Symbolic Veri cation With Gap-Order Constraints

Finite state automata with counters are useful for modeling systems with discrete parameters. The calculation of state invariants is an important tool in the analysis of such systems. Previous authors have presented techniques for the calculation of state invariants based on their approximation by convex polyhedra or periodic sets. In this paper we present a new method for the calculation of invariants for nite state automata with counters, based on their representation by gap-order constraints. This method diiers from previous approaches by exploiting existing techniques for the calculation of least xed points. The use of least xed points reduces the need for approximation and allows the generation of non-convex invariants. We do not need to specify the initial inputs to the automaton, but can leave them as uninstantiated parameters, or partially specify them using gap-order constraints.