Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Equational problems anddisunification
Journal of Symbolic Computation
Extending resolution for model construction
JELIA '90 Proceedings of the European workshop on Logics in AI
Equational formulae with membership constraints
Information and Computation
Handbook of logic in artificial intelligence and logic programming
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Speeding up algorithms on atomic representations of Herbrand models via new redundancy criteria
Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
An Improved Lower Bound for the Elementary Theories of Trees
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Working with Arms: Complexity Results on Atomic Representations of Herbrand Models
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Extending semantic resolution via automated model building: applications
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Generalizing DPLL and satisfiability for equalities
Information and Computation
A New Proposal Of Quasi-Solved Form For Equality Constraint Solving
Electronic Notes in Theoretical Computer Science (ENTCS)
Equational constraint solving via a restricted form of universal quantification
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
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Equational problems (i.e. first-order formulae with quantifier prefix ∃* ∀*, whose only predicate symbol is syntactic equality) are an important tool in many areas of automated deduction, e.g. restricting the set of ground instances of a clause via equational constraints allows the definition of stronger redundancy criteria and hence, in general, of more efficient theorem provers. Moreover, the inference rules themselves can be restricted via constraints. In automated model building, equational problems play an important role both in the definition of an appropriate model representation and in the evaluation of clauses in such models. Also, many problems in the area of logic programming can be reduced to equational problem solving. Finally, equational problems over a finite domain correspond to the evaluation of certain queries over relational databases.The goal of this work is a complexity analysis of the satisfiability problem of equational problems. The main results will be a proof of the NP-completeness (and, in particular, the NP-membership) of equational problems in CNF over an infinite domain and of the ΣP2-completeness in the case of CNF over a finite domain.