Abstract
In this survey we motivate, define and explain model checking of probabilistic deterministic and nondeterministic systems using the probabilistic computation tree logics PCTL and PCTL *. Juxtapositions to non-deterministic computation tree logic are made and algorithms are presented.
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References
Alur, Dill: A theory of timed automata. Theoretical Computer Science, 183–235 (1994)
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking for probabilistic real-time systems (extended abstract). In: Albert, J.L., Monien, B., Rodríguez-Artalejo, M. (eds.) Automata, Languages and Programming, 18th International Colloquium. LNCS, vol. 510, pp. 115–126. Springer, Heidelberg (1991)
Aziz, A., Singhal, V., Balarin, F., Brayton, R.K.: CAV 1995. LNCS, vol. 939, pp. 155–165. Springer, Heidelberg (1995)
Baier, C.: On algorithmic verification methods for probabilistic systems, Habilitation thesis (November 1998)
Baier, C., Katoen, J.-P., Hermanns, H.: Approximate symbolic model checking of continuous-time markov chains. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 146–161. Springer, Heidelberg (1999)
Baier, C., Clarke, E.M., Hartonas-Garmhausen, V., Kwiatkowska, M.Z., Ryan, M.: Symbolic model checking for probabilistic processes. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 430–440. Springer, Heidelberg (1997)
Beauquier, Slissenko: Polytime model checking for timed probabilistic computation tree logic. Acta Informatica 35, 645–664 (1998)
Beauquier, D., Slissenko, A.: Polytime model checking for timed probabilistic computation tree logic. Acta Informatica 35(8), 645–664 (1998)
Bianco, A., De Alfaro, L.: FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing, 11 (1998)
Clarke, E.M., Allen Emerson, E., Sistla, A.P.: Automatic verification of finite state concurrent systems using temporal logic specifications: A practical approach. ACM Transactions on Programming Languages and Systems 8(2), 244–263 (1986)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)
Courcoubetis, C., Yannakakis, M.: Verifying temporal properties of finite-state probabilistic programs. In: 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, October 24–26, pp. 338–345. IEEE, Los Alamitos (1988)
Courcoubetis, C., Yannakakis, M.: Markov decision processes and regular events (extended abstract). In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 336–349. Springer, Heidelberg (1990)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
D’Argenio, P.R., Jeannet, B., Jensen, H.E., Larsen, K.G.: Reduction and refinement strategies for probabilistic analysis. In: Hermanns, H., Segala, R. (eds.) Proceedings of Process Algebra and Probabilistic Methods. Performance Modeling and Verification. Joint International Workshop, PAPM-PROBMIV 2001, Copenhagen, Denmark. LNCS, Springer, Heidelberg (2001)
De Alfaro, L.: Temporal logics for the specification of performance and reliability. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 165–176. Springer, Heidelberg (1997)
de Alfaro, L.: Formal verification of probabilistic systems. Thesis CS-TR-98- 1601, Stanford University, Department of Computer Science, June 1998.
