从多项式时间中分离秩逻辑

IF 2.3 2区计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Journal of the ACM Pub Date : 2023-03-25 DOI:https://dl.acm.org/doi/10.1145/3572918

Moritz Lichter

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引用次数: 0

摘要

在寻找捕获多项式时间的逻辑时，最有希望的候选是无选择多项式时间(CPT)和秩逻辑。秩逻辑扩展了定点逻辑，使用秩算子对素数域进行计数。我们证明了CFI图的同构问题不能在秩逻辑中定义，即使基图是完全有序的。然而，CPT可以定义这个同构问题。因此我们将秩逻辑从CPT中分离出来，特别是从多项式时间中分离出来。

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Separating Rank Logic from Polynomial Time

In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ_2ⁱ cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time.

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来源期刊

Journal of the ACM 工程技术-计算机：理论方法

CiteScore

7.50

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The best indicator of the scope of the journal is provided by the areas covered by its Editorial Board. These areas change from time to time, as the field evolves. The following areas are currently covered by a member of the Editorial Board: Algorithms and Combinatorial Optimization; Algorithms and Data Structures; Algorithms, Combinatorial Optimization, and Games; Artificial Intelligence; Complexity Theory; Computational Biology; Computational Geometry; Computer Graphics and Computer Vision; Computer-Aided Verification; Cryptography and Security; Cyber-Physical, Embedded, and Real-Time Systems; Database Systems and Theory; Distributed Computing; Economics and Computation; Information Theory; Logic and Computation; Logic, Algorithms, and Complexity; Machine Learning and Computational Learning Theory; Networking; Parallel Computing and Architecture; Programming Languages; Quantum Computing; Randomized Algorithms and Probabilistic Analysis of Algorithms; Scientific Computing and High Performance Computing; Software Engineering; Web Algorithms and Data Mining