Extrapolating (omega-)regular model checking

(Omega-)Regular model checking is the name of a family of techniques in which states are represented by words, sets of states by finite automata on these objects, and transitions by finite automata operating on pairs of state encodings, i.e., finite-state transducers. In this context, the problem of computing the set of reachable states of a system can be reduced to the one of computing the iterative closure of the finite-state transducer representing its transition relation. In this tutorial article, we survey an extrapolation-based technique for computing the closure of a given transducer. The approach proceeds by comparing successive elements of a sequence of approximations of the iteration, detecting an “increment” that is added to move from one approximation to the next, and extrapolating the sequence by allowing arbitrary repetitions of this increment. The technique applies to finite-word and deterministic weak Büchi automata. Finally, we discuss the implementation of these results within the T(O)RMC toolsets and present case studies that show the advantages and the limits of the approach.