Finite Automaton）的状态转换矩阵又称为最小化DFA的等价类划分矩阵或者Hopcroft算法的划分表。

以下是求解最小化DFA的步骤和状态转换矩阵：构建DFA：首先根据正则表达式或其他方式构建出DFA，它包括了各个状态之间的转移关系。

初步划分：将DFA中所有非终态（即不接受字符串的状态）和终态（即接受字符串的状态）分别划分为两个等价类。

迭代划分：对于每个等价类，看看是否可以再次划分为更小的等价类，直到无法再继续划分为止。

具体做法是对于每一个等价类，取其中任意一个状态，观察它们在某个输入条件下能否被划分到不同的等价类中，如果可以，则进行划分。

确定最终状态转移：得到最小化DFA后，需要确定新的状态转移矩阵。

具体做法是遍历原始DFA的状态转移矩阵，对于每一组等价状态，找到它们在新DFA中的等价类，并根据这些等价类的转移关系来创建新的状态转移矩阵。

以下是一个示例，展示如何通过Hopcroft算法来最小化DFA：给定一个DFA的状态转移矩阵如下：a bq0q1q2q1q3q4q2q4q3q3q1q4q4q4q4初步划分将所有终态和非终态分别划分为{q0, q2, q4}和{q1, q3}两个等价类。

迭代划分我们从{q0, q2, q4}中选出其中一项q4，然后分别考虑在输入a和b时它的下一状态，可以发现当输入a时，q4会转移到自身，而当输入b时，q4会转移到q3。

而由于q4和q3不在同一等价类中，因此我们需要重新划分。

将{q0,q2,q4}划分为{q0,q2}和{q4}两个等价类，此时得到了一个新的划分结果：{{q0,q2},{q1,q3},{q4}}。

我们继续对每个等价类进行相同的操作，直到无法再继续划分为止。

确定最终状态转移根据新的等价类划分，我们可以构造出新的最小化DFA状态转移矩阵：a bA1A2A3A2A4A5A3A5A4A4A2A5A5A5A5其中，A1和A2分别对应原来的{q0,q2}和{q1,q3}等价类，A3则对应原来的{q4}等价类。

敏感词屏蔽处理算法

敏感词屏蔽处理算法敏感词屏蔽处理算法是一种用于过滤和屏蔽敏感词汇的技术，它在互联网应用中起到了重要的作用。

本文将介绍敏感词屏蔽处理算法的原理、应用场景以及一些常见的实现方法。

一、敏感词屏蔽处理算法的原理敏感词屏蔽处理算法的核心思想是通过对文本进行扫描和匹配，找出其中的敏感词汇并进行屏蔽或替换。

其基本原理可以概括为以下几个步骤：1. 构建敏感词库：首先需要建立一个包含各种敏感词汇的词库，这些词库可以包括政治敏感词、色情词汇、暴力词汇等。

词库的构建可以通过人工整理、爬虫抓取等方式进行。

2. 分词处理：对待检测的文本进行分词处理，将其切分成一个个词语或字符。

3. 敏感词匹配：将分词后的文本与敏感词库进行匹配，查找是否存在敏感词汇。

匹配算法可以采用常见的字符串匹配算法，如KMP 算法、AC自动机等。

4. 屏蔽处理：一旦发现文本中存在敏感词汇，可以选择进行屏蔽或替换操作。

屏蔽操作可以将敏感词汇替换为特定的符号或通用词汇，以达到过滤的效果。

敏感词屏蔽处理算法广泛应用于各种互联网应用中，包括社交媒体、论坛、聊天软件等。

以下是一些常见的应用场景：1. 社交媒体过滤：社交媒体平台可以利用敏感词屏蔽处理算法对用户发布的内容进行过滤，防止敏感词汇的传播和发布。

2. 聊天软件过滤：聊天软件可以通过敏感词屏蔽处理算法对用户发送的消息进行过滤，保护用户的隐私和安全。

3. 论坛管理：论坛管理员可以利用敏感词屏蔽处理算法对用户发表的帖子进行过滤，维护论坛的秩序和良好的讨论环境。

三、敏感词屏蔽处理算法的实现方法敏感词屏蔽处理算法的实现方法有多种，下面介绍几种常见的方法：1. Trie树算法：Trie树是一种多叉树结构，可以高效地进行字符串匹配。

