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

Kexu Wang; Xishun Zhao

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arXiv · 1912.03841

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

Kexu Wang·Xishun Zhao

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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.

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Kexu Wang, Xishun Zhao. 2019-12-09. A Logic that Captures $\beta$P on Ordered Structures. https://arxiv.org/abs/1912.03841

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