Undecidability of bisimilarity by defender's forcing

Journal of the ACM

Volumn 55, Issue 1, 2008, Pages

  Jančar, Petr ^a   Srba, Jivří ^b  

^a VSB TECHNICAL UNIVERSITY OF OSTRAVA   (Czech Republic)

^b AALBORG UNIVERSITY   (Denmark)

Author keywords

Bisimilarity; Process algebra; Pushdown automata; Undecidability

Indexed keywords

ALGEBRA; AUTOMATA THEORY; PROBLEM SOLVING;

BISIMILARITY; PREFIX REWRITE SYSTEMS; PROCESS ALGEBRA; PUSHDOWN AUTOMATA;

COMPUTABILITY AND DECIDABILITY;

EID: 40549093619     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1326554.1326559     Document Type: Article

References (44)

1. BAETEN, J., BERGSTRA, J., AND KLOP, J. 1993. Decidability of bisimulation equivalence for processes generating context-free languages. J. ACM 40, 3, 653-682.
2. BAETEN, J., AND WEIJLAND, W. 1990. Process Algebra. Number 18 in Cambridge Tracts in Theoretical. Computer Science. Cambridge University Press.
3. BALCAZAR, J., GABARRO, J., AND SANTHA, M. 1992. Deciding bisimilarity is P-complete. Formal Asp. Comput. 4, 6A, 638-648.
4. BOUAJJANI, A., ESPARZA, J., AND MALER, O. 1997. Reachability analysis of pushdown, automata: Application to model-checking. In Proceedings of the 8th International Conference on Concurrency Theory (CONCUR'97). Lecture Notes in Computer Science, vol. 1243. Springer-Verlag, New York, 135-150.
5. BÜCHI, J. 1964. Regular canonical systems. Arch. Math. Logik u. Grundlagenforschung 6, 91-111.
6. BURKART, O., CAUCAL, D., MOLLER, F., AND STEFFEN, B. 2001. Verification on infinite structures. In Handbook of Process Algebra, J. Bergstra, A. Ponse, and S. Smolka, Eds. Elsevier Science, Amsterdam, The Netherlands, Chapter 9, 545-623.
7. BURKART, O., CAUCAL, D., AND STEFFEN, B. 1995. An elementary decision procedure for arbitrary context-free processes. In Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science (MFCS'95). Lecture Notes in Computer Science, vol. 969. Springer-Verlag, New York, 423-433.
8. BURKART, O., AND ESPARZA, J. 1997. More infinite results. Bull. Europ. Assoc. Theor. Comput. Sci. 62, 138-159. Columns: Concurrency.
9. CACHAT, T. 2002. Uniform solution of parity games on prefix-recognizable graphs. Electron. Notes Theoret. Comput. Sci. 68, 6, 71-84.
10. CAUCAL, D. 1992. On the regular structure of prefix rewriting. Theoret. Comput. Sci. 106, 1, 61-86.
11. CAUCAL, D. 1995. Bisimulation of context-free grammars and of pushdown automata. In Modal Logic and Process Algebra. CSLI Lectures Notes, vol. 53. University of Chicago Press, 85-106.
12. CAUCAL, D. 1996. On infinite transition graphs having a decidable monadic theory. In Proceedings of the 23th International Colloquium on Automata, Languages and Programming (ICALP'96). Lecture Notes in Computer Science, Vol. 1099. Springer-Verlag, New York, 194-205.
13. CHRISTENSEN, S., HÜTTEL, H., AND STIRLING, C. 1995. Bisimulation equivalence is decidable for all context-free processes. Inf. Comput. 121, 143-148.
14. ESPARZA, J., HANSEL, D., ROSSMANTIH, P., AND SCHWOON, S. 2000. Efficient algorithms for model checking pushdown, systems. In Proceedings of the 12th International Conference on Computer Aided Verification (CAV'00). Lecture Notes in Computer Science, vol. 1855. Springer-Verlag, New York, 232-247.
15. HAREL, D. 1986. Effective transformations on infinite trees, with applications to high undecidability, dominoes, and fairness. J. ACM 33, 1, 224-248.
16. HENNESSY, M., AND MILNER, R. 1985. Algebraic laws for nondeterminism and concurrency. J. ACM 32, 1, 137-161.
17. HIRSHFELD, Y., AND JERRUM, M. 1999. Bisimulation equivalence is decidable for normed process algebra. In Proceedings of 26th International Colloquium on Automata, Languages and Programming (ICALP'99). Lecture Notes in Computer Science, vol. 1644. Springer-Verlag, New York, 412-421.
18. HIRSHFELD, Y., JERRUM, M., AND MOLLER, F. 1996. A polynomial algorithm for deciding bisimilarity of normed context-free processes. Theoret. Comput. Sci. 158, 1-2, 143-159.
19. JANČAR, P. 1995a. High undecidability of weak bisimilarity for Petri nets. In Proceedings of Colloquium on Trees in Algebra and Programming (CAAP'95). Lecture Notes in Computer Science, vol. 915. Springer-Verlag, New York, 349-363.
