The ghosts of forgotten things: A study on size after forgetting

IF 0.6 2区数学 Q2 LOGIC Annals of Pure and Applied Logic Pub Date : 2024-05-08 DOI:10.1016/j.apal.2024.103456

Paolo Liberatore

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Abstract

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of reducing information, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is $D^{p}$ -hard in $Σ_{2}^{p}$ . The same problem for unrestricted CNF propositional formulae is $D_{2}^{p}$ -hard in $Σ_{3}^{p}$ .

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被遗忘事物的幽灵遗忘后的大小研究

遗忘是从逻辑公式中删除变量，同时保留对其他变量的限制。尽管遗忘减少了信息量，但它并不总是减少公式的大小，有时可能会增加公式的大小。本文讨论了这种增加的影响，并分析了这种现象的计算特性。给定一个命题霍恩公式、一组变量和一个最大允许大小，在.NET中，决定从公式中遗忘变量是否可以用该大小表达是很难的。对于无限制的 CNF 命题式，同样的问题在 .

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.

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