不可满足子公式的长度

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-12-19 DOI:10.1007/s10469-024-09771-0

A. V. Seliverstov

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引用次数: 0

摘要

我们找到了一些命题公式的合取长度的一个界，其中每个不满足的公式都包含一个不满足的子公式。特别是，该技术适用于合取范式的公式，这些公式对每个初等析取中的真字面数有限制，也适用于2- cnf、对称的3- cnf和三个字面中的投票函数的合取。一些矩阵的秩下界用于证明。

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The Length of an Unsatisfiable Subformula

We find a bound for the length of a conjunction of some propositional formulas, for which every unsatisfiable formula contains an unsatisfiable subformula. In particular, this technique applies to formulas in conjunctive normal form with restrictions on the number of true literals within every elementary disjunction, as well as for 2-CNFs, for symmetric 3-CNFs, and for conjunctions of voting functions in three literals. A lower bound on the rank of some matrices is used in proofs.

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来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.