Logic Characterization of Floyd Languages

TL;DR

This paper provides a logical characterization of Floyd languages, showing their equivalence to automata recognizing these languages through a monadic second order logic framework.

Contribution

It introduces a monadic second order logic characterization of Floyd languages, establishing their equivalence with automata recognizing these languages.

Findings

Floyd languages are closed under certain operations.

MSO logic can characterize Floyd languages.

Automata and MSO formalizations are equivalent for Floyd languages.

Abstract

Floyd languages (FL), alias Operator Precedence Languages, have recently received renewed attention thanks to their closure properties and local parsability which allow one to apply automatic verification techniques (e.g. model checking) and parallel and incremental parsing. They properly include various other classes, noticeably Visual Pushdown languages. In this paper we provide a characterization of FL in terms a monadic second order logic (MSO), in the same style as Buchi's one for regular languages. We prove the equivalence between automata recognizing FL and the MSO formalization.