nested PLS

TL;DR

This paper introduces nested Polynomial Local Search (nPLS) problems and demonstrates their equivalence to definable NP search problems within a specific logical framework, expanding understanding of computational complexity.

Contribution

It defines the class of nested PLS problems and characterizes NP search problems in terms of this new class within the logical system T^2_2.

Findings

Nested PLS problems are equivalent to $ ext{NP}$ search problems definable in $T^2_2$.

Provides a new characterization of $ ext{NP}$ search problems using nested PLS.

Establishes a connection between search problems and logical definability.

Abstract

In this note we will introduce a class of search problems, called nested Polynomial Local Search (nPLS) problems, and show that definable NP search problems, i.e., $\Sigma^b_1$-definable functions in $T^2_2$ are characterized in terms of the nested PLS.