Logic Programming

Linear numerical constraints and their first-order theory, whether defined over the reals or the integers, are basic tools that appear in many areas of Computer Science. This paper overviews a set of techniques based on finite automata that lead to decision procedures and other useful algorithms, as well as to a normal form, for the first-order linear theory of the integers, of the reals, and of the integers and reals combined. This approach has led to an implemented tool, which has the so far unique capability of handling the linear first-order theory of the integers and reals combined.

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