1. 1 Modeling and Analyzing Distributed Systems Using I/O Automata Nancy Lynch, MIT Draper Laboratory, IR&D Kickoff Meeting Aug. 30, 2002

2. 2 Modeling using I/O Automata Mathematical, infinite-state, automaton models. Describe states, transitions. Describe system modularity: –Parallel composition of interacting components. –Levels of abstraction. Example: Generic distributed system: –Diagram represents interfaces only. –IOA models also describe behavior. –Abstract models for system components. –Channel: Implemented by TCP, modeled as reliable FIFO queue. –Node: Implemented by C++ or Java program, modeled as simple algorithm automaton.

3. 3 Reliable FIFO Channel Model Signature: –Inputs: send(m), m in M –Outputs: receive(m), m in M States: –queue, a finite sequence of elements of M, initially empty Transitions: –send(m) Effect: Add m to end of queue –receive(m) Precondition: m is first on queue Effect: remove first element of queue Channel(M) send(m)receive(m)

4. 4 Levels of Abstraction Used in system 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. 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. –Continue, implementing GCS in terms of lower-level network. TO-Bcast GCS

5. 5 Flavors of I/O Automaton Models Ordinary, basic IOAs deal with: –What happens, in what order (not when). –Discrete events (not continuous behavior). Timing: TIOA –For describing timeout-based algorithms. –Local clocks, clock synchronization. –Timing/performance analysis. Hybrid (continuous/discrete): HIOA –Systems with real world + computer components –Vehicle control: ground, air, space –Embedded systems

6. 6 What are these models good for? System documentation/specification –High-level, precise, reasonably easy to understand. Design validation: –Simulation of system behavior –Stating and proving correctness theorems. Manually, or with interactive theorem-provers. –Finite-state exploration, for debugging, for complete analysis of small pieces, small cases, small abstractions. Top-down system development Code validation: –Models as templates for code –Demonstrate consistency between model, code –Generate code automatically from low-level models?

7. 7 In the remaining minutes: I/O Automata –What they are (math) –Applications: Distributed algorithms, systems –Tool support: IOA language and toolset Timed I/O Automata –What they are –Applications: Communication, performance analysis Hybrid I/O Automata –What they are –Applications: Safety-critical systems

8. 8 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. Dynamic description: –Execution: s 0 a 1 s 1 a 2 s 2 … –Trace: Sequence of input and output actions; externally visible behavior. –A implements B: traces(A)  traces(B). Operations for building automata: –Parallel composition, identifying inputs and outputs. –Action hiding. Reasoning methods: –Invariant assertions: Property holds in all reachable states. –Simulation relations: Imply one automaton implements another. –Compositional methods

9. 9 Example Applications Theoretical distributed algorithms: –Mutual exclusion, Byzantine agreement, atomic object implementation, resource allocation, data management… 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. –Ensemble GC system: Models for key layers. Found, fixed logical error. Proofs. Algorithms for dynamic networks (new): –RAMBO reconfigurable atomic memory algorithm –Dynamic atomic broadcast algorithm

10. 10 IOA Language + Toolset Formally-defined programming/modeling language for describing and analyzing systems modelled as I/O automata. Current tools: Simulator, connection to theorem- prover. In progress: Invariant detector, connections to other theorem-provers, automatic code generator. Steve Garland will say more. I O A

11. 11 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. –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 –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. –Inductive proofs.

12. 12 Example Applications Theoretical distributed algorithms: –Mutual exclusion, consensus,… Timeout-based communication protocols: –TCP,… Group communication systems: –Using GCS to build TO-Bcast: Conditional performance analysis. –Scalable GCS: Performance analysis. –R AMBO : Performance analysis. Hybrid (continuous/discrete) systems: –Toy examples: RR crossing, steam boiler controller –Stretched TIOA capabilities; motivated HIOA.

13. 13 Hybrid I/O Automata (HIOA) TIOA plus facilities for representing continuous behavior. Static description: –States: input, output, internal variables; start states –Actions: input, output, internal –Discrete steps (s, a, s') –Trajectories , mapping time intervals to states Dynamic description: –Execution  0 a 1  1 a 2  2 … –Trace: Project on external variables, external actions. –A implements B if traces(A)  traces(B). Operations: Composition, hiding Reasoning methods: Invariants, simulation relations, compositional methods

14. 14 Example Applications Ground transportation: –People-mover (Raytheon) –California PATH automated highway system: Analysis of platoon maneuvers. Aircraft control: –TCAS (Lincoln Labs): Models, proofs. –Quanser helicopter system (MIT Aero/Astro). Spacecraft, …: –ACME

15. 15 TCAS model Aircraft Pilot Channel Conflict resolver Conflict detector Sensor Aircraft Conflict detector Conflict resolver Pilot Channel