将敏感词库构建成一棵Trie树，然后对待检测的文本进行遍历匹配，找出其中的敏感词汇。

2. DFA算法：DFA（Deterministic Finite Automaton）算法是一种有限状态自动机算法，可以用于高效地进行字符串匹配。

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A Deterministic Finite Automaton forFaster Protein Hit Detection in BLASTMichael Cameron1,Hugh E.Williams2,and Adam Cannane11School of Computer Science and Information TechnologyRMIT University,GPO Box2476V,Melbourne,Australia,3001{mcam,cannane}@.au2Microsoft CorporationOne Microsoft Way,Redmond,Washington98052-6399U.S.Ahughw@February8,2006AbstractBLAST is the most popular bioinformatics tool and is used to run millions of queries each day.However,evaluating such queries is slow,taking typically minutes on modern workstations. Therefore,continuing evolution of BLAST—by improving its algorithms and optimisations —is essential to improve search times in the face of exponentially-increasing collection sizes. We present an optimisation to theﬁrst stage of the BLAST algorithm speciﬁcally designed for protein search.It produces the same results as NCBI-BLAST but in around59%of the time on Intel-based platforms;we also present results for other popular architectures.Overall, this is a saving of around15%of the total typical BLAST search time.Our approach uses a deterministicﬁnite automaton(DFA),inspired by the original scheme used in the1990BLAST algorithm.The techniques are optimised for modern hardware,making careful use of cache-conscious approaches to improve speed.Our optimised DFA approach has been integrated into a new version of BLAST that is freely available for download at / Keywords:BLAST,homology search,sequence alignment1IntroductionBLAST is staggeringly popular:it is used over120,000times each day(McGinnis and Madden, 2004)at the NCBI website1,it is installed at hundreds of institutes,several hardware-dependent implementations are available and many variations of its algorithms have been published including PSI-BLAST(Altschul et al.,1997),MegaBLAST(Gotea et al.,2003),PHI-BLAST(Zhang et al., 1998)and RPS-BLAST(Schaﬀer et al.,1999).Indeed,the1997BLAST paper(Altschul et al., 1997)has been cited over10,000times2in electronically-available manuscripts.While BLAST is popular,it it not perfect.A typical search of a fraction of the GenBank database requires several minutes on modern desktop hardware.With perhaps millions of queries each day being run,this represents a very signiﬁcant investment in computing resources.Accord-ingly,there is enormous beneﬁt to any improvement of the BLAST algorithm that can reduce typical runtimes without aﬀecting accuracy.This paper proposes such an improvement to theﬁrst stage of the algorithm.Theﬁrst stage of BLAST—and many other homology search tools—involves identifying hits:short,high-scoring matches between the query sequence and the sequences from the collection being searched.The deﬁnition of a hit and how they are identiﬁed diﬀers between protein and nucleotide searches,mainly because of the diﬀerence in alphabet sizes.For example,for BLAST nucleotide search,an exact match of length11is required.However,for protein search,it requires a match of length3and inexact matches are permitted.Indeed,BLAST uses an algorithmically diﬀerent approach to hit detection for protein and nucleotide searches.Several nucleotide search tools use spaced seeds to perform hit detection,including MegaBLAST (Gotea et al.,2003),BLAT(Kent,2002),BLASTZ(Schwartz et al.,2002)and PatternHunter(Li et al.,2004;Ma et al.,2002).Spaced seeds use a binary mask string,such as111010010100110111, where matches in all of the1positions are required for a hit and0denotes allowed mismatches. PatternHunter uses spaced seeds to achieve better sensitivity and faster search times than BLAST for nucleotide queries but is not suitable for searching larger collections such as GenBank(Li et al., 2004).MegaBLAST,BLAT and BLASTZ are signiﬁcantly less sensitive than BLAST.Brown(2005) presents a framework for using spaced seeds in protein search and demonstrates that spaced seeds can achieve comparable search accuracy to the continuous seed used in BLAST and produce roughly 25%as many hits.However,we observe in Section2.2that reducing the number of hits does not necessary translate to faster search times.Further,Brown does not present experimental results comparing the two approaches.Therefore,the original BLAST approach of scanning the entire database using a continuous seed remains,to our knowledge,the fastest and most sensitive method for performing protein search.In this paper,we investigate algorithmic optimisations that aim to improve the speed of protein search.Speciﬁcally,we investigate the choice of data structure for the hit matching process,and ex-perimentally compare an optimised implementation of the current NCBI-BLAST