Simple and efficient clause subsumption with feature vector indexing

S Schulz�- Automated Reasoning and Mathematics: Essays in�…, 2013 - Springer
Automated Reasoning and Mathematics: Essays in Memory of William W. McCune, 2013Springer
This paper describes feature vector indexing, a new, non-perfect indexing method for clause
subsumption. It is suitable for both forward (ie, finding a subsuming clause in a set) and
backward (finding all subsumed clauses in a set) subsumption. Moreover, it is easy to
implement, but still yields excellent performance in practice. As an added benefit, by
restricting the selection of features used in the index, our technique immediately adapts to
indexing modulo arbitrary AC theories with only minor loss of efficiency. Alternatively, the�…
Abstract
This paper describes feature vector indexing, a new, non-perfect indexing method for clause subsumption. It is suitable for both forward (i.e., finding a subsuming clause in a set) and backward (finding all subsumed clauses in a set) subsumption. Moreover, it is easy to implement, but still yields excellent performance in practice. As an added benefit, by restricting the selection of features used in the index, our technique immediately adapts to indexing modulo arbitrary AC theories with only minor loss of efficiency. Alternatively, the feature selection can be restricted to result in set subsumption. Feature vector indexing has been implemented in our equational theorem prover E, and has enabled us to integrate new simplification techniques making heavy use of subsumption. We experimentally compare the performance of the prover for a number of strategies using feature vector indexing and conventional sequential subsumption.
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