Actions Speak Louder Than Words: Proving Bisimilarity for Context-Free Processes

Baeten Bergstra and Klop and later Caucal have proved the remarkable result that bisimulation equivalence is decidable for irre dundant context free grammars In this paper we provide a much simpler and much more direct proof of this result using a tableau de cision method involving goal directed rules The decision procedure also provides the essential part of the bisimulation relation between two processes which underlies their equivalence We also show how to obtain a sound and complete sequent based equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful tableau An earlier shorter version of this paper appeared at the th Annual Symposium on Logic in Computer Science LICS Amsterdam

[1]  Jan Friso Groote,et al.  A Short Proof of the Decidability of Bisimulation for Normed BPA-Processes , 1992, Inf. Process. Lett..

[2]  Faron Moller,et al.  Decomposability, decidability and axiomatisability for bisimulation equivalence on basic parallel processes , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[3]  Lu Tian,et al.  On Deciding Readiness and Failure Equivalences for Processes , 1995, Inf. Comput..

[4]  Lu Tian,et al.  Deciding Bisimilarity of Normed Context-Free Processes is in Sigma^p_2 , 1994, Theor. Comput. Sci..

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

[6]  R. J. vanGlabbeek.  The linear time - branching time spectrum , 1990 .

[7]  David Walker,et al.  CCS, Liveness, and Local Model Checking in the Linear Time Mu-Calculus , 1989, Automatic Verification Methods for Finite State Systems.

[8]  Antonín Kucera,et al.  How to Parallelize Sequential Processes , 1997, CONCUR.

[9]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[10]  Didier Caucal,et al.  Graphes canoniques de graphes algébriques , 1990, RAIRO Theor. Informatics Appl..

[11]  Søren Christensen,et al.  Bisimulation Equivalence is Decidable for Context-Free Processes , 2005 .

[12]  Didier Caucal,et al.  On the transition graphs of automata and grammars , 1990, WG.

[13]  Faron Moller,et al.  A Polynomial Algorithm for Deciding Bisimilarity of Normed Context-Free Processes , 1994, Theor. Comput. Sci..

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

[15]  Jan Friso Groote,et al.  Undecidable Equivalences for Basic Process Algebra , 1994, Inf. Comput..

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

[17]  Jan A. Bergstra,et al.  Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages , 1987, PARLE.

[18]  Colin Stirling,et al.  Verifying Temporal Properties of Processes , 1990, CONCUR.

[19]  Bruno Courcelle.  An Axiomatic Approach to the Korenjak-Hopcroft Algorithms , 1981, ICALP.

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

[21]  Hans Hüttel,et al.  Silence is Golden: Branching Bisimilarity is Decidable for Context-Free Processes , 1991, CAV.

[22]  John E. Hopcroft,et al.  Simple Deterministic Languages , 1966, SWAT.

[23]  Colin Stirling,et al.  Decidability of bisimulation equivalence for normed pushdown processes , 1998, SIGA.

[24]  Hans Hüttel,et al.  Undecidable equivalences for basic parallel processes , 1994, Inf. Comput..

[25]  Jan A. Bergstra,et al.  Process theory based on bisimulation semantics , 1988, REX Workshop.

[26]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .