Short proofs for tricky formulas
Acta Informatica
A term equality problem equivalent to graph isomorphism
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Graph Isomorphism is Low for PP
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The Crisis in Finite Mathematics: Automated Reasoning as Cause and Cure
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Ten challenges in propositional reasoning and search
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
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One important issue of automated theorem proving is the complexity of the inference rules used in theorem provers. If Krishnamurty's general symmetry rule is to be used, then one should provide some way of computing non trivial symmetries. We show that this problem is NP-complete. But this general rule can be simplified by restricting it to what we call 5- symmetries, yielding the well-known symmetry rule. We show that computing 5-symmetries is in the same complexity class as the graph isomorphism problem, which appears to be neither polynomial nor NP-complete. However it is sufficient to compute the set of all 5-symmetries at the beginning of the proof search, and since it is a permutation group, there exist some efficient techniques from computational group theory to represent this set. We also show how these techniques can be used for applying the S-symmetry rule in polynomial time.