The theory of concatenation over finite models

TL;DR

The paper introduces FC, a new finite-model logic based on word equations, which is more expressive than FO[<] and supports efficient model checking and complexity class characterization.

Contribution

It develops FC, a logic combining finite model theory and concatenation, with properties akin to FO on finite models and enhanced expressive power.

Findings

FC is more expressive than FO[<]

FC supports efficient model checking

Captures various complexity classes

Abstract

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast to it, its semantics are defined to only allow finite models, by limiting the universe to a word and all its factors. As a consequence of this, FC has many of the desirable properties of FO on finite models, while being far more expressive than FO[<]. Most noteworthy among these desirable properties are sufficient criteria for efficient model checking, and capturing various complexity classes by adding operators for transitive closures or fixed points. Not only does FC allow us to obtain new insights and techniques for expressive power and efficient evaluation of document spanners, but it also provides a general framework for logic on words that also has potential applications in other areas.