Short proofs for tricky formulas
Acta Informatica
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
Tractability of cut-free Gentzen type propositional calculus with permutation inference
Theoretical Computer Science
The symmetry rule in propositional logic
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
No feasible monotone interpolation for simple combinatorial reasoning
Theoretical Computer Science
Tractability of Cut-free Gentzen-type propositional calculus with permutation inference II
Theoretical Computer Science
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Local Symmetries in Propositional Logic
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Homomorphisms of conjunctive normal forms
Discrete Applied Mathematics - The renesse issue on satisfiability
Generalizing Boolean satisfiability I: background and survey of existing work
Journal of Artificial Intelligence Research
Generalizing Boolean satisfiability II: theory
Journal of Artificial Intelligence Research
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We generalize Krishnamurthy's well-studied symmetry rule for resolution systems by considering homomorphisms instead of symmetries; symmetries are injective maps of literals which preserve complements and clauses; homomorphisms arise from symmetries by releasing the constraint of being injective.We prove that the use of homomorphisms yields a strictly more powerful system than the use of symmetries by exhibiting an infinite sequence of sets of clauses for which the consideration of global homomorphisms allows exponentially shorter proofs than the consideration of local symmetries. It is known that local symmetries give rise to a strictly more powerful system than global symmetries; we prove a similar result for local and global homomorphisms. Finally, we pinpoint an exponential lower bound for the resolution system enhanced by the local homomorphism rule.