Complexity of the Problem of Being Equivalent to Horn Formulas

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2022-04-29 DOI:10.1007/s10469-022-09665-z

N. T. Kogabaev

引用次数: 1

Abstract

We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete \( {\Sigma}_1^0 \) set.

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Horn公式等价问题的复杂性

我们研究了与给定句子等价的Horn句子（同一性、准同一性，∀-句子，∃-语句）存在性问题的复杂性。证明了如果签名包含至少一个arity k≥2的符号，则所提到的每个问题都是m-完全\（｛\ Sigma｝_1^0\）集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.