Branching Bisimilarity Checking for PRS

Recent studies reveal that branching bisimilarity is decidable for both nBPP (normed Basic Parallel Process) and nBPA (normed Basic Process Algebra). These results lead to the question if there are any other models in the hierarchy of PRS (Process Rewrite System) whose branching bisimilarity is decidable. It is shown in this paper that the branching bisimilarity for both nOCN (normed One Counter Net) and nPA (normed Process Algebra) is undecidable. These results essentially imply that the question has a negative answer.

[1]  Rocco De Nicola,et al.  Back and Forth Bisimulations , 1990, CONCUR.

[2]  Jirí Srba,et al.  Highly Undecidable Questions for Process Algebras , 2004, IFIP TCS.

[3]  Yuxi Fu,et al.  Checking Equality and Regularity for Normed BPA with Silent Moves , 2013, ICALP.

[4]  Richard Mayr.  Undecidability of Weak Bisimulation Equivalence for 1-Counter Processes , 2003, ICALP.

[5]  Antonín Kucera,et al.  Equivalence-checking on infinite-state systems: Techniques and results , 2002, Theory and Practice of Logic Programming.

[6]  Jirí Srba.  Undecidability of Weak Bisimilarity for PA-Processes , 2002, Developments in Language Theory.

[7]  Slawomir Lasota,et al.  Decidability of Branching Bisimulation on Normed Commutative Context-Free Processes , 2013, Theory of Computing Systems.

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

[9]  Jirí Srba,et al.  Undecidability of bisimilarity by defender's forcing , 2008, JACM.

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

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

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

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

[14]  Jirí Srba,et al.  Undecidability of Weak Bisimilarity for Pushdown Processes , 2002, CONCUR.

[15]  Colin Stirling,et al.  The Joys of Bisimulation , 1998, MFCS.

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

[17]  Jirí Srba,et al.  Roadmap of Infinite Results , 2002, Bull. EATCS.

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

[19]  Mark Jerrum,et al.  Bisimulation Equivanlence Is Decidable for Normed Process Algebra , 1999 .

[20]  Jirí Srba.  Completeness Results for Undecidable Bisimilarity Problems , 2003, INFINITY.

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

[22]  Rob J. van Glabbeek,et al.  Branching time and abstraction in bisimulation semantics , 1996, JACM.

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

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

[25]  Sergey Yekhanin,et al.  Towards 3-query locally decodable codes of subexponential length , 2008, JACM.