Abstract
We consider the model checking problem for interval Markov chains with open intervals. Interval Markov chains are generalizations of discrete time Markov chains where the transition probabilities are intervals, instead of constant values. We focus on the case where the intervals are open. At first sight, open intervals present technical challenges, as optimal (min, max) value for reachability may not exist. We show that, as far as model checking (and reachability) is concerned, open intervals does not cause any problem, and with minor modification existing algorithms can be used for model checking interval Markov chains against PCTL formulas.
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References
Baier, C., Katoen, J.-P.: Principles of Model Checking (Representation and Mind Series). The MIT Press (2008)
Bianco, A., De Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Caillaud, B., Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wasowski, A.: Constraint Markov chains. Theoretical Computer Science 412(34), 4373–4404 (2011)
Chatterjee, K., Henzinger, T., Sen, K.: Model-checking omega-regular properties of interval Markov chains. In: Amadio, R.M. (ed) Foundations of Software Science and Computation Structure (FoSSaCS) 2008, pp. 302–317, March 2008
Clarke Jr., E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42(4), 857–907 (1995)
Allen Emerson, E.: Temporal and modal logic. In: Handbook of Theoretical Computer Science (vol. b), pp. 995–1072. MIT Press, Cambridge (1990)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: LICS, pp. 266–277. IEEE Computer Society (1991)
Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals. part i: Introduction. preliminaries. the geometry of semi-algebraic sets. the decision problem for the existential theory of the reals. Journal of Symbolic Computation 13(3), 255–299 (1992)
Sen, K., Viswanathan, M., Agha, G.: Model-checking Markov Chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394–410. Springer, Heidelberg (2006)
Walley, P.: Measure of uncertainty in expert systems. Artificial Intelligence 83(1), 1–58 (1996)
Škulj, D.: Discrete time Markov Chains with interval probabilities. International Journal of Approximate Reasoning 50(8), 1314–1329 (2009). Special Section on Interval/Probabilistic Uncertainty
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Chakraborty, S., Katoen, JP. (2015). Model Checking of Open Interval Markov Chains. In: Gribaudo, M., Manini, D., Remke, A. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2015. Lecture Notes in Computer Science(), vol 9081. Springer, Cham. https://doi.org/10.1007/978-3-319-18579-8_3
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DOI: https://doi.org/10.1007/978-3-319-18579-8_3
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