Abstract
The two central decision problems that arise during the design of safety critical systems are the satisfiability and the model checking problem. While model checking can only be applied after implementing the system, satisfiability checking answers the question whether a system that satisfies the specification exists. Model checking is traditionally considered to be the simpler problem – for branching-time and fixed point logics such as CTL, CTL*, ATL, and the classical and alternating time μ-calculus, the complexity of satisfiability checking is considerably higher than the model checking complexity. We show that ATL* is a notable exception of this rule: Both ATL* model checking and ATL* satisfiability checking are 2EXPTIME-complete.
This work was partly supported by the German Research Foundation (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).
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
Wolper, P.: Synthesis of Communicating Processes from Temporal-Logic Specifications. PhD thesis, Stanford University (1982)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Proc. IBM Workshop on Logics of Programs, pp. 52–71. Springer, Heidelberg (1981)
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49, 672–713 (2002)
Emerson, E.A.: Temporal and modal logic, pp. 995–1072. MIT Press, Cambridge (1990)
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. Transactions On Programming Languages and Systems 8, 244–263 (1986)
Kupferman, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. Journal of the ACM 47, 312–360 (2000)
Walther, D., Lutz, C., Wolter, F., Wooldridge, M.: Atl satisfiability is indeed exptime-complete. Journal of Logic and Computation 16, 765–787 (2006)
Kremer, S., Raskin, J.F.: A game-based verification of non-repudiation and fair exchange protocols. Journal of Computer Security 11, 399–430 (2003)
Schewe, S., Finkbeiner, B.: Satisfiability and finite model property for the alternating-time μ-calculus. In: Proc. CSL, pp. 591–605. Springer, Heidelberg (2006)
Even, S., Yacobi, Y.: Relations among public key signature systems. Technical Report 175, Technion, Haifa, Israel (1980)
de Alfaro, L., Henzinger, T.A., Majumdar, R.: From verification to control: Dynamic programs for omega-regular objectives. In: Proc. LICS, pp. 279–290. IEEE Computer Society Press, Los Alamitos (2001)
van Drimmelen, G.: Satisfiability in alternating-time temporal logic. In: Proc. LICS, pp. 208–217. IEEE Computer Society Press, Los Alamitos (2003)
Wilke, T.: Alternating tree automata, parity games, and modal μ-calculus. Bull. Soc. Math. Belg. 8 (2001)
Kupferman, O., Vardi, M.Y.: Church’s problem revisited. The bulletin of Symbolic Logic 5, 245–263 (1999)
Wilke, T.: CTL + is exponentially more succinct than CTL. In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 110–121. Springer, Heidelberg (1999)
Kupferman, O., Vardi, M.: Safraless decision procedures. In: Proc. 46th IEEE Symp. on Foundations of Computer Science, Pittsburgh, pp. 531–540 (2005)
Kupferman, O., Piterman, N., Vardi, M.Y.: Safraless compositional synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006)
Schewe, S., Finkbeiner, B.: Bounded synthesis. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 474–488. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schewe, S. (2008). ATL* Satisfiability Is 2EXPTIME-Complete. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-70583-3_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70582-6
Online ISBN: 978-3-540-70583-3
eBook Packages: Computer ScienceComputer Science (R0)