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Ichiro Hasuo Tracing Anonymity with Coalgebras

Ichiro Hasuo Tracing Anonymity with Coalgebras. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A. The ultimate aim. Better mathematical understanding of computer systems. Coalgebras. Coalgebras. Overview. In Sets : bisimilarity.

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Ichiro Hasuo Tracing Anonymity with Coalgebras

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  1. Ichiro Hasuo Tracing Anonymity with Coalgebras TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

  2. The ultimate aim Better mathematical understanding of computer systems

  3. Coalgebras

  4. Coalgebras

  5. Overview

  6. InSets: bisimilarity • category = “universe” • Sets, Top, Stone, Vect, CLat, …

  7. Bisimilarity vs. trace semantics  a a a Also captured by final coalgebra? = c b c b

  8. Coalgebraic trace semantics • “Kleisli category” • a category where • branching is implicit • XY : “branching function” from X to Y • T : parameter for branching-type captures… Generic Trace Semantics via Coinduction IH, Bart Jacobs & Ana Sokolova Logical Method in Comp. Sci. 3(4:11), 2007  =

  9. Different “branching-types” in Kl(T) captures trace semantics T : parameter for “branching-type” trace semantics: a  b a  c trace semantics: a  b : 1/3 a  c : 2/3 T = P T = D non-deterministic branching probabilistic branching a a a a c c b 1 1 b

  10. Coalgebraic simulations (Ch. 3) observation lax morphism = forward simulation oplaxmorphism = backward simulation • genericity again: both for • T = P (non-determinism) • T = D (probability) theorem (soundness) 9fwd/bwd simulation  trace inclusion Generic Forward and Backward Simulations IH Proc. CONCUR 2006 LNCS 4137

  11. Summary so far • genericity : both for • T = P (non-determinism) • T = D (probability) Ch. 3 Ch. 2 theory of bisimilarity theory of traces and simulations

  12. Case study: probabilistic anonymity (Ch. 4) Simulation-based proof method for non-deterministic anonymity [KawabeMST06] T = P generic, coalgebraic theory of traces and simulations [Ch. 2-3] Probabilistic Anonymity via Coalgebraic Simulations IH & YoshinobuKawabe Proc. ESOP 2007 LNCS 4421 T = D Simulation-based proof method for probabilistic anonymity

  13. Concurrency CkD running C and D in parallel “concurrency” , “behavior” category of coalgebras inner k 2 final coalgebra outer k the microcosm principle

  14. Concurrency and the microcosm principle (Ch. 5) science of computer systems concurrency, compositionality, behavior, … generic compositionality theorem formalization of microcosm principle in 2-categories The Microcosm Principle and Concurrency in Coalgebra IH, Bart Jacobs & Ana Sokolova To appear in Proc. FoSSaCS 2008 LNCS mathematics

  15. Summary

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