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Mathematical Models for Distributed Programs

Explore using abstract I/O automaton models for creating actual distributed programs, leveraging a simple mathematical basis to describe system structure and behavior. Develop models to refine service specs and distributed algorithms.

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Mathematical Models for Distributed Programs

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  1. I A O IOA: Mathematical Models  Distributed Programs Nancy Lynch November 15, 2000 Collaborators: Steve Garland, Josh Tauber, Anna Chefter, Antonio Ramirez, Michael Tsai, Chris Luhrs, Rui Fan, Laura Dean, Andrej Bogdanov

  2. What we want to do: See how abstract I/O automatonmodels of distributed algorithms and services could be used in producing and maintaining actual distributed programs.

  3. Why use models? • Models let you: • Build very complex things and get them right • Change things and understand the consequences • Explain clearly how things work • Other engineering disciplines use them

  4. But why I/O automaton models? • Very simple mathematical basis for describing structure + behavior of systems of interacting components • Already used for: • Distributed algorithms, impossibility results • System case studies: • Group communication services (Orca, Transis, Ensemble,…) • Communication protocols (TCP, T/TCP,…) • Hybrid (continuous/discrete) systems (TCAS,…) • ...

  5. What are I/O automata? • Nondeterministic state machines • Infinite state • Input/output/internal actions • Transitions, executions, traces • Supports modularity: • Composition • Levels of abstraction • Math model, language-independent

  6. Using I/O automata • Model service specs, distributed algorithms • Refine, from high level global service spec to detailed distributed algorithm • Make models as nondeterministic as possible • Prove correctness, using invariants, simulation relations, composition

  7. TO TO Broadcast Service Spec Signature: input: broadcast(a,p) output: receive(a,p,q) internal: order(a,p) State: queue, sequence of (a,p), initially empty for each p: pending[p], sequence of a, initially empty next[p], positive integer, initially 1

  8. Transitions: broadcast(a,p) Effect: append a to pending[p] order(a,p) Precondition: a is head of pending[p] Effect: remove head of pending[p]; append (a,p) to queue receive(a,p,q) Precondition: queue[next[q]] = (a,p) Effect: next[q] := next[q] + 1 TO Broadcast Spec

  9. I A O For proofs For simulation, code generation IOA Language[Garland, Lynch 97] • Programming/specification language for defining I/O automata • Similar to pseudocode • Explicitly describes: • Signature, structured state, precondition/effects • Nondeterministic choice, composition, invariants, levels of abstraction • Declarative + imperative

  10. IOA Tools • Front end: Parser, static checker, intermediate Java representation [Garland, Ramirez] • Support for: • Composing models [Chefter 98] [Garland, Lynch] • Refining models, from global specification to low-level distributed algorithm model: Step correspondence [Ramirez 00]

  11. IOA Tools • Prototype code generator, for generating distributed code from low-level distributed algorithm models [Tauber, Tsai] • Validation tools: • Simulator [Chefter 98] [Ramirez 00] Paired simulation: • Theorem-prover interfaces: PVS [Devillers], Isabelle? LP? NuPRL? [Nolte] • Automatic?

  12. CodeGenerator • Start from node models + channel models • Implementing node automata: • Generate code (Java, C++) automatically • Use library of hand-written data type implementations • Implementing channel automata: • Use real communication service (TCP, MPI) • Abstract channels

  13. Abstract Channels • Model with nodes and abstract channels (e.g., FIFO queue): • Algorithm that implements abstract channel in terms of real channel (model):

  14. Abstract Channels Generate Code

  15. Modeling Projects • Distributed spanning tree algorithms [Luhrs, Nolte] • Distributed replicated data management algorithms: Lamport state machines; Attiya, Bar-Noy, Dolev, … [Dean, Karlovich, Rosen] • Future: • Practical communication protocols, services • Interacting Java objects

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