Monoid automata for displacement context-free languages

TL;DR

This paper extends algebraic and automata-theoretic characterizations to displacement context-free languages, introducing monoid automata and two-stack automata, and demonstrating their equivalence through geometric interpretations.

Contribution

It provides a new algebraic interpretation and automata model for displacement context-free languages, expanding the theoretical framework beyond traditional context-free languages.

Findings

Characterization of k-displacement context-free languages via monoid automata

Introduction of simultaneous two-stack automata and their variants

Equivalence of automata definitions based on geometric memory operations

Abstract

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages. We also obtain a characterization of k-displacement context-free languages in terms of monoid automata and show how such automata can be simulated on two stacks. We introduce the simultaneous two-stack automata and compare different variants of its definition. All the definitions considered are shown to be equivalent basing on the geometric interpretation of memory operations of these automata.