This paper surveys some techniques and tools for achieving reachability analysis over term rewriting systems. The core of those techniques is a generic tree automata completion algorithm used to compute in an exact or approximated way the set of descendants (or reachable terms). This algorithm has been implemented in the Timbuk tool. Furthermore, we show that many classes with regular sets of descendants of the literature corresponds to specific instances of the tree automata completion algorithm and can thus be efficiently computed by Timbuk. An extension of the completion algorithm to conditional term rewriting systems and some applications are also presented.

We propose a logical framework for the control theory of reactive systems modeled by discrete event systems. The logic is the conjunctive nu-calculus, an expressive fragment of the powerful mu-calculus. Conjunctive nu-calculus possesses an alternative presentation based on modal specifications, with simple graphical representations. We exploit modal specification to specify and to solve the basic centralized control problem: our class of control objectives strictly subsumes the class of regular languages, normally used in the classic control theory of discrete-event systems, but the existence of maximally permissive solutions is however preserved.

We study an