The saturation algorithm for symbolic state-space exploration

Abstract

We present various algorithms for generating the state space of an asynchronous system based on the use of multiway decision diagrams to encode sets and Kronecker operators on boolean matrices to encode the next-state function. The Kronecker encoding allows us to recognize and exploit the “locality of effect” that events might have on state variables. In turn, locality information suggests better iteration strategies aimed at minimizing peak memory consumption. In particular, we focus on the saturation strategy, which is completely different from traditional breadth-first symbolic approaches, and extend its applicability to models where the possible values of the state variables are not known a priori. The resulting algorithm merges “on-the-fly” explicit state-space generation of each submodel with symbolic state-space generation of the overall model.Each algorithm we present is implemented in our tool SmArT. This allows us to run fair and detailed comparisons between them on a suite of representative models. Saturation, in particular, is shown to be many orders of magnitude more efficient in terms of memory and time with respect to traditional methods.