I／O Automaton Models∶ Basic, Timed, Hybrid, Probab

• Hybrid (continuous/discrete): HIOA
– Systems with real world + computer components
– Vehicle control: ground, air, space
– Embedded systems
• Probabilistic: PIOA, PTIOA, PHIOA
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Timed I/O Automata (TIOA)
• Add special time-passage actions, pass(t), to IOA model.
• Example: Reliable FIFO channel that always delivers messages within time d.
– Inductive proofs.
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Example Applications
• Theoretical distributed algorithms:
– Mutual exclusion, consensus,…
• Timeout-based communication protocols:
• Transitions:
– send(m)
• Effect: Add m to end of queue
– receive(m)
• Precondition: m is first on queue
• Effect: remove first element of queue
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Levels of Abstraction
Based on work with Roberto Segala, Frits Vaandrager
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I/O Automata
• Mathematical, infinite-state, automaton models. • Describe states, transitions. • Describe system modularity:
compositional methods 12
Example Applications
• Ground transportation:
• Operations for building automata:
– Parallel composition, identifying inputs and outputs.
– Action hiding.
• Reasoning methods:
– Invariant assertions: Property holds in all reachable states.
– pass(t)
• Precondition: for all (m,u) in queue, now + t u
• Effect: now := now + t
• Can use standard automaton-based reasoning methods:
– Invariant: for all (m,u) in queue, now u now + d.
– Randomized distributed algorithms
– Security protocols
– Safety-critical systems
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Talk Outline
1. Brief overview of the models 2. HIOA model, in more detail (Lynch) 3. TIOA model (Kirli) 4. PIOA model (Lynch) 5. Future work on models 6. Future work on applications
– send(m)
• Effect: Add (m, now + d) to end of queue
– receive(m)
• Precondition: (m,u) is first on queue (for some u)
• Effect: remove first element of queue
– RR crossing, steam boiler controller – Stretched TIOA capabilities; motivated HIOA.
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Hybrid I/O Automata (HIOA)
• TIOA plus facilities for representing continuous behavior. • Statiystem development by successive refinement.
• Top level: Specification for allowed behaviors.
• Can write in same automaton style.
• Refine through many levels, to code-like, detailed description.
• Dynamic description:
– Execution 0 a1 1 a2 2 … – Trace: Project on external variables, external actions. – A implements B if traces(A) traces(B).
• Operations: Composition, hiding • Reasoning methods: Invariants, simulation relations,
– Simulation relations: Imply one automaton implements another.
– Compositional methods
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Example Applications
• Theoretical distributed algorithms:
– Mutual exclusion, Byzantine agreement, atomic object implementation, resource allocation, data management…
• Dynamic description:
– Execution: s0 a1 s1 a2 s2 … – Trace: Sequence of input and output actions; externally visible behavior.
– A implements B: traces(A) traces(B).
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1. Brief Overview of the Models
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I/O Automata (IOA)
• Static description:
– Actions a (input, output, internal)
– States s, start states
– Transitions (s, a, s'); input actions enabled in all states.
• Example: Group communication:
– Automata used to represent totally-ordered reliable broadcast service, group communication service, and algorithm.
– Composition of algorithm and GCS automata implements TO-Bcast automaton.
automaton.
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Reliable FIFO Channel Model
• Signature:
– Inputs: • send(m), m in M
send(m)
receive(m)
Channel(M)
– Outputs:
• receive(m), m in M
• States:
– queue, a finite sequence of elements of M, initially empty
– TCP,…
• Group communication systems:
– Using GCS to build TO-Bcast: Conditional performance analysis.
– Scalable GCS: Performance analysis.
• RAMBO: Performance analysis. • Hybrid (continuous/discrete) systems:
• Distributed systems:
– Orca DSM system: Two-layer model, following the implementation. Found, fixed logical error. Proofs.
– Transis group communication system: Models for key layers. Proofs. Algorithmic improvements.
– Discrete events (not continuous behavior).
• Timing: TIOA
– For describing timeout-based algorithms.
– Local clocks, clock synchronization.
– Timing/performance analysis.
I/O Automaton Models: Basic, Timed, Hybrid, Probabilistic, Etc.