Symbolic Model Checking of Concurrent Probabilistic Systems Using MTBDDs and the Simplex Algorithm

Symbolic model checking for purely probabilistic processes using MTB-DDs 12] was introduced in 4] and further developed in 20, 3]. In this paper we consider models for concurrent probabilistic systems similar to those of 28, 7, 5] and the concurrent Markov chains of 35, 13], which extend the purely probabilistic processes through the addition of nondeterministic choice. As a speciication formalism we use the probabilistic branching-time temporal logic PBTL of 5, 7], which allows us to express properties such as \under any scheduling of nondeterministic choices, the probability of holding until is true is at least 0.78". In 5, 7] it is shown that the veriication of \until" properties can be reduced to a linear programming problem and solved with the help of e.g. the simplex algorithm, but no symbolic model checking is considered. Based on the algorithms of 5, 7], we derive symbolic model checking procedure for PBTL over concurrent probabilistic systems using MTBDDs, and extend it with fairness constraints. We furthermore implement an experimental model checker using the Colorado University Decision Diagram (CUDD) package 32]. Our key contribution is an implementation of the simplex algorithm in terms of MTBDDs.