Abstract
We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance be used to model real-time programs with procedure calls. It is long known that the reachability problem for this model is decidable. The goal of this paper is to identify subclasses of timed pushdown automata for which the language inclusion problem and related problems are decidable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdulla, P.A., Cerans, K.: Simulation is decidable for one-counter nets (extended abstract). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 253–268. Springer, Heidelberg (1998)
Abdulla, P.A., Deneux, J., Ouaknine, J., Quaas, K., Worrell, J.: Universality analysis for one-clock timed automata. Fundam. Inform. 89(4), 419–450 (2008)
Adams, S., Ouaknine, J., Worrell, J.B.: Undecidability of universality for timed automata with minimal resources. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 25–37. Springer, Heidelberg (2007)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Madhusudan, P.: Decision problems for timed automata: A survey. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 1–24. Springer, Heidelberg (2004)
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Babai, L. (ed.) STOC, pp. 202–211. ACM (2004)
Bouajjani, A., Echahed, R., Robbana, R.: On the automatic verification of systems with continuous variables and unbounded discrete data structures. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds.) Hybrid Systems II. LNCS, vol. 999, pp. 64–85. Springer, Heidelberg (1995)
Bouchy, F., Finkel, A., Sangnier, A.: Reachability in timed counter systems. Electr. Notes Theor. Comput. Sci. 239, 167–178 (2009)
Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 61–70. ACM (2010)
Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008)
Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound-constrained runs in weighted timed automata. Perform. Eval. 73, 91–109 (2014)
Brand, D., Zafiropulo, P.: On communicating finite-state machines. J. ACM 30(2), 323–342 (1983)
Brázdil, T., Jančar, P., Kučera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010)
Dang, Z.: Pushdown timed automata: a binary reachability characterization and safety verification. Theor. Comput. Sci. 302(1-3), 93–121 (2003)
Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3) (2009)
Demri, S., Lazić, R.S., Sangnier, A.: Model checking Freeze LTL over one-counter automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 490–504. Springer, Heidelberg (2008)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Amer. J. Math. 35, 413–422 (1913)
Emmi, M., Majumdar, R.: Decision problems for the verification of real-time software. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 200–211. Springer, Heidelberg (2006)
Ésik, Z., Fahrenberg, U., Legay, A., Quaas, K.: Kleene algebras and semimodules for energy problems. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 102–117. Springer, Heidelberg (2013)
Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy games in multiweighted automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 95–115. Springer, Heidelberg (2011)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)
Greibach, S.A.: An infinite hierarchy of context-free languages. J. ACM 16(1), 91–106 (1969)
Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 2, 236–366 (1952)
Hofman, P., Lasota, S., Mayr, R., Totzke, P.: Simulation over one-counter nets is PSPACE-complete. In: Seth, A., Vishnoi, N.K. (eds.) FSTTCS. LIPIcs, vol. 24, pp. 515–526. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)
Hofman, P., Totzke, P.: Trace inclusion for one-counter nets revisited. CoRR, abs/1404.5157 (2014)
Ibarra, O.H.: Restricted one-counter machines with undecidable universe problems. Mathematical Systems Theory 13, 181–186 (1979)
Jančar, P., Esparza, J., Moller, F.: Petri nets and regular processes. J. Comput. Syst. Sci. 59(3), 476–503 (1999)
Jančar, P., Kucera, A., Moller, F., Sawa, Z.: DP lower bounds for equivalence-checking and model-checking of one-counter automata. Inf. Comput. 188(1), 1–19 (2004)
Juhl, L., Guldstrand Larsen, K., Raskin, J.-F.: Optimal bounds for multiweighted and parametrised energy games. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) He Festschrift. LNCS, vol. 8051, pp. 244–255. Springer, Heidelberg (2013)
Information Sciences Institute of the University of Southern California. Transmission Control Protocoll (DARPA Internet Program Protocol Specification) (1981), http://www.faqs.org/rfcs/rfc793.html
Ouaknine, J., Worrell, J.: On the language inclusion problem for timed automata: Closing a decidability gap. In: LICS, pp. 54–63. IEEE Computer Society (2004)
Ouaknine, J., Worrell, J.: On the decidability of metric temporal logic. In: LICS, pp. 188–197. IEEE Computer Society (2005)
Ouaknine, J., Worrell, J.B.: On metric temporal logic and faulty turing machines. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 217–230. Springer, Heidelberg (2006)
Quaas, K.: On the interval-bound problem for weighted timed automata. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 452–464. Springer, Heidelberg (2011)
Quaas, K.: Model checking metric temporal logic over automata with one counter. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) LATA 2013. LNCS, vol. 7810, pp. 468–479. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Quaas, K. (2014). Verification for Timed Automata Extended with Unbounded Discrete Data Structures. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_35
Download citation
DOI: https://doi.org/10.1007/978-3-662-44584-6_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44583-9
Online ISBN: 978-3-662-44584-6
eBook Packages: Computer ScienceComputer Science (R0)