An Approach to Biological Computation Unicellular Core-Memory Creatures Evolved Using Genet

An Approach to Biological Computation:UnicellularCore-Memory Creatures Evolved Using Genetic Algorithms Hideaki SuzukiATR Human Information Processing Research Laboratories2-2Hikaridai Seika-choSoraku-gunKyoto619-0288Japanhsuzuki@hip.atr.co.jpKeywordscore memory,unicellular creature, membrane,biological computation, algorithmic complexity,machine lan-guage genetic programming,genetic algorithmsAbstract A novel machine language genetic programmingsystem that uses one-dimensional core memories is proposedand simulated.The core is compared to a biochemicalreaction space,and in imitation of biological molecules,fourtypes of data words(Membrane,Pure data,Operator,andInstruction)are prepared in the core.A program isrepresented by a sequence of Instructions.During executionof the core,Instructions are transcribed into correspondingOperators,and Operators modify,create,or transfer Puredata.The core is hierarchically partitioned into sections bythe Membrane data,and the data transfer between sectionsby special channel Operators constitutes a tree data- owstructure among sections in the core.In the experiment,genetic algorithms are used to modify program information.A simple machine learning problem is prepared for theenvironment data set of the creatures(programs),and thetness value of a creature is calculated from the Pure dataexcreted by the creature.Breeding of programs that canoutput the prede ned answer is successfully carried out.Several future plans to extend this system are also discussed.1IntroductionRecent approaches for the designing of an automatic programming system in imitation of biological evolution are based on the notion that during the long history of evolution, some lineage of living things has increased the degree of complexity that is de ned as the number of functional genes in a living cell.For example,higher organisms such as mammals are expected to have about50,000genes in each cell,which is about10 times more than the number of genes that a yeast cell has.Of course it is controversial whether or not“functional”or“structural”complexity increases at all in evolution[29], and yet so-called“genomic”complexity which we may view as the number of genes, has clearly increased during evolution[13].If one could clarify the mechanisms(the necessary and suf cient conditions)that have facilitated this growth of complexity,we might be able to devise a computational system that can increase algorithmic complexity by implementing those clari ed mechnisms.This is a strong motivation for many researchers in genetic programming,and with the aim of implementing such a system,various schemes have been proposed and tested[1–3,5,11,26–28,35,38–40,45].Here I focus on two groups of studies that have much relevance to this article.The rst group is studies on machine language genetic programming.Several sys-tems have been proposed in this area.Nordin[34,35]devised the compiling genetic programming system(CGPS),which directly manipulates the machine code on a Sun SPARC station.Ray[38–40]proposed the famous Tierra system,which uses a core memory for breeding self-replicating programs.The author[44,45]and Huelsbergen [23,24]independently proposed machine language genetic programming systems that use genetic algorithms(GAs)[21,22,32,33,43,46,49,50]to evolve programs.The most successful system among them is Tierra,which accomplished the emergence of higher functions such as parasitism between programs.Tierra is the rst system that demonstrated that programs can experience a kind of open-ended evolution under an appropriate environment.Since this system was proposed,a number of different ap-proaches have been taken to extend Tierra to a more advanced system that can evolve programs with much algorithmic complexity.One of them is Ray and Hart’s Network Tierra[41].In this system,the tierran core was extended to a vast memory space that consists of a large number of computers distributed throughout the world.Several interesting phenomena are observed in this system;however,it seems that creating programs with much algorithmic complexity has not yet been accomplished therein. Another approach to extend Tierra was taken by Adami and Adami and Brown[1–3]. The Avida system devised by them demonstrated how quite complex programs can be evolved in the Tierra-type architecture.The second group that is relevant to this article comprises approaches to chemi-cal computation in some mathematical medium.Fontana[20]proposed Algorithmic chemistry(ALChemy),which manipulates Lisp trees as objects(molecules)and allows combinations of trees as reactions between objects.A similar approach was recently taken by Szuba[51]who designed a chemical-reaction-like system that proceeds with Prolog inference.Rasmussen and colleagues[37,36]devised a core memory system in which core words react with one another and change their inner codes.Banzhaf and