Combining unification algorithms for confined regular equational theories
Proc. of the first international conference on Rewriting techniques and applications
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Associative-Commutative Unification
Proceedings of the 7th International Conference on Automated Deduction
The role of term symmetry in e-unification and e-completion
The role of term symmetry in e-unification and e-completion
| Hi-index | 0.00 |
A major portion of the work and time involved in completing an incomplete set of reductions using an E-completion procedure such as the one described by Knuth and Bendix or its extension to associative-commutative equational theories as described by Peterson and Stickel is spent calculating critical pairs and subsequently testing them for confluence and coherence. A pruning technique which removes from consideration those critical pairs that represent redundant or superfluous information can make a marked difference in the run time and efficiency of an E-completion procedure to which it is applied. In this paper, a technique is proposed for removing critical pairs from consideration at various points before, during, or after their formation. This method is based on the property of term symmetry, which will be defined and explored with respect to E-unification and E-completion procedures. Informally, term symmetry exists between two terms when one can be transformed into the other through variable renaming. By identifying and eliminating various forms of term symmetry which arise between syntactic structures such as, reductions, critical pairs, subterms, and unifiers, it is possible to derive an E-completion procedure that produces the same results without processing these symmetric redundancies.