Abstract
We show that the regularity and equivalence problems are decidable for deterministic weak pushdown ω-automata, giving a partial answer to a question raised by Cohen and Gold in 1978. We prove the decidability by a reduction to the corresponding problems for deterministic pushdown automata on finite words. Furthermore, we consider the problem of deciding for pushdown games whether a winning strategy exists that can be implemented by a finite automaton. We show that this problem is already undecidable for games defined by one-counter automata or visibly pushdown automata with a safety condition.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC, pp. 202–211 (2004)
Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)
Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the AMS 138, 295–311 (1969)
Cachat, T.: Symbolic Strategy Synthesis for Games on Pushdown Graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 704–715. Springer, Heidelberg (2002)
Chandra, A.K., Kozen, D., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)
Cohen, R.S., Gold, A.Y.: Omega-computations on deterministic pushdown machines. JCSS 16(3), 275–300 (1978)
Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient Algorithms for Model Checking Pushdown Systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000)
Hague, M., Ong, C.-H.L.: Winning Regions of Pushdown Parity Games: A Saturation Method. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 384–398. Springer, Heidelberg (2009)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)
Löding, C.: Efficient minimization of deterministic weak omega-automata. Information Processing Letters 79(3), 105–109 (2001)
Perrin, D., Pin, J.-É.: Infinite words. Pure and Applied Mathematics, vol. 141. Elsevier (2004)
Segoufin, L., Sirangelo, C.: Constant-Memory Validation of Streaming XML Documents Against DTDs. In: Schwentick, T., Suciu, D. (eds.) ICDT 2007. LNCS, vol. 4353, pp. 299–313. Springer, Heidelberg (2006)
Segoufin, L., Vianu, V.: Validating streaming XML documents. In: PODS, pp. 53–64 (2002)
Sénizergues, G.: L(A)=L(B)? decidability results from complete formal systems. Theor. Comput. Sci. 251(1-2), 1–166 (2001)
Staiger, L.: Finite-state ω-languages. JCSS 27(3), 434–448 (1983)
Stearns, R.E.: A regularity test for pushdown machines. Information and Control 11(3), 323–340 (1967)
Straubing, H.: Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Basel (1994)
Valiant, L.G.: Regularity and related problems for deterministic pushdown automata. J. ACM 22(1), 1–10 (1975)
Walukiewicz, I.: Pushdown processes: Games and model checking. Information and Computation 164(2), 234–263 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Löding, C., Repke, S. (2012). Regularity Problems for Weak Pushdown ω-Automata and Games. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_66
Download citation
DOI: https://doi.org/10.1007/978-3-642-32589-2_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32588-5
Online ISBN: 978-3-642-32589-2
eBook Packages: Computer ScienceComputer Science (R0)