colleagues[8–10,18,19]introduced a kind of information object that catalyzes the change of another object.They expressed the objects by binary strings and made them work not only as“operands”but also“operators”of computation.These stud-ies succeeded in inducing so-called catalytic networks,in which reaction arrows are connected to each other and constitute intricate topology-like loops.However,from the viewpoint of automatic programming,the functions achieved in these systems are still pared to these systems,the functions of real organisms are much higher and more complicated.Processes of a biological system,molecular re-actions in a cell,are not simple chemical reactions.They are biochemical reactions catalyzed by enzymes that are created from genetic information that has evolved over three billion years.To create a computational system that can evolve complex func-tions,we might have to make a computational system that imitates biological systems more elaborately.Here,I propose a novel evolutionary programming system called SeMar.SeMar is an abbreviation of the sea of matter.SeMar uses a core memory.The core is compared to a biochemical reaction space,and in imitation of biological matter(substances),four types of data words are prepared in the core.These are the Membrane,Pure data, Operator,and Instruction.The Membrane can be compared to a lipid bilayer,the Pure data can be compared to a small molecule,the Operator can be compared to a protein,and the Instruction can be compared to a gene.In the experiment,GAs are used to modify a sequence of Instructions that a creature(program)has as its genetic information.To calculate the tness value of each creature,a core memory is prepared for each creature and the Instruction sequence is substituted for the core together with a sequence of environmental data(Pure data).The execution of the core proceeds with the transcription of Instructions to Operators and the actions of Operators to inducemodi cations of Pure data.During these processes,an arbitrary number of Membranes, Pure data,or Operators are inserted or deleted at an arbitrary address of the core.The principal part of this article has already been described in preliminary reports [47,48].However,the brevity of those papers allowed only a brief description of the model.The background of the model is scarcely described.Here,I remedy those problems and give a full description of the basic strategy for SeMar.The organization of the article is as follows:Section2describes several results of preliminary exper-iments that led me to devise SeMar.In Section3,I demonstrate a concrete imple-mentation of SeMar and the simulation procedure using GAs.The results of a SeMar simulation are given in Section4,where an external problem is imposed upon the crea-tures and it is shown that SeMar creatures succeed in creating a program that outputs the desired answer.In Section5,the characteristics of SeMar are brie y summarized and the differences between SeMar and other programming systems are discussed. The nal section(Section6)is devoted to description of future plans to extend Se-Mar.2Prelimiary ExperimentsSeMar has stemmed from the study on a machine language genetic programming system called MUNCs(MUltiple von Neumann Computers)devised by the author[44,45].In this section,I survey the journey that has led me from MUNCs to SeMar.MUNCs form a system in which machine language programs evolve using GAs. In several experiments using environmental problems,MUNCs succeeded in creating a small functional program[45];and yet they could not succeed in creating a higher (longer)program with much algorithmic complexity.One of the most serious problems MUNCs suffer from is what I call“evolutionary dead end”(Figure1).In MUNCs,a sequence of instructions is put into action one by one using an instruction pointer.A “jump”instruction can move this pointer to an earlier address,and once such a loop has been accomplished,the other program regions are not tested,no matter how good the functions within them are.(In an extreme case,a program appeared that executed only5of the200instructions it had.)The crossover operation cannot destroy jump instructions that are xed in the population,so the evolutionary speed conspicuously drops.I tried several modi cations of the CPU hardware architecture and the basic instruction set to no avail.Evolutionary dead end is a serious and inevitable problem for any sequentially executed programming system that evolves using GAs.A similar problem occurred in the early form of Tierra too;it was solved to some extent by preparing multiple pointers or multiple threads to execute a program(see the later version of Tierra[52]and Avida by Adami et al.