NP-completeness of the set unification and matching problems
Proc. of the 8th international conference on Automated deduction
Unification in commutative idempotent monoids
Theoretical Computer Science
Journal of Computer and System Sciences
Introduction to algorithms
Set constructors in a logic database language
Journal of Logic Programming
The Z notation: a reference manual
The Z notation: a reference manual
Combination techniques and decision problems for disunification
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
Data on the Web: from relations to semistructured data and XML
Data on the Web: from relations to semistructured data and XML
Type dependencies for logic programs using ACI-unification
Theoretical Computer Science
Sets and constraint logic programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
Knowlege in action: logical foundations for specifying and implementing dynamical systems
Knowlege in action: logical foundations for specifying and implementing dynamical systems
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Reasoning about Actions with CHRs and Finite Domain Constraints
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Comparing Expressiveness of Set Constructor Symbols
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
A Set-Theoretic Model for Real-Time Specification and Reasoning
MPC '98 Proceedings of the Mathematics of Program Construction
Solving Disequations in Equational Theories
Proceedings of the 9th International Conference on Automated Deduction
Logical Aspects of Set Constraints
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
A uniform approach to constraint-solving for lists, multisets, compact lists, and sets
ACM Transactions on Computational Logic (TOCL)
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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.