Abstract
Probabilistic model checkers like PRISM check the satisfiability of probabilistic CTL (pCTL) formulas against discrete-time Markov chains. We prove soundness and completeness of their underlying algorithm in Isabelle/HOL. We define Markov chains given by a transition matrix and formalize the corresponding probability measure on sets of paths. The formalization of pCTL formulas includes unbounded cumulated rewards.
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Hölzl, J., Nipkow, T. (2012). Verifying pCTL Model Checking. In: Flanagan, C., König, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2012. Lecture Notes in Computer Science, vol 7214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28756-5_24
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