20. JANČAR, P. 1995b. Undecidability of bisimilarity for Petri, nets and some related, problems. Theoret. Comput. Sci. 148, 2, 281-301.
21. JANČAR, P., AND SRBA, J. 2006. Undecidability results for bisimilarity on prefix rewrite systems. Tech. Rep. RS-06-7, BRICS Research Series.
22. KANELLAKIS, P., AND SMOLKA, S. 1990. CCS expressions, finite state processes, and three problems of equivalence. Inf. Comput. 86, 1, 43-68.
23. KUČERA, A., AND JANČAR, P. 2006. Equivalence-checking on infinite-state systems: Techniques and results. Theory Pract. Logic Prog. 6, 3, 227-264.
24. KUČERA, A., AND MAYR, R. 2002. On the complexity of semantic equivalences for pushdown automata and BPA. In Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science (MFCS'02). Lecture Notes in Computer Science, vol. 2420. Springer-Verlag, New York, 433-445.
25. MAYR, R. 2000. Process rewrite systems. Inf. Comput. 156, 1, 264-286.
26. MILNER, R. 1989. Communication and Concurrency. Prentice-Hall, Englewood Cliffs, NJ.
27. MOLLER, F. 1996. Infinite results. In Proceedings of the 7th International Conference on Concurrency Theory (CONCUR'96). Lecture Notes in. Computer Science, vol. 1119. Springer-Verlag, New York, 195-216.
28. PAIGE, R., AND TARJAN, R. 1987. Three partition refinement algorithms. SIAM J. Comput. 16, 6, 973-989.
29. PARK, D. 1981. Concurrency and automata on. infinite sequences. In Proceedings of the 5th GI Conference. Lecture Notes in Computer Science, vol. 104. Springer-Verlag, New York, 167-183.
30. PETRI, C. 1962. Kommunikation mit automaten. Ph.D. dissertation, Darmstadt.
31. RUOHONEN, K. 1985. Reversible machines and Post's correspondence problem for biprefix morphisms. Elektronische Informationsverarbeitung und Kybernetik 21, 12, 579-595.
32. SĚNIZERGUES, G. 1998. Decidability of bisimulation equivalence for equational. graphs of finite out-degree. In Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS' 98). IEEE Computer Society Press, Los Alamitos, CA, 120-129.
33. SĚNIZERGUES, G. 2001. L(A)=L(B)? Decidability results from complete formal systems. Theoret. Comput. Sci. 251, 1-2, 1-166.
34. SĚNIZERGUES, G. 2005. The bisimulation problem for equational graphs of finite out-degree. SIAM J. Comput. 34, 5, 1025-1106.
35. SIPSER, M. 2005. Introduction to the Theory of Computation, 2nd ed. Course Technology.
36. SRBA, J. 2002. Strong bisimilarity and regularity of basic process algebra is PSPACE-hard. In Proceedings of the 29th International Colloquium on Automata, Languages and Programming (ICALP'02). Lecture Notes in. Computer Science, vol. 2380. Springer-Verlag, New York, 716-727.
37. SRBA, J. 2004. Roadmap of Infinite results. Vol. 2: Formal Models and Semantics. World Scientific Publishing Co. (Updated version can. be downloaded from the author's home-page).
38. STIRLING, C. 1995. Local model checking games. In Proceedings of the 6th International Conference on Concurrency Theory (CONCUR'95). Lecture Notes in Computer Science, vol. 962. Springer-Verlag, New York, 1-1.1.
39. STIRLING, C. 1996. Decidability of bisimulation equivalence for normed pushdown, processes. In Proceedings of the 7th International Conference on Concurrency Theory (CONCUR'96). Lecture Notes in Computer Science, vol. 1119. Springer-Verlag, New York, 217-232.
40. STIRLING, C. 1998. Decidability of bisimulation equivalence for normed pushdown processes. Theoret. Comput. Sci. 195, 2, 113-131.
41. STIRLING, C. 2000. Decidability of bisimulation equivalence for pushdown, processes. Research Report EDI-INF-RR-0005, School of Informatics, Edinburgh University. Jan. (The latest version is downloadable from the author's home-page.)
42. STIRLING, C. 2001. Decidability of DPDA equivalence. Theoret. Comput. Sci. 255, 1-2, 1-31.
43. STIRLING, C. 2003. Bisimulation and language equivalence. In Logic for Concurrency and Synchronisation. Trends in Logic, vol. 18. Kluwer Academic Publishers, 269-284.
44. THOMAS, W. 1993. On the Ehrenfeucht-Fraïssé game in theoretical computer science (extended abstract). In Proceedings of the 4th International Joint Conference CAAPIFASE, Theory and Practice of Software Development (TAPSOFT' 93). Lecture Notes in Computer Science, vol. 668. Springer-Verlag, New York, 559-568.