codeword lookup approach to the use of a deterministicﬁnite automaton(DFA).Our DFA is highly optimised and carefully designed to take advantage of CPU cache on modern workstations.Our results show that the DFA approach reduces total search time by6%–30%compared to codeword lookup,depending on platform and parameters.This represents an around41%reduction in the time required by BLAST to perform hit detection;this is an important gain,given the millions of searches that are executed each day.Furthermore,the new approach can be applied to a range of similar protein search tools.We also explore the eﬀect of varying the word length and neighbourhood threshold on the hit detection process.This paper is organised as follows.We describe the BLAST algorithm and experiment with varying the word size and threshold in Section2.In Section3we discuss the data structures used for hit detection in BLAST.We compare our new DFA approach to the original codeword lookup scheme in Section4.Finally,we provide concluding remarks and describe planned future work in Section5.2BackgroundThis section presents a background on the four stages of the BLAST algorithm,a detailed descrip-tion of theﬁrst stage hit detection process used in NCBI-BLAST,and key BLAST parameters. 2.1BLASTThe BLAST algorithm has four stages.Theﬁrst identiﬁes hits and is the focus of this paper.The second performs ungapped extensions,the third performs gapped alignment,and fourth computes tracebacks for result presentation to the user.A brief summary of stages two to four is presented here,and detail can be found elsewhere(Altschul et al.,1990,1997).Stage1In theﬁrst stage,BLAST carries out a comparison of a query sequence q to each subject sequence s from the collection of sequences being searched using the algorithm of Wilbur and Lipman(1983). To do this,ﬁxed-length overlapping subsequences of length W are extracted from the query sequence q and the current subject sequence s.For example,suppose W=3and the following short sequence is processed:ACDEFGHIKLMNPQ.The words extracted from the sequence are as follows:ABC,BCD, CDE,DEF,EFG,GHI,HIK,and so on.In theﬁrst stage,all subject sequences are exhaustively, sequentially processed from the collection being searched,that is,each subject sequence is read from the database,parsed into words of length W,and matched against the query.The matching process identiﬁes words in the query that are hits with words in the subject. Hits may not be exact:a match between a pair of words is considered high scoring if the words are identical,or the match scores above a given threshold T when scored using a mutation data matrix.The T parameter is discussed in Section2.2.To match query and subject words,BLAST uses a lookup table—as illustrated in Figure1—constructed from the query sequence and alignment scoring matrix.The table contains an entry for every possible word,of which there are a W for an alphabet of size a;the example in Figure1 illustrates the table for an alphabet of size a=3,with three symbols A,B,and C,and a word length W=2.Associated with each word in the table is a list of query positions that denote the one or more oﬀsets of a hit to that word in the query sequence.In the example table,the word AB has hits at query positions1and3.The query sequence is shown at the base of theﬁgure,where the exact word AB occurs at position1and a close-matching hit(CB)occurs at position3.The search process using the lookup table is straightforward.First,the subject sequence is parsed into words.Second,each subject word is searched for in the query lookup table.Third, for each matching position in the query,a hit is st,when a hit is recorded,a pair of positions,i,j,that identify the match between the query and subject are passed to the second stage.Theﬁrst stage of NCBI-BLAST consumes on average37%of the total search time(Cameron et al.,2004).In Section3,we discuss the design of the lookup table in more detail,including how entries are accessed and query positions are stored within the structure.25−12−160402Scoring matrix:C B A A B C Query sequence: A B C B B123451, 31, 3242Lookup table (W=2 T=7):Figure 1:The lookup table used to identify hits.In this example,the alphabet contains 3characters:A ,B ,and C .The lookup table to the left is constructed using the scoring matrix and query sequence to the right with a word size W =2and threshold T =7.The table contains a W =32=9entries,one for each possible word,and each entry has an associated list of query positions.The query positions identify the starting position of words in the query that score above T when aligned to the subject word.Stage 2The second stage determines the diagonal d of each hit by calculating the diﬀerence in the query and subject oﬀsets,that is,d =j −i .If two hits h 1[i 1,j 1]and h 2[i 2,j 2]are located on the same diagonal and are within A residues,that is,i 2−i 1≤A ,an ungapped extension is performed.An ungapped extension links two hits by computing scores for matches or substitutions between the hits;it ignores insertion and deletion events,which are more computationally expensive to evaluate and calculated only in the third and fourth stages.After linking the hits,the ungapped extension is processed outward until the score decreases by a pre-deﬁned threshold.If the resulting ungapped alignment scores above the threshold S 1,it is passed to the third stage of the algorithm.The second stage of NCBI-BLAST consumes on average 31%of the total search time (Cameron et al.,2004).The ﬁrst two stages are illustrated on the left side of Figure 2.The short black lines represent high-scoring hits of length W between a query and subject sequence.There are eight hits in total and two cases where a pair of hits are located on the same diagonal less than A residues apart.For these two cases,an ungapped extension is performed as illustrated by a grey line.In this example,the longer,central ungapped alignment scores above the threshold S 1and is passed onto the third stage of the algorithm;the shorter alignment to the left does not.BLAST can also be run in one hit mode,where a single hit rather than two hits is required to trigger an ungapped extension.This leads to an increase in the number of ungapped extensions performed,increasing runtimes and improving search accuracy.To reduce the number of hits,a larger value of the neighbour threshold T is typically used when BLAST is run in one hit mode.The original BLAST algorithm (Altschul et al.,1990)used the one hit mode of operation,and the approach of using two hits to trigger an ungapped extension was one of the main changes introduced in the 1997BLAST paper (Altschul et al.,1997).3Query sequence Query sequenceFigure2:The four stages of the BLAST algorithm.In stage1,short hits between the query and subject are identiﬁed,shown as short black lines in the leftﬁgure.In stage2,an ungapped extension is performed,as shown as grey lines in the leftﬁgure.The rightﬁgure illustrates gapped alignment, where the high-scoring ungapped alignment from stage2is explored in stages3and4.Stages3and4In the third stage,dynamic programming is used in an attempt toﬁnd a gapped alignment that passes through the ungapped region.To do this,a start or seed point is chosen from the ungapped alignment,then dynamic programming is used toﬁnd the highest-scoring gapped alignment that passes through that point.If a high-scoring alignment is found,it is passed to the fourth stage where alignment traceback information is recorded for display to the user.The right side of Figure2illustrates the gapped alignment stages.In this example,the high-scoring ungapped alignment identiﬁed in the second stage is considered as the basis of a gapped alignment.The black line shows the resulting high-scoring alignment identiﬁed in stage three.The third and fourth stages of NCBI-BLAST consume on average32%of the total search time.We have recently described optimisations to these stages elsewhere(Cameron et al.,2004).2.2Varying the word size and thresholdThe T parameter described in the previous section aﬀects the speed and accuracy of BLAST. Consider the example mutation data matrix and query sequence shown in Figure1and a setting of T=7.Observing the matrix,a match between the word BA and BC scores8,since the intersection of the row and column labelled B is a score of6and between A and C is2.Since the threshold is T=7,a match between BA and BC is a hit,and so occurrences of BA or BC in the query match occurrences of BA or BC in the subject.High values of T restrict the number of neighbourhood words that match a word,resulting in less sensitive but fast search.Low values of T expand the number of neighbourhood words,with the opposite eﬀects.Careful choice of T,for each W and scoring matrix pair,is crucial to BLAST performance.NCBI-BLAST uses default values of W=3and T=11for protein search(Altschul et al.,1997). To investigate the eﬀect of varying these two parameters we conducted the following experiment:for each value of W=2,3,4,5,we identiﬁed a value of T that provided a similar accuracy to the default of W=3and T=11.We then used our own implementation of BLAST to perform100searches for each parameter pair between queries selected randomly from the GenBank non-redundant protein4Table1:A comparison of BLAST statistics for pairs of W and T that result in similar accuracy. The average number of hits,ungapped extensions,and gapped extensions and SCOP test ROC50 scores are