科巴姆定理的强版本

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2024-01-17 DOI:10.1137/22m1538065

Philipp Hieronymi, Chris Schulz

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引用次数: 0

摘要

SIAM 计算期刊》，提前印刷。摘要设 [math] 是两个乘法独立整数。科巴姆的著名定理指出，当且仅当一个集合[math]在普雷斯伯格算术中是可定义的时，它既是[math]可识别的，又是[math]可识别的。在此，我们展示如下加强：设[math]是[math]可识别的，且设[math]是[math]可识别的，使得[math]和[math]在普雷斯伯格算术中都不可定义。那么[math]的一阶逻辑理论就是不可判定的。这与布奇（Büchi）的一个著名定理相反，该定理指出[math]的一阶逻辑理论是可判的。

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A Strong Version of Cobham’s Theorem

SIAM Journal on Computing, Ahead of Print.
Abstract. Let [math] be two multiplicatively independent integers. Cobham’s famous theorem states that a set [math] is both [math]-recognizable and [math]-recognizable if and only if it is definable in Presburger arithmetic. Here we show the following strengthening: let [math] be [math]-recognizable, and let [math] be [math]-recognizable such that both [math] and [math] are not definable in Presburger arithmetic. Then the first-order logical theory of [math] is undecidable. This is in contrast to a well-known theorem of Büchi stating that the first-order logical theory of [math] is decidable.

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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.