Monoid automata for displacement context-free languages

Abstract

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schützenberger theorem for context-free languages. We solve an analogous task for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages giving an interpretation of the corresponding theorem for that class in terms of monoid automata. We also show how such automata can be simulated on two stacks, introducing the simultaneous two-stack automaton. We compare different variants of its definition and show their equivalence basing on geometric interpretation of its memory operations. © 2014 Springer-Verlag Berlin Heidelberg.