On Second-Order Monadic Monoidal and Groupoidal Quantifiers

TL;DR

This paper explores the expressive power of second-order monadic monoidal and groupoidal quantifiers in logic, linking them to computational complexity classes and language classes like regular and context-free languages.

Contribution

It provides a classification of the expressive power of these logics and characterizes ATIME(n) using second-order monadic monoidal quantifiers.

Findings

Logics with these quantifiers correspond to regular and context-free languages.

ATIME(n) can be characterized by second-order monadic monoidal quantifiers.

The study offers a computational classification over strings with various built-in predicates.

Abstract

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers.