A Logic that Captures $\beta$P on Ordered Structures

Kexu Wang; Xishun Zhao

A Logic that Captures $\beta$P on Ordered Structures

Logic in Computer Science 2022-09-07 v4 Computational Complexity Logic

Authors: Kexu Wang , Xishun Zhao

Abstract

We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited nondeterminism class $\beta\text{P}$ . In order to study its expressive power, we also design a new version of Ehrenfeucht-Fra\"iss\'e game for this logic and show that our capturing result will not hold on the general case, i.e. on all the finite structures.

Keywords

first-order logic modal logic algebraic theory

Cite

@article{arxiv.1912.03841,
  title  = {A Logic that Captures $\beta$P on Ordered Structures},
  author = {Kexu Wang and Xishun Zhao},
  journal= {arXiv preprint arXiv:1912.03841},
  year   = {2022}
}

Comments

15 pages. This article was reported with a title "Logarithmic-Bounded Second-Order Quantifiers and Limited Nondeterminism" in National Conference on Modern Logic 2019, on November 9 in Beijing

A Logic that Captures $\beta$P on Ordered Structures

Abstract

Keywords

Cite

Comments

Related papers