Using Approximation for the Verification of Token-Scaling Models

Abstract

In the model checking domain, the state explosion problem is the core issue. The cause is usually the sheer size of the model or the cardinality of tokens in the initial state. For the latter, which we call token-scaling models, we propose an under-approximation for reachable states. The idea is to freeze tokens in the initial state (i.e. they are not used for firing transitions) and thus reducing the state space. If in the reduced state space a witness path is found, then the witness path can also be executed in the original state space. This method preserves existential temporal properties (ECTL$^*$) using a simulation relation between the reduced and the original state space. Since the cardinality of the initial marking varies from only a few tokens to multi-digit numbers of tokens, we apply heuristics to compute the number of tokens that should be frozen. We implemented the new method in the explicit model checker LoLA 2. The experiments, done on the model checking contest benchmark, show that this method can speed up the model checking process and verify additional queries.