shown.W=2,T=10812,500,08180,571,43353,0630.382W=3,T=11428,902,03817,785,57847,2640.380W=4,T=13219,446,0686,113,40943,6820.380W=5,T=15111,574,0453,670,76840,1160.3783.1NCBI-BLAST Codeword LookupWe have shown a schematic of the lookup table used by NCBI-BLAST in Figure1.This section describes the implementation in more detail.In NCBI-BLAST,each collection to be searched is pre-processed once using the formatdb tool and each amino-acid coded as a5-bit binary value.The representation is5bits because there are 24symbols—20amino-acids and4IUPAC-IUBMB amino-acid wildcard character substitutions —and24<25.For fast table lookup,W5-bit representations are read and concatenated together, then used as an oﬀset into the codeword lookup table;this provides unambiguous,perfect hashing, that is,a guaranteed O(1)lookup for matching query positions to each subject sequence word.The table has a W slots for an alphabet of size a and word length W.For a=24symbols and W=3, a word requires15bits and the table has243=13,824slots.During search,collection sequences are read code-by-code,that is,5-bit binary values between 0and23decimal inclusive are read into main-memory.Since codewords overlap,each codeword (except theﬁrst two in each sequence)shares two symbols with the previous codeword.Therefore, to construct the current codeword,5bits are read from the sequence,and binary mask(&),bit-shift (<<),and OR(|)operations applied.Consider an example.After reading codes for the letters T,Q,and A,the current codeword contains a15-bit representation of the three-letter codeword TQA.Suppose the code for C is read next,and the codeword needs to be updated to represent the codeword QAC.To achieve this,three operations are performed:ﬁrst,a binary masking operation is used to remove theﬁrst5bits from the codeword,resulting in a10-bit binary representation of QA;second,a left binary shift of5places is performed;and,last,a binary OR operation is used to insert the code for C at the end of the codeword,resulting in a binary representation of the new codeword QAC.The new codeword is then used to look up an entry in the table.Each slot in the lookup table contains four integers.Theﬁrst integer speciﬁes the number of hits in the query sequence for the codeword,and the remaining three integers specify the query positions of up to three of these hits.If there are more than three hits,theﬁrst query position is stored in the table and the remaining query positions are stored outside the table,with their location recorded in the entry in place of the second query position.Figure3illustrates a fraction of the lookup table:the example shows two codewords that have two and zero query positions,and one codeword that uses the external structure to store a total ofﬁve word positions.Storing up to three query positions in the lookup table improves spatial locality and,therefore, takes advantage of CPU caching eﬀects.A codeword with less than three hits can be accessed without jumping to an external main-memory address.Assuming slots are within cache,the query positions can be retrieved without accessing main-memory.However,storing query positions in the table increases the table size:as the size increases,less slots are stored in the CPU cache.In addition to the primary lookup table,NCBI-BLAST uses a secondary lookup table to reduce search times.For each word,the secondary table contains one bit that indicates if there are any hits for that word.If no hits exist,the search advances immediately to the next word without the need to search the larger primary table.This potentially results in faster search times because the smaller secondary table is compact(it stores a W bits)and can be accessed faster than the larger primary table.The average sizes of the NCBI-BLAST codeword lookup tables for the values of W and T used previously are shown in the left column of Table2.As W increases,so does the table size:when W=4,the table is around12Mb in size,much larger than the available cache on most modern hardware.This is probably why word sizes of W=4or larger are disabled by default in NCBI-BLAST.The secondary table is considerably smaller than the primary table across the range of word lengths,so that codewords that do not generate a hit are less likely to result in a cache miss.6QTAQTBQTCFigure3:Three slots from the lookup table structure used by NCBI-BLAST.In this example,W=3 and the words QTA,QTB,and QTC have two,zero,andﬁve associated query positions respectively. Since QTC has more than three query positions,theﬁrst is stored in the table and the remaining positions are stored at an external address.Table2:Average size of the codeword lookup and DFA lookup table structures for100queries randomly selected from the GenBank non-redundant protein database.Values of W and T with comparable accuracy were used.Experiments were conducted