Concurrent LSC Verification: On Decomposition Properties of Partially Ordered Symbolic Automata

Abstract

Partially Ordered Symbolic Automata (POSAs) are used as the semantical foundation of visual formalisms like the scenario based language of Live Sequence Charts (LSCs). To check whether a model satisfies an LSC requirement, the LSC's POSA can be composed in parallel to the model as an observer automaton or it can be translated to a CTL or LTL formula. Thus by the well-known complexity properties of CTL and LTL model-checking, the size of an LSC's POSA directly contributes to the runtime of the model-checking task. The size grows with the concurrency allowed by the LSC, e.g. when the observation order of LSC elements is relaxed by enclosing the elements in a coregion. We investigate decomposition properties of POSAs with deterministic states, i.e. states with disjointly annotated outgoing transitions. We devise a procedure to decompose a POSA with deterministic states into a set of POSAs whose intersection language is equal to the language of the original POSA. When decomposing at dominating states, the obtained POSAs are strictly smaller. As the majority of states in POSAs obtained for LSCs are deterministic and dominating, model-checking of LSCs can effectively be distributed.