On the construction of automata from linear arithmetic constraints

This paper presents an overview of algorithms for constructing automata from linear arithmetic constraints. It identifies one case in which the special structure of the automata that are constructed allows a linear-time determinization procedure to be used. Furthermore, it shows through theoretical analysis and experiments that the special structure of the constructed automata does, in quite a general way, render the usual upper bounds on automata operations vastly overpessimistic

Model Checking in CLP

We show that Constraint Logic Programming (CLP) can serve as a conceptual basis and as a practical implementation platform for the model checking of infinite-state systems. Our contributions are: (1) a semantics-preserving translation of concurrent systems into CLP programs, (2) a method for verifying safety and liveness properties on the CLP programs produced by the translation. We have implemented the method in a CLP system and verified well-known examples of infinitestate programs over integers, using here linear constraints as opposed to Presburger arithmetic as in previous solutions

Little Engines of Proof

The automated construction of mathematical proof is a basic activity in computing. Since the dawn of the field of automated reasoning, there have been two divergent schools of thought. One school, best represented by Alan Robinson's resolution method, is based on simple uniform proof search procedures guided by heuristics. The other school, pioneered by Hao Wang, argues for problem-specific combinations of decision and semi-decision procedures. While the former school has been dominant in the past, the latter approach has greater promise. In recent years, several high quality inference engines have been developed, including propositional satisfiability solvers, ground decision procedures for equality and arithmetic, quantifier elimination procedures for integers and reals, and abstraction methods for finitely approximating problems over infinite domains. We describe some of these "little engines of proof" and a few of the ways in which they can be combined. We focus in particular on combining different decision procedures for use in automated verification