Abstract
All bisimulation problems for pushdown automata are at least PSPACE-hard. In particular, we show that (1) Weak bisimilarity of pushdown automata and finite automata is PSPACE-hard, even for a small fixed finite automaton, (2) Strong bisimilarity of pushdown automata and finite automata is PSPACE-hard, but polynomial for every fixed finite automaton, (3) Regularity (finiteness) of pushdown automata w.r.t. weak and strong bisimilarity is PSPACE-hard.
Chapter PDF
Similar content being viewed by others
References
J.C.M. Baeten and W.P. Weijland. Process algebra. Cambridge Tracts in Theoretical Computer Science, 18, 1990.
J. Balcazar, J. Gabarro, and M. Santha. Deciding bisimilarity is P-complete. Formal Aspects of Computing, 4:638–648, 1992.
A. Bouajjani, J. Esparza, and O. Maler. Reachability analysis of pushdown automata: application to model checking. In International Conference on Concurrency Theory (CONCUR’97), volume 1243 of LNCS. Springer Verlag, 1997.
O. Burkart, D. Caucal, and B. Steffen. An elementary bisimulation decision procedure for arbitrary context-free processes. In MFCS’95, volume 969 of LNCS. Springer Verlag, 1995.
O. Burkart, D. Caucal, and B. Steffen. Bisimulation collapse and the process taxonomy. In U. Montanari and V. Sassone, editors, Proceedings of CONCUR’96, volume 1119 of LNCS. Springer Verlag, 1996.
D. Caucal. On the regular structure of prefix rewriting. Journal of Theoretical Computer Science, 106:61–86, 1992.
S. Christensen, Y. Hirshfeld, and F. Moller. Bisimulation equivalence is decidable for Basic Parallel Processes. In E. Best, editor, Proceedings of CONCUR 93, volume 715 of LNCS. Springer Verlag, 1993.
Y. Hirshfeld and M. Jerrum. Bisimulation equivalence is decidable for normed process algebra. In Proc. of ICALP’99, volume 1644 of LNCS. Springer Verlag, 1999.
Y. Hirshfeld, M. Jerrum, and F. Moller. A polynomial algorithm for deciding bisimilarity of normed context-free processes. Theoretical Computer Science, 158:143–159, 1996.
Y. Hirshfeld, M. Jerrum, and F. Moller. A polynomial-time algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes. Journal of Mathematical Structures in Computer Science, 6:251–259, 1996.
J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison Wesley, 1979.
P. Jančar. Undecidability of bisimilarity for Petri nets and some related problems. Theoretical Computer Science, 148:281–301, 1995.
P. Jančar and J. Esparza. Deciding finiteness of Petri nets up to bisimulation. In F. Meyer auf der Heide and B. Monien, editors, Proceedings of ICALP’96, volume 1099 of LNCS. Springer Verlag, 1996.
P. Jančar, A. Kučera, and R. Mayr. Deciding bisimulation-like equivalences with finite-state processes. In Proc. of ICALP’98, volume 1443 of LNCS. Springer Verlag, 1998.
P. Jančar and F. Moller. Checking regular properties of Petri nets. In Insup Lee and Scott A. Smolka, editors, Proceedings of CONCUR’95, volume 962 of LNCS. Springer Verlag, 1995.
A. Kučera. Regularity is decidable for normed PA processes in polynomial time. In Foundations of Software Technology and Theoretical Computer Science (FST&TCS’96), volume 1180 of LNCS, Springer Verlag, 1996.
A. Kučera and R. Mayr. Weak bisimilarity with infinite-state systems can be decided in polynomial time. In Proc. of CONCUR’99, volume 1664 of LNCS. Springer Verlag, 1999.
R. Lipton. The reachability problem requires exponential space. Technical Report 62, Department of Computer Science, Yale University, January 1976.
R. Mayr. On the complexity of bisimulation problems for Basic Parallel Processes. In Proc. of ICALP’2000, volume ? of LNCS.Springer Verlag, 2000.
R. Mayr. Process rewrite systems. Information and Computation, 156(1):264–286, 2000.
R. Milner. Communication and Concurrency. Prentice Hall, 1989.
F. Moller. Infinite results. In Ugo Montanari and Vladimiro Sassone, editors, Proceedings of CONCUR’96, volume 1119 of LNCS. Springer Verlag, 1996.
M. Oyamaguchi, N. Honda, and Y. Inagaki. The equivalence problem for real-time strict deterministic languages. Information and Control, 45:90–115, 1980.
R. Paige and R. Tarjan. Three partition refinement algorithms. SIAM Journal of Computing, 16(6):973–989, 1987.
J.L. Peterson. Petri net theory and the modeling of systems. Prentice-Hall, 1981.
G. Sénizergues. The Equivalence Problem for Deterministic Pushdown Automata is Decidable. In Proceedings of ICALP’97, volume 1256 of LNCS, pages 671–681. Springer Verlag, 1997.
G. Sénizergues. Decidability of bisimulation equivalence for equational graphs of finite out-degree. In Proc. of FOCS’98. IEEE, 1998.
J. Stříbrná. Hardness results for weak bisimilarity of simple process algebras. Electronic Notes in Theoretical Computer Science (ENTCS), 18, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mayr, R. (2000). On the Complexity of Bisimulation Problems for Pushdown Automata. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds) Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. TCS 2000. Lecture Notes in Computer Science, vol 1872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44929-9_33
Download citation
DOI: https://doi.org/10.1007/3-540-44929-9_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67823-6
Online ISBN: 978-3-540-44929-4
eBook Packages: Springer Book Archive