Abstract
In this paper we introduce recursive probabilistic computation-tree logic as a restriction of \({\mu }{{\textsc {pctl}}}\). We introduce the logic in detail and show its usefulness for verifying systems. We illustrate this by means of some examples. Roughly speaking, we include recursive operators within pctl, which enable one to identify repeating patterns of probability. This new feature seems in particular useful for expressing properties regarding stability of system executions; such properties are usual, for instance, in those scenarios where one is interested to verify whether the system under verification stays in, or revisits, a subset of safe states. Also, the logic makes it possible to reason about set of executions with zero measure; something no possible in related logics.
This work was partially supported by FP7-PEOPLE-IRESES-2011 MEALS project, EPSRC EP/L007177/1 project, PICT 2013-0080 project and PICT 2012-1298 project.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We note that this extension is orthogonal to the power added by \({\textsc {pctl}}^*\), or other mechanisms for describing regular path properties.
References
Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: a tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Ciesinski, F., Baier, C.: LiQuor: a tool for qualitative and quantitative linear time analysis of reactive systems. In: QEST, pp. 131–132. IEEE Computer Society (2006)
Eisner, C., Fisman, D.: A Practical Introduction to PSL. Springer, New York (2006)
Cohen, B., Venkataramanan, S., Kumari, A., Piper, L.: System Verilog Assertions Handbook. VhdlCohen Publishing (2010)
Armoni, R., Fix, L., Flaisher, A., Gerth, R., Ginsburg, B., Kanza, T., Landver, A., Mador-Haim, S., et al.: The ForSpec temporal logic: a new temporal property-specification language. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, p. 296. Springer, Heidelberg (2002)
Eisner, C., Fisman, D., Havlicek, J., McIsaac, A., Campenhout, D.V.: The definition of a temporal clock operator. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 857–870. Springer, Heidelberg (2003)
Mio, M.: Game Semantics for Probabilistic \(\mu \)-Calculi. Ph.D. thesis, University of Edinburgh (2012)
Castro, P.F., Kilmurray, C., Piterman, N.: Tractable probabilistic \(\mu \)-calculus that expresses probabilistic temporal logics. In: 32nd International Symposium on Theoretical Aspects of Computer Science. LIPIcs, Garching, Germany, pp. 211–223 (2015)
Huth, M., Piterman, N., Wagner, D.: p-automata: new foundations for discrete-time probabilistic verification. Perform. Eval. 69, 356–378 (2012)
Arora, A., Gouda, M.: Closure and convergence: a foundation of fault-tolerant computing. TOSEM 19, 1015–1027 (1993)
Attie, P., Arora, A., Emerson, A.: Synthesis of fault-tolerant concurrent programs. TOPLAS 26, 125–185 (2004)
Huth, M., Kwiatkowska, M.: Quantitative analysis and model checking. In: 12th IEEE Symposium on Logic in Computer Science, pp. 111–122. IEEE Computer Society (1997)
McIver, A., Morgan, C.: Results on the quantitative qm\(\mu \). ACM Trans. Comput. Log. 8 (2007)
Mio, M., Simpson, A.: Łukasiewicz \(\mu \)-calculus. In: FICS (2013)
Liu, W., Song, L., Wang, J., Zhang, L.: A simple probabilistic extension of model \(\mu \)-calculus. In: 23rd International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina. AAAI Press, pp. 882–888 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Castro, P.F., Kilmurray, C., Piterman, N. (2015). A Recursive Probabilistic Temporal Logic. In: Butler, M., Conchon, S., Zaïdi, F. (eds) Formal Methods and Software Engineering. ICFEM 2015. Lecture Notes in Computer Science(), vol 9407. Springer, Cham. https://doi.org/10.1007/978-3-319-25423-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-25423-4_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25422-7
Online ISBN: 978-3-319-25423-4
eBook Packages: Computer ScienceComputer Science (R0)