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The Kahn Principle for Networks of Endochronous Programs

This paper introduces the concept of endochronous systems and presents the Kahn principle for deterministic networks of such systems. It outlines the proof of the theorem and discusses practical consequences and future work.

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The Kahn Principle for Networks of Endochronous Programs

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  1. The Kahn Principle for Networks of Endochronous Programs Dumitru Potop-Butucaru IRISA, France

  2. Outline • Introduction • Motivation • Endo/Isochrony • Endochronous systems • The Kahn principle • Proof outline • Conclusion. Future work

  3. Introduction • Synchronous systems, composition • Desynchronization: • Goals: Input reading from async. sources Semantics preservation: (Σ1| Σ2)a= Σ1a || Σ2a Σ Σa

  4. Endo/Isochrony (Benveniste et al.) • Endochrony (of a system) • Do not use input signal presence information • Isochrony (of a pair of systems) • Non conflicting transitions are composable Theorem: a. Isochrony  semantics preservation b. Endochrony  semantics preservation  Isochrony • Non-deterministic, no intra-instant causality

  5. Endochronous system model Σ=(S,V=INOUT,O,θ,) Microstep states: M ={(s,I,φ)|sS,IIN, φ:I  D } Output functions: O:M P(OUT) ; Θ(μ):O(μ) D Input decision function, monotonous: READ:MP (IN), IREAD(s,I,φ) Transitions: (s,I,φ)(s’,I’,φ’): intra-instant: s=s’ and II’READ(s,I,φ) and φφ’ state change: READ(s,I,φ)=I and I’= and φ’=

  6. Endochronous system model • Incrementally read the inputs from input channels (e.g. unbounded FIFOs) • The decision to read a signal is never revoked (s,{i1},{(i1,v1)}),READ={i1,i2} (s,{i1,i2},{(i1,v1),(i2,v2)}),READ={i1,i2} (s,,),READ={i1,i2} (s,{i2},{(i2,v2)}),READ={i1,i2}

  7. Asynchronous network model • Network: Synchronous systems + FIFOs • FIFO state: words over D • Network state: component, FIFO states • Network transition: component trans. • Possible if the FIFOs to read are not empty • Change the status of the component and the status of some adjacent FIFOs

  8. The Kahn Principle Theorem Asynchronous networks of endochronous systems are deterministic as I/O functions • Inter-component concurrency does not affect the semantics of the system • The result holds for bounded FIFOs • Isochrony 1-place FIFOs are enough

  9. Proof outline • Step 1: I/O determinism of a component for an instant (monotony of READ) • Step 2: I/O determinism of a component (step 1 + state change determinism) • Step 3: determinism of the network (Finite derivations, from step 2. Infinite, by continuity.)

  10. Practical consequences • Make systems endochronous (Signal compiler, add “clock” signals) • When testing, varying the transmission delays (and jitter) of the FIFOs does not influence the outcome of the computation • only one run is necessary for a given asynchronous history

  11. Conclusion • Endochronous component model with causality • Asynchronous system model • The Kahn principle • Future work: extend endochrony to allow internal concurrency

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