Regular languages definable by Lindström quantifiers

Regular languages definable by Lindström quantifiers

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.

Regular Languages Definable by Majority Quantifiers with Two Variables

In this paper we consider the class of all regular languages definable by the extended majority quantifier and the order predicate but using only two variables. The main part of the paper is the presentation of a geometric method which is used to show that a given regular language cannot be defined by such formulas. Applying this method we can give a necessary condition in terms of an equation ...

A Perspective on Lindström Quantifiers and Oracles

Lindström Quantifiers and Leaf Language Definability

We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now kn...

Capturing Complexity Classes with Lindström Quantifiers