Toward a Compositional Theory of Leftist Grammars and Transformations

TL;DR

This paper develops a formal theory of leftist grammars as word transformers, proving their closure properties and establishing NP-completeness of bounded reachability even with acyclic rules.

Contribution

It introduces a compositional framework for leftist grammars and demonstrates their computational complexity properties.

Findings

Leftist transformations are closed under composition and transitive closure.

Bounded reachability in leftist grammars is NP-complete with acyclic rules.

Provides foundational results for analyzing the computational power of leftist grammars.

Abstract

Leftist grammars [Motwani et al., STOC 2000] are special semi-Thue systems where symbols can only insert or erase to their left. We develop a theory of leftist grammars seen as word transformers as a tool toward rigorous analyses of their computational power. Our main contributions in this first paper are (1) constructions proving that leftist transformations are closed under compositions and transitive closures, and (2) a proof that bounded reachability is NP-complete even for leftist grammars with acyclic rules.