Bisimulation Equivalence of First-Order Grammars

A decidability proof for bisimulation equivalence of first-order grammars (i.e., finite sets of labelled rules for rewriting roots of first-order terms) is presented. The result, generalizing the decidability of the DPDA (deterministic pushdown automata) equivalence, is equivalent to the result achieved by Senizergues (1998, 2005) in the framework of equational graphs, or of PDA with restricted e-steps, but the framework of classical first-order terms seems to be particularly useful for providing a concise proof that should be understandable for a wider audience.

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

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

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

[4]  Jan A. Bergstra,et al.  Decidability of bisimulation equivalence for process generating context-free languages , 1987, JACM.

[5]  Igor Walukiewicz,et al.  Krivine machines and higher-order schemes , 2011, Inf. Comput..

[6]  Géraud Sénizergues,et al.  L(A)=L(B)? A simplified decidability proof , 2002, Theor. Comput. Sci..

[7]  Slawomir Lasota,et al.  Fast equivalence-checking for normed context-free processes , 2010, FSTTCS.

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

[9]  C.-H. Luke Ong,et al.  Recursion Schemes and Logical Reflection , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[10]  Petr Jancar.  Equivalences of Pushdown Systems Are Hard , 2014, FoSSaCS.

[11]  Géraud Sénizergues,et al.  L(A) = L(B)? Decidability Results from Complete Formal Systems , 2002, ICALP.

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

[13]  Stanislav Böhm,et al.  Bisimilarity of One-Counter Processes Is PSPACE-Complete , 2010, CONCUR.

[14]  Yuxi Fu,et al.  Dividing Line between Decidable PDA's and Undecidable Ones , 2014, ArXiv.

[15]  Géraud Sénizergues,et al.  The Equivalence Problem for t-Turn DPDA Is Co-NP , 2003, ICALP.

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

[17]  Petr Jancar,et al.  Bisimilarity on Basic Process Algebra is in 2-ExpTime (an explicit proof) , 2012, Log. Methods Comput. Sci..

[18]  Petr Jancar,et al.  Decidability of DPDA Language Equivalence via First-Order Grammars , 2012, 2012 27th Annual IEEE Symposium on Logic in Computer Science.

[19]  Søren Christensen,et al.  Bisimulation Equivalence is Decidable for all Context-Free Processes , 2022 .

[20]  Seymour Ginsburg,et al.  Deterministic Context Free Languages , 1965, Inf. Control..

[21]  Sylvain Schmitz,et al.  Complexity Hierarchies beyond Elementary , 2013, TOCT.

[22]  Joël Ouaknine,et al.  On the Complexity of the Equivalence Problem for Probabilistic Automata , 2011, FoSSaCS.

[23]  Géraud Sénizergues,et al.  L(A) = L(B) ? decidability results from complete formal systems , 2001 .

[24]  Jorge A. Pérez,et al.  On the Expressiveness and Decidability of Higher-Order Process Calculi , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.

[25]  Andrzej S. Murawski,et al.  Bisimilarity of Pushdown Automata is Nonelementary , 2013, 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science.

[26]  Antonín Kucera,et al.  On the complexity of checking semantic equivalences between pushdown processes and finite-state processes , 2010, Inf. Comput..

[27]  Colin Stirling,et al.  Decidability of DPDA equivalence , 2001, Theor. Comput. Sci..

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

[29]  Bruno Courcelle,et al.  Recursive Applicative Program Schemes , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[30]  Bernhard Steffen,et al.  An Elementary Bisimulation Decision Procedure for Arbitrary Context-Free Processes , 1995, MFCS.

[31]  Stefan Kiefer.  BPA bisimilarity is EXPTIME-hard , 2013, Inf. Process. Lett..

[32]  Xiuting Tao,et al.  Branching Bisimilarity Checking for PRS , 2014, ICALP.

[33]  Géraud Sénizergues,et al.  The Bisimulation Problem for Equational Graphs of Finite Out-Degree , 2000, SIAM J. Comput..

[34]  C. Stirling.  Decidability of Bisimulation Equivalence for Pushdown Processes , 2000 .

[35]  Stanislav Böhm,et al.  Language Equivalence of Deterministic Real-Time One-Counter Automata Is NL-Complete , 2011, MFCS.

[36]  Gheorghe Paun,et al.  Current Trends in Theoretical Computer Science: The Challenge of the New Century , 2004 .

[37]  Colin Stirling,et al.  Deciding DPDA Equivalence Is Primitive Recursive , 2002, ICALP.