Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
Explicit versus implicit representations of subsets of the Herbrand universe
Theoretical Computer Science
Negation Elimination from Simple Equational Formulae
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Patterns in Words versus Patterns in Trees: A Brief Survey and New Results
PSI '99 Proceedings of the Third International Andrei Ershov Memorial Conference on Perspectives of System Informatics
Solving Equational Problems Efficiently
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
On the complexity of equational problems in CNF
Journal of Symbolic Computation - Special issue: First order theorem proving
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
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An Atomic Representation of a Herbrand Model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM reprents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of Computer Science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs. The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMS, and evaluating clauses over ARMS. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In spite of this, by developing new decision procedures, we are able to prove that all mentioned problems are coNP-complete.