[1–3]).Biological systems,on the other hand,do not seem to suffer from evolutionary dead end.Of course the genome of a higher organism ordinarily includes many uncoded regions(base sequences that are not transcribed to proteins);however,these regions include several regulatory sequences and determine regulatory pathways of genes. Modi cations in the uncoded regions cannot only make new coded regions(new genes) but also change regulatory networks among present structural proteins.There is a biological theory that these modi cations had contributed most to the development of complexity[14].To make modi cations in the uncoded regions affect the entire genetic network,the uncoded as well as coded regions have to be watched all the time.In a living cell,this is done by a large number of proteins that work in parallel.A set of proteins for transcription are diffused throughout a cell or nucleus,and if there is a particular DNA sequence to react with these proteins,transcription is begun at that place.In a biological system,evolutionary dead end is circumvented by parallel execution of transcription proteins.This suggested that to overcome evolutionary deadFigure1.Evolutionary dead end in MUNCs.end,I needed to abandon sequential execution of machine codes and design a system that executes instructions logically in parallel.Based upon this reasoning,I next devised a system that consists of multiple com-puters with data- ow(data-driven)architecture.A data- ow machine is a parallel execution computer,whose program is represented by a directed graph.Nodes of a graph denote operators(instructions)and arrows of a graph represent ows of operand data[15–17,30,31,42].I prepared a population of matrices that represent program graphs and evolved them using GAs.From several experiments using problem data sets,I found that this system did not suffer from evolutionary dead end.The data- ow architecture enabled every operator to start execution only by a local modi cation of the connection matrix.An operator no longer needed to wait for a visit from the instruction pointer;thus the evolutionary dead end was not a problem with this machine.However,a population of data- ow computers was still unable to evolve programs with much algorithmic complexity.They could not answer dif cult problems prepared in an environmental data set within a practical simulation time.To revise this system to a more ef cient one,I next focused on another parallel process in living systems.Although an operator in the data- ow computer manipulates only one operand datum a time,a protein(enzyme)in a living cell can catalyze1000 chemical reactions per second,on average[4].This“parallel”execution of molecules can include slightly different versions of catalytic reactions,which might be a test-bed of the search for more advantageous reaction processes in a cell.To imitate this mechanism,I revised the data- ow architecture so that it might be able to deal with multiple operand data at one time.Here I call this system the“array-data-type”data-driven architecture.I prepared an operator matrix and an operand soup.The operator matrix,that is,genetic information modi ed by GAs,contains a sequence of instruction-template sets that are executed in parallel.At each time step, every operator chooses all operand data using its template data from the soup,modi es them,and puts them back into the soup.The soup is a size-variable array of label-value sets with no address number.As an enzyme selects substrates by conformational matching,so operand data are selected from the soup by the matching of the instruction template and data labels.After several experiments that used GAs to evolve a population of programs(op-erator matrices),I found that this system could evolve particular kinds of programs ef ciently,and yet it suffers from a serious drawback as a computational system.As is well known,for a system to be able to execute any kind of computation,or for a computational system to be equivalent to the universal Turing machine,it must be able to execute some kind of judging operations.In the data- ow architecture,this operation is typically achieved by a speci c type of operator(a comparator)that com-pares two operand data and outputs a control datum.In the present system,however, this operation cannot work well because the template matching typically selects many operands at once and a comparator cannot choose an appropriate pair of operands for the judgment(Figure2).The multiple selection of operands,which was at rst devised to improve the performance of the system,destroys the computational capability of the system.In a biological system,on the other hand,this problem is solved in the following way.In a living cell,substrate molecules(and catalytic molecules also)are not dispersed uniformly in the solvent.Typically,a living cell is structurally partitioned into sections by membranes,and in a particular section,molecules that are necessary for speci c catalytic reactions are concentrated.This partitioning of the cell not only increases the rate of catalytic reactions in a cell,but helps select controlling molecules that serve as switches for succeeding reactions.Inspired by this partitioning of a living cell,I revised the previous system in thefollowing