Emerson, Mok, Sistla, Srinivasan: Quantitative temporal reasoning. Journal of Real Time System, 331–352 (1992)
Emerson, E.A., Halpern, J.Y.: ‘Sometimes’ and ‘not never’ revisited: on branching time versus linear time temporal logic. Journal of the ACM 33(1), 151–178 (1986)
Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 995–1072. Elsevier Science Publishers, Amsterdam (1990)
Feller, W.: An Intro. to Probability Theory and its application. John Wiley and Sons, New York (1968)
Hansson, H.: Time and Probability in Formal Design of Distributed Systems. In: Series in Real-Time Safety Critical Systems. Elsevier, Amsterdam (1994)
Hansson, H., Jonsson, B.: A calculus for communicating systems with time and probabitilies. In: IEEE Computer Society Press (ed.) Proceedings of the Real- Time Systems Symposium - 1990, Lake Buena Vista, Florida, USA, pp. 278–287. IEEE Computer Society Press, Los Alamitos (1990)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)
Hansson, H.A.: Time and probability in formal design of distributed systems. SICS Dissertation Series 05, Swedish Institute of Computer Science, Box 1263, S-164 28 Kista, Sweden (1994)
Hart, S., Sharir, M., Pnueli, A.: Termination of probabilistic concurrent programs. ACM Transactions on Programming Languages and Systems (TOPLAS) 5(3), 356–380 (1983)
Jagadeesan, R., Desharnais, J., Gupta, V., Panangaden, P.: Weak bisimulation is sound and complete for PCTL*. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 355–370. Springer, Heidelberg (2002)
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proceedings, Sixth Annual IEEE Symposium on Logic in Computer Science, Amsterdam, The Netherlands, July15–18, pp. 266–277. IEEE Computer Society Press, Los Alamitos (1991)
Jou, C.-C., Smolka, S.A.: Equivalences, congruences, and complete axiomatizations for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 367–383. Springer, Heidelberg (1990)
Larsen, K., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94, 1–28 (1991)
Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Princeton University Press, Princeton (1960)
Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 75–95. Springer, Heidelberg (1999)
Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Verifying quantitative properties of continuous probabilistic timed automata. LNCS, vol. 1877. Springer, Heidelberg (2000)
Kwiatkowska, M., Norman, G., Sproston, J.: Probabilistic model checking of the IEEE 802.11 wireless local area network protocol. In: Hermanns, H., Segala, R. (eds.) PROBMIV 2002, PAPM-PROBMIV 2002, and PAPM 2002. LNCS, vol. 2399, pp. 169–187. Springer, Heidelberg (2002)
Kwiatkowska, M.Z., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Computer Performance Evaluation / TOOLS, pp. 200–204 (2002)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems. Springer, New York (1992)
McMillan, K.L.: Symbolic Model Checking. PhD thesis, Carnegie Mellon University, Pittsburgh (1993)
Pnueli, A., Zuck, L.: Verification of multiprocess probabilistic protocols. Distributed Computing 1, 53–72 (1986)
Pnueli, A., Zuck, L.: Probabilistic verification by tableaux. In Proceedings. In: Symposium on Logic in Computer Science, Cambridge, Massachusetts, June 16–18, pp. 322–331. IEEE Computer Society, Los Alamitos (1986)
Pnueli, A., Zuck, L.D.: Probabilistic verification. Information and Computation 103(1), 1–29 (1993)
Puterman, M.L.: Markov Decision Processes—Discrete Stochastic Dynamic Programming. John Wiley & Sons, Inc., New York (1994)
Safra, S.: On the complexity of ω-automata. In: 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, October 24–26 1988, pp. 319–327. IEEE, Los Alamitos (1988)
R. Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (June 1995); Available as Technical Report MIT/LCS/TR-676
Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. LNCS, vol. 836, pp. 481–496. Springer, Heidelberg (1994)
Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (Summer 1995)
Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. 4, pp. 133–191. Elsevier Science Publishers B.V., Amsterdam (1990)
Campos, S., Hartonas-Garmhausen, V., Clarke, E.: Probverus: Probabilistic symbolic model checking. LNCS, vol. 1601, pp. 96–110. Springer, Heidelberg (1999)
Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: 26th Annual Symposium on Foundations of Computer Science, Los Angeles, Ca., USA, October 1985, pp. 327–338. IEEE Computer Society Press, Los Alamitos (1985)
Vardi, M.Y.: Probabilistic linear-time model checking: An overview of the automata-theoretic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 265–276. Springer, Heidelberg (1999)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Proceedings, Symposium on Logic in Computer Science, Cambridge, Massachusetts, June 16–18, pp. 332–344. IEEE Computer Society, Los Alamitos (1986)
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Ciesinski, F., Größer, M. (2004). On Probabilistic Computation Tree Logic. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, JP., Siegle, M. (eds) Validation of Stochastic Systems. Lecture Notes in Computer Science, vol 2925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24611-4_5
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DOI: https://doi.org/10.1007/978-3-540-24611-4_5
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