Disuni cation in ACI1 Theories

Disuniication is the problem of deciding satissability of a system of equations and dise-quations with respect to a given equational theory. In this paper we study the disuniication problem in the context of ACI1 equational theories. This problem is of great importance, for instance, for the development of constraint solvers over sets. Its solution opens new possibilities for developing automatic tools for static analysis and software veriication. In this work we provide a characterization of the interpretation structures suitable to model the axioms in ACI1 theories. The satissability problem is solved using known techniques for the equality constraints and novel methodologies to transform disequation constraints to manageable solved forms. We propose four solved forms, each ooering an increasingly more precise description of the set of solutions. For each solved form we provide the corresponding rewriting algorithm and we study the time complexity of the transformation. Remarkably, two of the solved forms can be computed and tested in polynomial time. All these solved forms are adequate to be used in the context of a Constraint Logic Programming system|e.g., they do not introduce universal quantiications, as instead happens in some of the existing solved forms for disuniication problems .