POLYNOMIAL LOCAL SEARCH IN THE POLYNOMIAL HIERARCHY AND WITNESSING IN FRAGMENTS OF BOUNDED ARITHMETIC

Author:

BECKMANN ARNOLD1,BUSS SAMUEL R.2

Affiliation:

1. Department of Computer Science, Swansea University, Swansea SA2 8PP, UK

2. Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA

Abstract

The complexity class of [Formula: see text]-polynomial local search (PLS) problems is introduced and is used to give new witnessing theorems for fragments of bounded arithmetic. For 1 ≤ i ≤ k + 1, the [Formula: see text]-definable functions of [Formula: see text] are characterized in terms of [Formula: see text]-PLS problems. These [Formula: see text]-PLS problems can be defined in a weak base theory such as [Formula: see text], and proved to be total in [Formula: see text]. Furthermore, the [Formula: see text]-PLS definitions can be skolemized with simple polynomial time functions, and the witnessing theorem itself can be formalized, and skolemized, in a weak base theory. We introduce a new [Formula: see text]-principle that is conjectured to separate [Formula: see text] and [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Approximate counting and NP search problems;Journal of Mathematical Logic;2022-06-22

2. Mining the Surface: Witnessing the Low Complexity Theorems of Arithmetic;Logic, Language, Information, and Computation;2022

3. INCOMPLETENESS IN THE FINITE DOMAIN;The Bulletin of Symbolic Logic;2017-12

4. Total Search Problems in Bounded Arithmetic and Improved Witnessing;Logic, Language, Information, and Computation;2017

5. FRAGMENTS OF APPROXIMATE COUNTING;The Journal of Symbolic Logic;2014-06

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