Short proofs for tricky formulas
Acta Informatica
Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
The symmetry rule in propositional logic
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Investigations on autark assignments
Discrete Applied Mathematics - Special issue on Boolean functions and related problems
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
Annals of Mathematics and Artificial Intelligence
Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
Theoretical Computer Science
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
Local Symmetries in Propositional Logic
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
An Upper Bound for Minimal Resolution Refutations
Proceedings of the 12th International Workshop on Computer Science Logic
NP-Completeness of Refutability by Literal-Once Resolution
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
An Application of Matroid Theory to the SAT Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Information Processing Letters
The Complexity of Resolution with Generalized Symmetry Rules
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Homomorphisms and Renamings for Minimal Unsatisfiable Formulas
Annals of Mathematics and Artificial Intelligence
Computing unsatisfiable k-SAT instances with few occurrences per variable
Theoretical Computer Science
Complexities of homomorphism and isomorphism for definite logic programs
Journal of Computer Science and Technology
The local lemma is tight for SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We study homomorphisms of propositional formulas in CNF generalizing symmetries considered by Krishnamurthy. If φ:H → F is a homomorphism, then unsatisfiability of H implies unsatisfiability of F. Homomorphisms from F to a subset F' of F (endomorphisms) are of special interest, since in such cases F and F' are satisfiability-equivalent. We show that the smallest subsets F' of a formula F for which an endomorphism F → F' exists are mutually isomorphic. Furthermore, we study connections between homomorphisms and autark assignments. We introduce the concept of "proof by homomorphism" which is based on the observation that there exist sets Γ of unsatisfiable formulas such that (i) formulas in Γ can be recognized in polynomial time, and (ii) for every unsatisfiable formula F there exist some H ∈ Γ and a homomorphism φ: H → F. We identify several sets Γ of unsatisfiable formulas satisfying (i) and (ii) for which proofs by homomorphism w.r.t. Γ and tree resolution proofs can be simulated by each other in polynomial time.