ways.First,I introduced a special type of membrane data that partition theoperand soup into small sections.Then I merged the operator matrix into the operand soup so that an operator can select its operand data only in the section to which it belongs.This constitutes the framework of SeMar.The detailed design of SeMar described in the next section was established by making small modi cations on this baseline.3The ModelSeMar(the sea of matter)is a simulation of a one-dimensional core memory.The core satis es the periodic boundary condition(constitutes an endless loop)and is addressed with logical addresses.Since logical addresses are different from physical ones,the core is amenable to the insertion or deletion of any number of words(size-variable).In this section,I rst describe the metaphor that I used in the design of SeMar and then give a detailed explanation of the model.Although the nal version of SeMar(see future plans described in Section6)does not necessarily use GAs,I here use GAs to evolve creatures toward the desired direction.The entire simulation procedure using GAs is described in the last subsection(Section3.6).3.1MetaphorWhen designing MUNCs[45],I compared a MUNC instruction to a gene and a register operation in a CPU to a chemical reaction in a living cell.The analogy by which SeMar is designed is an extension of the above similarity.I compare the SeMar core to a biochemical reaction space(a solvent in which various biological substrates are dissolved or agglomerated),and I compare a computational operation in the core to a chemical reaction between biological molecules.In imitation of biological substrates, I prepare four types of data words in the core.These are the Membrane,Pure data, Operator,and Instruction.The Membrane can be compared to a lipid bilayer(a septum or a cytoplasmic membrane),the Pure data can be compared to a small molecule that functions as a substrate or a ligand,the Operator can be compared to a protein,and the Instruction can be compared to a gene(see Figure3).Like lipid bilayers in a solvent, the Membrane data work as core“walls”and partition the core into small sections (compartments).The data words located on the other side of the Membrane cannot be mixed without the use of data transfer by the speci c Operators.Each section can be compared to an organelle or a cell in living systems.3.2The Core Words and Their NotationEach word in the core is coded in a sequence of32binary bits,and according to the data type,it is expressed by the notation shown in Figure4.Depending upon the data type,a data word includes a Header,Type,Label,Value,Mnemonic,or Address. The Type of Membrane data is either Bgn or End.A section is delimited by a pair of Membranes(MEM:Bgn and MEM:End)that have the same Label bits.The Address of the Operator or Instruction is the ordinal number in the sequence of Instructions that a creature holds as its genetic information.At that address,not only machine code (Mnemonic)but a Label and several Templates are also stored.Templates are used for bit matching with Label bits and help to choose the appropriate data word necessary for the execution of the Instruction/Operator.3.3Execution of the CoreWhereas the operation of MUNCs(and any other machine language programming sys-tems)is directly activated by an instruction,the biochemical reaction in a cell is not directly catalyzed by a gene.The reaction is catalyzed by an enzyme(protein),andFigure3.Analogy between the SeMar core and a biochemical reaction space.Figure4.Notation of the four types of data words in the core.Figure5.An example picture(a snapshot)of a part of the core memory in the execution of an Operator.a gene works only as original information from which a corresponding protein is cre-ated.In a cell,proteins take the initiative in all actions.I imitate this system and make the execution of SeMar proceed with the actions of the Operators and Instructions. (Although in a future version of SeMar,I plan to accomplish all the workings of the core by the actions of Operators by preparing a new Operator for the transcription of Instructions to Operators(Section6),here I give both the Operators and Instruc-tions the initiative in the actions.)The actions of the Instructions and Operators are as follows.The execution of an Instruction transcribes itself to create the corresponding Oper-ator or a pair of Membranes.When transcribed to an Operator,the Operator is created in the nuclear section(the precise de nition of“nuclear”is given later)or in a section chosen by matching between the Template and Label,depending upon the kind of Instruction.Figure5shows a snapshot of a part of the core in which an Operator is in action. The Operator pointed at by the black triangle searches the core in the direction of earlier logical addresses,moves to the nearest operand datum,and modi es it.An operand datum is chosen by matching between the Operator Template and Pure dataLabels.This modi cation of data is continued