using our own implementation of the DFA structure and the codeword lookup structure used by NCBI-BLAST version2.2.10with minor modiﬁcations to allow word sizes4and greater.W=2T=1013Kb 1Kb2KbW=3T=11392Kb3Kb22KbW=4T=1312,329Kb96Kb257KbW=5T=15393,374Kb3,072Kb3,011KbABC B A C AB state Query pos = 2Query pos = none Query pos = noneNext state = BA Next state = BCNext state = BB t r a n s i t i o n s Figure 4:The original DFA structure used by BLAST.In this example a =3and the query sequence is BABBC .The three states shown are those visited when the subject sequence CBABB is processed.alphabet with size a =3and an example query sequence BABBC .Three states with a total of nine transitions are shown.The B transition from the BA state contains the single query position 1because the word BAB appears in the query beginning at the ﬁrst character.Similarly,the B transition from the AB state contains the single query position 2because the word ABB appears in the query beginning at the second character.The structure is used as follows.Suppose the subject sequence CBABB is processed.After the ﬁrst two symbols C and B are read,the current state is CB .Next,the symbol A is read and the transition A from state CB is followed.The transition does not contains any query positions and the search advances to the BA state.The next symbol read is B and the B transition is followed from state BA to state AB .The transition contains the query position 1,which is used to record a hit.Finally,the symbol B is read and this produces a single hit because the B transition out of state AB contains the query position value 2.The structure we have described is as used in the original version of BLAST.The original DFA implementation used a linked list to store query positions and stored redundant information,making it unnecessarily complex and not cache-conscious.This is not surprising:in 1990,general-purpose workstations did not have onboard caches and genomic collections were considerably smaller,mak-ing the design suitable for its time.However,the general DFA approach has several advantages over the lookup table approach,which we have exploited in our own DFA design:1.It is more compact.The lookup table structure has unused slots,since eight of the 5-bit codes are unused2.Flexibility is possible in where query positions are stored,without aﬀecting caching behavior.We take advantage of this in the DFA structure we propose:we store query positions outside of the matching structure,immediately preceding the states;this reduces the likelihood of a cache miss when an external list is accessed.We terminate query position lists with a zero value3.Words do not map to codewords,that is,to oﬀsets within the structure.Therefore,data can be organised to cluster frequently-accessed states,maximising the chances that frequently-accessed data is cached.In the DFA we propose,we store the most-frequently accessed states clustered at the centre of the structure;to do this we use the Robinson and Robinson background amino-acid frequencies (Robinson and Robinson,1991)4.Transitions within each state can be arranged from most-to least-frequently occurring amino-acid residue,improving caching eﬀects and minimising the size of the oﬀset to the query positions.We do this in our DFA by assigning binary values to amino-acids in descending order of frequency8ABB ABA ABC w o r d s Query pos = noneQuery pos = none Query pos = 2AB prefix words BAB BAA BAC w o r d s Query pos = none Query pos = none Query pos = 1BA prefix words Query pos = noneQuery pos = noneQuery pos = none CBA CBB CBC w o r d sCB prefix wordsBAC t r a n s i t i o n s A B C Figure 5:The new DFA structure.In this example a =3and the query sequence is BABBC .The ﬁgure shows the portion of the new structure that is traversed when the example subject sequence CBABB is processed.A drawback of the original DFA is the requirement of an additional pointer for each word,resulting in a signiﬁcant increase in the size of the lookup structure.To examine this eﬀect,we experimented with 100query sequences randomly selected from the GenBank database and found that pointers consume on average 61%of the total size of the structure when default parameters are used.However,it is possible to reduce the number of pointers as we discuss next.The next state in the automaton is dependent only on the suﬃx of length W −1of the current word and not the entire word.We can therefore optimise the structure further:each state corre-sponds to the suﬃx of length W −2of a word,and each transition corresponds to the suﬃx of length W −1.Each transition has two pointers:one to the next state,and one to a collection of words that share a common preﬁx.The words are represented by entries that contain a reference to a list