Intractability of read-once resolution

Iwama, Kazuo; Miyano, Eiji

doi:10.1109/sct.1995.514725

Cited by 46 publications

(50 citation statements)

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“…The problem of search tree size has been already analyzed for various proof systems. For backtracking, this problem has been shown NP-complete [20,19,1]. The membership into NP, however, only holds if the number k of the question "is there any proof of size bounded by k?"…”

Section: Discussionmentioning

confidence: 99%

“…The proof size problem is known to be NP-complete [20,19,1]. Membership to NP only holds if the maximal size of proofs is represented in unary notation, while the results presented in this paper hold for the binary notation.…”

Section: Introductionmentioning

confidence: 95%

“…The variant of OTS where k is in unary notation has already been investigated and proved NP complete [20,9,19] (the assumption that k is in unary is necessary to prove the membership to NP.) Assuming that k is in unary notation means that the complexity of the problem is not measured w.r.t.…”

Section: Name: Optimal Tree Size (Ots)mentioning

confidence: 99%

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Complexity results on DPLL and resolution

Liberatore

2006

ACM Trans. Comput. Logic

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DPLL and resolution are two popular methods for solving the problem of propositional satisfiability. Rather than algorithms, they are families of algorithms, as their behavior depend on some choices they face during execution: DPLL depends on the choice of the literal to branch on; resolution depends on the choice of the pair of clauses to resolve at each step. The complexity of making the optimal choice is analyzed in this paper. Extending previous results, we prove that choosing the optimal literal to branch on in DPLL is ∆ p 2 [log n]-hard, and becomes NP PP -hard if branching is only allowed on a subset of variables. Optimal choice in regular resolution is both NP-hard and coNP-hard. The problem of determining the size of the optimal proofs is also analyzed: it is coNP-hard for DPLL, and ∆ p 2 [log n]-hard if a conjecture we make is true. This problem is coNP-hard for regular resolution.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Complexity results on DPLL and resolution

Liberatore

2006

ACM Trans. Comput. Logic

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“…of possible leaf labels of trees is (properly) contained in the class of clause-set refutable by "read-once" resolution (resolution refutations in tree form, where every input clause can be used at most once), shown to be NP-complete in [10]. It is an interesting question whether also the problem "…”

Section: Theorem 311 Considermentioning

confidence: 99%

An application of matroid theory to the SAT problem

Kullmann

Proceedings 15th Annual IEEE Conference on Computational Complexity

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“…There have been a number of results, including [1,2,[8][9][10], about the hardness of finding resolution proofs, or of determining whether resolution proofs exist. Theorem 1, however, is more in the spirit of hardness results by Buss and Hoffmann [5] and Hoffmann [7]: these show that, given a particular resolution refutation, it is hard to determine if it satisfies extra conditions.…”

Section: Theoremmentioning

confidence: 99%