Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
Journal of Combinatorial Theory Series A
Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
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
Intriactability of Read-Once Resolution
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
On Exact Selection of Minimally Unsatisfiable Subformulae
Annals of Mathematics and Artificial Intelligence
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We investigate the complexity of deciding whether a propositional formula has a read-once resolution proof. We give a new and general proof of Iwama–Miynano's theorem which states that the problem whether a formula has a read-once resolution proof is iNP-complete. Moreover, we show for fixed ik⩾2 that the additional restriction that in each resolution step one of the parent clauses is a ik-clause preserves the iNP-completeness. If we demand that the formulas are minimal unsatisfiable and read-once refutable then the problem remains iNP-complete. For the subclasses iMU(ik) of minimal unsatisfiable formulas we present a pol-time algorithm deciding whether a iMU(ik)-formula has a read-once resolution proof. Furthermore, we show that the problems whether a formula contains a iMU(ik)-subformula or a read-once refutable iMU(ik)-subformula are iNP-complete.