of query positions.As each symbol is read,both pointers are followed:one to locate the query positions for the new word and the other to locate the next state in the structure.This new DFA is illustrated in Figure 5.Again,we use the example query sequence BABBC and the diagram only shows the portion of the structure that is traversed when the subject sequence CBABB is processed.Consider now the processing of the subject sequence.After the ﬁrst symbol C is read,the current state is C .Next,the symbol B is read and the B transition is considered.It provides two pointers:the ﬁrst to the new current state,B ,and the second to the CB preﬁx words.The next symbol read is A and two events occur:ﬁrst,the word CBA from the CB preﬁx words is checked to obtain the query positions for the word,of which there are none in this example;and,second,the current state advances to A .Next,the symbol B is read and the word BAB in the collection of BA preﬁx words accessed and a single hit is recorded,with query position 1.The current state then advances to B .Finally,the symbol B is read and the word ABB of the AB preﬁx words is consulted and a single hit is recorded,with query position 2.This new DFA structure requires more computation to traverse than the original:as each symbol is read,two pointers are followed and two array lookups are performed.In contrast,the original DFA structure requires one pointer to be followed and one array lookup to be performed.However,the new DFA is considerably smaller and more cache-conscious,since the structure contains signiﬁcantly fewer pointers.Despite each state containing two pointers,there are a (W −1)instead of a W states.Further,there are additional optimisations that have been applied to the new DFA,as we describe9ABB w o r d sABA ABCABB w o r d sABA ABC Figure 6:Example of query position reuse.The word ABB produces a hit at query positions 16,67,and 93,the word ABA produces a hit at query position 16and the word ABC does not produce any hits.A simple arrangement is shown on the left.A more space eﬃcient arrangement that reuses query positions is shown on the right.next.The new structure oﬀers the ability to reuse collections of words with a common preﬁx,such as those shown in Figure 5.If two collections share the same set of query positions,for the same respective suﬃx symbols,a single collection can be used for both.In this event,the words block ﬁeld of the two transitions point to a single collection of words.This reuse leads to a further reduction in the overall size of the lookup structure.In the new DFA,query positions are stored immediately preceding each collection of words with a common preﬁx.The distance between the ﬁrst word in the collection and the start of the query positions list is recorded for each word,where a zero value indicates an empty list.As part of this new structure,we have developed a technique for reusing query positions between words with a common preﬁx.An existing list of query positions M =m 1,...,m |M |can be reused to store a second list N =n 1,...,n |N |in memory if |N |≤|M |and N is the suﬃx of M ,that is,M |M |−i =N |N |−i for all 0≤i ≤|N |.Because the order of the query positions within an entry is unimportant,the lists can be rearranged to allow more reuse.We have developed a greedy algorithm that produces a near-optimal arrangement for minimising memory usage.The algorithm processes the new lists from shortest to longest,and considers reusing existing lists in order from longest to shortest.A more detailed study of the query position rearrangement and reuse problem is planned for future work.However,in practice,our results show that our current approach is eﬃcient and eﬀective.An example of query position reuse is shown in Figure 6.A simple and less space eﬃcient arrangement is shown on the left-hand side.On the right-hand side of the ﬁgure the query positions are rearranged to permit reuse between the words ABA and ABB .The strategy further reduces the table size without any computational penalty.To further optimise the new structure for longer word lengths,we have reduced the alphabet size from a =24to a =20during construction of the structure by excluding the four wildcard characters:V ,B ,Z ,and X .These four characters are highly infrequent,contributing a total of less than 0.1%of symbol occurrences in the GenBank non-redundant database.To do this,we replace each wildcard character with an amino-acid symbol that is used only during the ﬁrst phase of BLAST.This has a negligible eﬀect on accuracy:Table 3shows there is no perceivable change in ROC score for the SCOP test,despite a small change in total hits between the queries and subject sequences.The approach of replacing wildcard characters with bases is already employed10。