Toward a Compositional Theory of Leftist Grammars and Transformations

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.