CAESAR_SOLVE: A generic library for on-the-fly resolution of alternation-free Boolean equation systems

Boolean equation systems (Bess) provide a useful framework for modeling various verification problems on finite-state concurrent systems, such as equivalence checking and model checking. These problems can be solved on the fly (i.e., without constructing explicitly the state space of the system under analysis) by using a demand-driven construction and resolution of the corresponding Bes. In this article, we present a generic software library dedicated to on-the-fly resolution of alternation-free Bess. Four resolution algorithms are currently provided by the library: algorithms A1 and A2 are general, the latter being optimized to produce small-depth diagnostics, whereas algorithms A3 and A4 are specialized for handling acyclic and disjunctive/conjunctive Bess in a memory-efficient way. The library has been developed within the Cadp verification toolbox using the generic Open/Caesar environment and is currently used for three purposes: on-the-fly equivalence checking modulo five widely used equivalence relations, on-the-fly model checking of regular alternation-free modal μ-calculus, and on-the-fly reduction of state spaces based on τ-confluence .