Abstract
We show that CTL with knowledge modalities but without common knowledge has an undecidable satisfiability problem in the synchronous perfect recall semantics. We also present an adaptation of the classical model-checking algorithm for CTL that handles knowledge operators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions of Programming Languages and Systems 8(2), 244–263 (1986)
Dickhöfer, M., Wilke, T.: Timed alternating tree automata: The automata-theoretic solution to the TCTL model checking problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 281–290. Springer, Heidelberg (1999)
Elgaard, J., Klarlund, N., Møller, A.: Mona 1.x: New techniques for ws1s and ws2s. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 516–520. Springer, Heidelberg (1998)
Elgot, C.C., Rabin, M.O.: Decidability and undecidability of extensions of second (first) order theory of (generalized) successor. Journal of Symbolic Logic 31(2), 169–181 (1966)
Fagin, R., Halpern, J., Vardi, M.: Reasoning about knowledge. The MIT Press, Cambridge (2004)
Halpern, J.Y., Vardi, M.Y.: The complexity of reasoning about knowledge and time: Extended abstract. In: Proceedings of STOC 1986, pp. 304–315 (1986), https://www.cs.rice.edu/~vardi/papers/stoc86r1.pdf.gz
Halpern, J.Y., Vardi, M.Y.: The complexity of reasoning about knowledge and time. I. Lower bounds. Journal of Computer System Sciences 38(1), 195–237 (1989)
Kacprzak, M., Lomuscio, A., Niewiadomski, A., Penczek, W., Raimondi, F., Szreter, M.: Comparing BDD and SAT based techniques for model checking Chaum’s Dining Cryptographers Protocol. Fundamenta Informaticae 72(1-3), 215–234 (2006)
Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Lomuscio, A., Raimondi, F.: The complexity of model checking concurrent programs against CTLK specifications. In: Baldoni, M., Endriss, U. (eds.) DALT 2006. LNCS, vol. 4327, pp. 29–42. Springer, Heidelberg (2006)
Raimondi, F., Lomuscio, A.: Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams. Journal of Applied Logic 5(2), 235–251 (2005)
Shilov, N.V., Garanina, N.O.: Model checking knowledge and fixpoints. In: Proceedings of FICS 2002, Extended version available as Preprint 98, pp. 25–39. Ershov Institute of Informatics, Novosibirsk (2002)
Thomas, W.: Infinite trees and automaton-definable relations over ω-words. Theoretical Computer Science 103(1), 143–159 (1992)
van Benthem, J., Pacuit, E.: The tree of knowledge in action: Towards a common perspective. In: Governatori, G., Hodkinson, I.M., Venema, Y. (eds.) Proceedings of AiML 2006, pp. 87–106. College Publications (2006)
van der Meyden, R.: Common knowledge and update in finite environments. Information and Computation 140(2), 115–157 (1998)
van der Meyden, R., Shilov, N.V.: Model checking knowledge and time in systems with perfect recall (extended abstract). In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 432–445. Springer, Heidelberg (1999)
van der Meyden, R., Su, K.: Symbolic model checking the knowledge of the dining cryptographers. In: Proceedings of the 17th IEEE Computer Security Foundations Workshop (CSFW-17 2004), p. 280. IEEE Computer Society Press, Los Alamitos (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dima, C. (2009). Revisiting Satisfiability and Model-Checking for CTLK with Synchrony and Perfect Recall. In: Fisher, M., Sadri, F., Thielscher, M. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2008. Lecture Notes in Computer Science(), vol 5405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02734-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-02734-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02733-8
Online ISBN: 978-3-642-02734-5
eBook Packages: Computer ScienceComputer Science (R0)