until the Operator bumps into the nearest Membrane and disappears.As I mentioned before,the Membrane works as a core wall and the Operator cannot move beyond the Membrane.The execution pointer represented by the gray triangle holds the address of the next Operator/Instruction to be ing this pointer,all Operators and Instructions are put into action one by one in the order of their logical addresses in the core.The entire action of the core, that is,logically a parallel process,is considered to be simulated by this sequential execution.3.4Elementary InstructionsTable1shows16elementary Instructions that I prepared.They are classi ed into four groups.The rst group(CP o and CP e)consists of receptors for regulatory Operators. INS:CP o and INS:CP e are not transcribed and serve only as starting or terminating signals for consecutive Instructions whose activity values(values representing tran-scription capability)are regulated simultaneously.(In imitation of biology,I designate such a sequence of Instructions as an“operon.”)The second group(which includes only MEMB)is a special Instruction to create a Membrane pair.When this Instruction is put into action,the appropriate“outer”section is chosen by matching between the Instruction Template and Membrane Labels,and a new“inner”section is created in it by inserting a pair of Membranes(MEM:Bgn and MEM:End).Thus,all sections in the core have their own“outer”sections,so the core is partitioned hierarchically.The third group(Prom and Repr)consists of regulatory Instructions.Like regulatory genes in a living cell,when transcribed,INS:Prom and INS:Repr create OPE:Prom and OPE:Repr only in the“nuclear”section,respectively.(As in biology,where the organelle that contains genes(DNA)is called the nucleus,I call only the section that includes a sequence of Instructions the nuclear section.)These Operators search for the matched INS:CP o or INS:CP e(operands),move to it,and regulate the activity value of the succeeding operon.The fourth group(cre0to lt2)consists of structural Instructions.When a structural Instruction is put into action,the corresponding structural Operator is created in any matched section.A structural operator searches for an appropriate operand(a Pure data whose Label matches with the Operator Template),moves to it,and changes its value or creates a new Pure data according to the de ned function.During these processes,all regulatory and structural Operators choose not only operand data but also“ligand”data by the matching process.Like an allosteric protein in a cell,the activity value of an Operator changes by the effect of the ligand data and when the value is zero(it is inert),the Operator cannot modify the operand data.Finally in this section,I describe the exible description-length matching that is used to choose an appropriate operand,ligand,or Membrane(See Figure6).The matching is tested between a32-bit Template that an Operator/Instruction has and a16-bit Label that a Pure data/Membrane has.A Template consists of the16-bit Mask and the16-bit Pattern.At the matching process,the Pattern and the Label are compared only at the bit sites in which the Mask has bit1s.If the Pattern bits and the Label bits are all the same at those bit sites,the Template and the Label are regarded as matched.3.5Tree Data-Flow Structure Among SectionsAlthough the operations of almost all Operators cannot reach beyond the Membrane, only the two structural Operators OPE:CHO1and OPE:CHI1can violate this rule.These Operators are devised in imitation of membrane proteins in a cell.Membrane proteins are channels between compartments in a cell.They are anchored to the lipid bilay-Table1.The basic Instruction set.Mnemonic Function as an Instruction Function as an Operator CP ofor OPE:Prom.CP e Works as a receptorfor OPE:Repr.MEMB Creates a new pair ofMembranes in the matchedsection.Prom Creates OPE:Prom in the Promotes the transcription capability of nuclear section.Instructions(an operon)succeeding thematched INS:CP o.Repr Creates OPE:Repr in the Represses the transcription capability of nuclear section.Instructions(an operon)succeeding thematched INS:CP e.cre0Creates OPE:cre0in the Creates new Pure data at the beginning matched section.of the section.cop1Creates OPE:cop1in the Creates DAT:(a new Label)matched section.:(operand Value).inc1Creates OPE:inc1in the Creates DAT:(a new Label)matched section.:(operand Value C1).dec1Creates OPE:dec1in the Creates DAT:(a new Label)matched section.:(operand Value¡1).s 1Creates OPE:s 1in the Creates DAT:(a new Label)matched section.:(operand Value£2).CHO1Creates OPE:CHO1in the Transfers the operand DAT to the outer matched section.section or the answer stack.CHI1Creates OPE:CHI1in the Transfers the operand DAT to the inner matched section.section.cop2Creates OPE:cop2in the Copies the Value of the second operand matched section.to the rst one.add2Creates OPE:add2in the Creates DAT:(a new Label):(the rst matched section.operand Value C the second operand Value).gt2Creates OPE:gt2in the Creates new Pure data if(the rst operand matched section.Value)>(the second operand Value).lt2Creates OPE:lt2in the Creates new Pure data ifmatched section.