Generalized Constraint Solving by Elimination Methods

In this survey paper on our work in the field of constraint solving techniques, we discuss generalizations of constraint solving over various domains. These generalizations comprise paradigms from both computational algebra (e.g. parameterization) as well as from logic (e.g. expressiveness of full first-order logic). The domains include real numbers, p-adic numbers, integers, differential fields, term algebras, and quantified propositional calculus. Our central technique is the use of effective quantifier elimination procedures in their pure form and in several variants. As a next step, such techniques are used to realize constraint solvers within the framework of constraint logic programming (CLP). The capabilities of these constraint solvers go considerably beyond those discussed in the literature so far. This establishes, beyond providing excellent tools for automated problem solving over isolated domains, a formal framework for combining computations over several domains. The purpose of this paper is to summarize the original contributions of the publications listed in the References A and their relations among one another.