Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Lecture notes in computer science on Foundations of logic and functional programming
Equational problems anddisunification
Journal of Symbolic Computation
Sufficient-completeness, ground-reducibility and their complexity
Acta Informatica
Extending resolution for model construction
JELIA '90 Proceedings of the European workshop on Logics in AI
Equational formulae with membership constraints
Information and Computation
Negation elimination in empty of permutative theories
Journal of Symbolic Computation
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Working with ARMs: complexity results on atomic representations of herbrand models
Information and Computation
The Explicit Representability of Implicit Generalizations
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
The Negation Elimination from Syntactic Equational Formula is Decidable
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
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
Stop losing sleep over incomplete data type specifications
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Model representation via contexts and implicit generalizations
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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In Lassez and Marriott (J. Automat. Reson. 3 (3) (1987) 301-317), explicit and implicit generalizations were studied as representations of subsets of some fixed Herbrand universe H. An explicit generalization E = r1V ... V rl represents all ground terms that are instances of at least one of the terms ti, whereas an implicit generalization I = t/t1 V ... V tm represents all H-ground instances of t that are not instances of any term ti. More generally, a disjunction I = I1 V ... V In of implicit generalizations contains all ground terms that are contained in at least one of the implicit generalizations Ij.Implicit generalizations have applications to many areas of Computer Science like machine learning, unification, specification of abstract data types, logic programming, functional programming, etc. In these areas, the so-called finite explicit representability problem plays an important role, i.e. given a disjunction of implicit generalizations I =I1 V ... V In, does there exist an explicit generalization E, s.t. I and E are equivalent? We shall prove the coNP-completeness of this decision problem.Implicit generalizations can be represented as equational formulae, i.e., first-order formulae whose only predicate symbol is syntactic equality. Closely related to the finite explicit representability problem is the so-called negation elimination problem of equational formulae, i.e. given an arbitrary equational formula p is p semantically equivalent to an equational formula without universal quantifiers and negation. In this work we study the negation elimination problem of equational formulae with purely existential quantifier prefix. We prove the coNP-completeness for such formulae in DNF and the Π2p -hardness in case of CNF.