Abstract not found

Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in [12] where the relevant uni cation algorithms have been also parametrically developed. In this paper we extend these results considering more general constraints including not only equality but also membership constraints as well as their negative counterparts. This amounts to de ne the privileged structures for the considered axiomatic theories and to solve the relevant constraint satisfaction problems in each of the theories. We adopt a highly parametric approach which allows all the results obtained separately for each single theory to be easily combined so as to obtain a general framework where it is possible to deal with more than one data structure at a time.

Disunification is the problem of deciding satisfiability of a system of equations and disequations with respect to a given equational theory. In this paper we study the disunification 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 verification. In this work we provide a characterization of the interpretation structures suitable to model the axioms in ACI1 theories. The satisfiability 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 offering 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 quantifications, as instead happens in some of the existing solved forms for disunification problems.