(the rst operand Value)<(the second operand Value).ers and transfer speci c molecules from one side to the other.Like these proteins, OPE:CHO1and OPE:CHI1transfer operands to the outer or inner section,respectively. As described before,the Membrane partitions the core hierarchically.Every section has its outer section.The above channel Operators transfer data between the outer section and the inner section,so that the data ow among sections in the core constitutes a tree structure with one“outermost”section.The left-hand image in Figure7shows a typical partitioning of the core with the data ow by channel Operators expressed as arrows.In this example,the core consistsFigure6.Flexible description-length matching for data selection.Figure7.The partitioned core and the data transfer between sections.of two parts,the environmental section and the outermost section,and the outermost section includes three inner sections.The lowest inner section is the nuclear section. The root of the tree,that is,the outermost section,imports Pure data from the environ-mental section and exports Pure data to the answer stack that is prepared apart from the core.Although after the transfer,the source data are ordinarily deleted from the core;only data in the environmental section are not deleted with the transfer.This is a representation of the in nity of the environment.In Figure7,the corresponding biological system is also illustrated on the right-hand side.As is clear from this gure,the data stored in the answer stack can be comparedto molecules excreted by a unicellular creature.The tness value of each creature used in GAs is calculated from this excreted data.3.6Simulation Procedure Using Genetic AlgorithmsThe evolution of creatures is driven by genetic algorithms(GAs),especially those called simple GAs[21].Every creature has a sequence of Instructions,Labels,and Templates as its program information and a sequence of Pure data as its initial data of execution. All this genetic information is expressed as a long sequence of binary bits,and GAs modify a population of these sequences using a generation cycle of selection,mutation, and crossover operations.The tness value of each creature for selection is calculated using the execution process.In the execution,I prepare a core for each creature.A sequence of Instructions, initial Pure data,and an environmental data set are substituted for the core,and the core is put into practice.When the size of the answer stack is not changed for a long time or it reaches the prede ned maximum value,the execution process is terminated and the contents of the stack are examined.The tness value is calculated from the ratio of the“correct”value in this answer stack.The higher the ratio,the larger the tness value.The generation cycle of GAs is continued until a creature that can output the correct answer in the stack dominates the population.4Results of ExperimentsFirst I show a snapshot of the SeMar core in Figure8.In this gure all words are lined up in the order of their logical addresses.(The number on the left-hand side of each word is the physical address.)The outermost section includes two inner sections in this example,and among them,one section has its inner section.Active Instructions (Instructions that are able to be transcribed)are colored in dark gray,and inactive ones (those that are unable to be transcribed)are colored in light gray.At this moment the activity values of Instructions are determined by the initial setting,so that an operon, which is delimited by receptors(INS:CP o or INS:CP e),does not necessarily have the same activity value.Next I show the results of an experiment in which the SeMar creatures are given a problem to be solved.The problem is a simple machine learning problem that is the same as that was used in the experiment of MUNCs(a problem that was called a“larger-of-two-entries”problem in[44,45]).Figure9shows the environmental(problem)data set I prepared.In this gure,each column of numbers(32numbers)represents a data set,so in other words,eight data sets are shown in this gure.I prepared500 different problem data sets.All problem numbers E[dp]are random integers that range from0to99,and for each problem data set,the teaching value(T)is calculated usingT D max f E[6],E[7]g.In this case,the teaching value is the larger of two numbers,the sixth and the seventh entries.At the beginning of the execution process of a creature,one problem data set is randomly chosen out of the500data sets and is used as the environment data in the core. At this time,a problem number E[dp]is translated into the Pure data DAT:dp:E[dp]. When calculating the tness value from the answer stack,I judged a number stored in the stack to be correct when its value is the same as the teaching value T.。