Note on the Tableau Technique for Commutative Transition Systems

We define a class of transition systems called effective commutative transition systems (ECTS) and show, by generalising a tableau-based proof for BPP, that strong bisimilarity between any two states of such a transition system is decidable. It gives a general technique for extending decidability borders of strong bisimilarity for a wide class of infinite-state transition systems. This is demonstrated for several process formalisms, namely BPP process algebra, lossy BPP processes, BPP systems with interrupt and timed-arc BPP nets.

[1]  L. Dickson.  Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors , 1913 .

[2]  Jan A. Bergstra,et al.  Syntax and defining equations for an interrupt mechanism in process algebra , 1985 .

[3]  F. Jones.  There and back again , 1989, Nature.

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

[5]  Tommaso Bolognesi,et al.  From timed Petri nets to timed LOTOS , 1990, PSTV.

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

[7]  B. Jonsson,et al.  Verifying programs with unreliable channels , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[8]  Faron Moller,et al.  Bisimulation Equivalence is Decidable for Basic Parallel Processes , 1993, CONCUR.

[9]  Hans-Michael Hanisch.  Analysis of Place/Transition Nets with Timed Arcs and its Application to Batch Process Control , 1993, Application and Theory of Petri Nets.

[10]  Petr Jancar.  Undecidability of Bisimilarity for Petri Nets and Some Related Problems , 1995, Theor. Comput. Sci..

[11]  A. G. Engels,et al.  Disrupt and interrupt in MSC : Possibilities and problems , 1998 .

[12]  Faron Moller,et al.  Techniques for Decidability and Undecidability of Bisimilarity , 1999, CONCUR.

[13]  Ahmed Bouajjani,et al.  Model Checking Lossy Vector Addition Systems , 1999, STACS.

[14]  Richard Mayr,et al.  Process rewrite systems , 1999, EXPRESS.

[15]  Philippe Schnoebelen,et al.  Verifying Performance Equivalence for Timed Basic Parallel Processes , 2000, FoSSaCS.

[16]  J. Bergstra,et al.  Mode transfer in process algebra , 2000 .

[17]  David de Frutos-Escrig,et al.  Decidability of Properties of Timed-Arc Petri Nets , 2000, ICATPN.

[18]  Jirí Srba,et al.  Basic process algebra with deadlocking states , 2001, Theor. Comput. Sci..

[19]  Ivan Damgård,et al.  From Known-Plaintext Security to Chosen-Plaintext Security , 2001 .

[20]  Lars Kristiansen.  The Implicit Computational Complexity of Imperative Programming Languages , 2001 .

[21]  Harald Ruess,et al.  Predicate Abstraction for Dense Real-Time Systems , 2001 .

[22]  Ivan Damgård,et al.  An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates , 2001, IACR Cryptol. ePrint Arch..

[23]  Jiri Srba.  Note on the Tableau Technique for Commutative Transition Systems , 2001 .

[24]  Faron Moller,et al.  Verification on Infinite Structures , 2001, Handbook of Process Algebra.

[25]  Colin Stirling,et al.  Decidability of Weak Bisimilarity for a Subset of Basic Parallel Processes , 2001, FoSSaCS.

[26]  Ivan Damgård,et al.  Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor , 2001, CRYPTO.

[27]  Jirí Srba,et al.  Properties of Distributed Timed-Arc Petri Nets , 2001, FSTTCS.

[28]  Jirí Srba.  Strong Bisimilarity and Regularity of Basic Process Algebra Is PSPACE-Hard , 2002, ICALP.

[29]  Frank D. Valencia,et al.  Temporal Concurrent Constraint Programming: Applications and Behavior , 2001, Formal and Natural Computing.

[30]  Olivier Danvy,et al.  A first-order one-pass CPS transformation , 2001, Theor. Comput. Sci..

[31]  Richard Mayr.  Undecidable problems in unreliable computations , 2003, Theor. Comput. Sci..

[32]  Olivier Danvy,et al.  CPS transformation of flow information, Part II: administrative reductions , 2003, J. Funct. Program..