Compositional Reasoning for Probabilistic Finite-State Behaviors

We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch's simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes parallel composition and (guarded) recursion. The presence of the parallel composition introduces various technical difficulties and some restrictions are necessary in order to achieve complete axiomatizations.

[1]  Roberto Segala,et al.  Axiomatizations for Probabilistic Bisimulation , 2001, ICALP.

[2]  Kim G. Larsen,et al.  Compositional Verification of Probabilistic Processes , 1992, CONCUR.

[3]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[4]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[5]  Wolfgang Bibel,et al.  Mathematical Methods of Specification and Synthesis of Software Systems '85 , 1986, Lecture Notes in Computer Science.

[6]  Bengt Jonsson,et al.  CONCUR ’94: Concurrency Theory , 1994, Lecture Notes in Computer Science.

[7]  Robin Milner,et al.  A Complete Inference System for a Class of Regular Behaviours , 1984, J. Comput. Syst. Sci..

[8]  Jan A. Bergstra,et al.  Process Algebra for Synchronous Communication , 1984, Inf. Control..

[9]  Faron Moller,et al.  Decidable Subsets of CCS , 1994, Comput. J..

[10]  J. Baeten.  Applications of process algebra , 1990 .

[11]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[12]  Robin Milner,et al.  A Complete Axiomatisation for Observational Congruence of Finite-State Behaviors , 1989, Inf. Comput..

[13]  Mario Bravetti,et al.  Deciding and axiomatizing weak ST bisimulation for a process algebra with recursion and action refinement , 2002, TOCL.

[14]  Søren Christensen.  Decidability and decomposition in process algebras , 1993 .

[15]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[16]  Z. Ésik,et al.  Equational Axioms for Probabilistic Bisimilarity (Preliminary Report) , 2002 .

[17]  Christel Baier,et al.  Validation of Stochastic Systems , 2004, Lecture Notes in Computer Science.

[18]  Robin Milner,et al.  Calculi for Synchrony and Asynchrony , 1983, Theor. Comput. Sci..

[19]  Jan Friso Groote,et al.  Linearization in parallel pCRL , 2000, J. Log. Algebraic Methods Program..

[20]  G. Plotkin,et al.  Proof, language, and interaction: essays in honour of Robin Milner , 2000 .

[21]  Bengt Jonsson,et al.  Probabilistic Process Algebra , 2001 .

[22]  Jan A. Bergstra,et al.  Axiomatizing Probabilistic Processes: ACP with Generative Probabilities , 1995, Inf. Comput..

[23]  Scott A. Smolka,et al.  A complete axiom system for finite-state probabilistic processes , 2000, Proof, Language, and Interaction.

[24]  Robin Milner.  Action Calculi, or Syntactic Action Structures , 1993, MFCS.

[25]  Rob J. van Glabbeek,et al.  A Complete Axiomatization for Branching Bisimulation Congruence of Finite-State Behaviours , 1993, MFCS.

[26]  Jos C. M. Baeten,et al.  Process Algebra , 2007, Handbook of Dynamic System Modeling.

[27]  Frits W. Vaandrager,et al.  Root Contention in IEEE 1394 , 1999, ARTS.

[28]  Joost-Pieter Katoen,et al.  On Generative Parallel Composition , 1998, PROBMIV.

[29]  Stephen Gilmore,et al.  Specifying Performance Measures for PEPA , 1999, ARTS.

[30]  Jan A. Bergstra,et al.  Verification of an alternating bit protocol by means of process algebra , 1985, Mathematical Methods of Specification and Synthesis of Software Systems.

[31]  Nancy A. Lynch,et al.  Proving time bounds for randomized distributed algorithms , 1994, PODC '94.

[32]  Jos C. M. Baeten,et al.  A Ground-Complete Axiomatization of Finite State Processes in Process Algebra , 2005, CONCUR.

[33]  Luca Aceto,et al.  The Quest for Equational Axiomatizations of Parallel Composition: Status and Open Problems , 2006, APC 25.

[34]  Vincent Danos,et al.  Transactions in RCCS , 2005, CONCUR.

[35]  Roberto Segala,et al.  Verification of the randomized consensus algorithm of Aspnes and Herlihy: a case study , 2000, Distributed Computing.

[36]  Erik P. de Vink,et al.  Probabilistic Automata: System Types, Parallel Composition and Comparison , 2004, Validation of Stochastic Systems.

[37]  Yuxin Deng,et al.  Axiomatisations and Types for Probabilistic and Mobile Processes. (Axiomatisations et types pour des processus probabilistes et mobiles) , 2005 .

[38]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[39]  Jan Friso Groote,et al.  Verifying a Sliding Window Protocol in µCRL , 2004, AMAST.

[40]  Scott A. Smolka,et al.  Algebraic Reasoning for Probabilistic Concurrent Systems , 1990, Programming Concepts and Methods.

[41]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[42]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[43]  Jan A. Bergstra,et al.  A complete inference system for rgular processes with silent moves , 1984 .

[44]  Yuxin Deng,et al.  Axiomatizations for Probabilistic Finite-State Behaviors , 2005, FoSSaCS.