Verifying Randomized Distributed Algorithms with PRISM?

In this paper we describe our experience with model checking randomized distributed algorithms using PRISM, a symbolic model checker for concurrent probabilistic systems currently being developed. PRISM uses Multi-Terminal Binary Decision Diagrams (MTBDDs) as supplied by the CUDD package of Fabio Somenzi. Implemented in Java, PRISM has a system description language similar to Reactive Modules and supports model checking of probabilistic temporal logic PCTL (also under fairness constraints). Our experiments indicate that using the BDD variable ordering induced from the Kronecker representation yields very efficient MTBDD representations of randomized distributed algorithms. In particular, we are able to construct models of up to 10 states in seconds. Model checking of ‘with probability 1’ PCTL properties is also fast. The efficiency of numerical computation with MTBDDs, however, and hence also model checking of quantitative probabilistic temporal logic properties, is still considerably poorer than e.g. for sparse matrices. Descriptions and statistics obtained for several case studies can be found at http://www.cs.bham.ac.uk/~dxp/prism.