On some derivation mechanisms and the complexity of their Szilard languages

A Szilard language is a language theoretical tool used to describe the derivation process in a formal grammar or grammar system. We investigate computational resources used by (alternating) Turing machines to accept Szilard languages of Chomsky grammars, regulated grammars and grammar systems. The results are related to the circuit complexity   classes NC1NC1 and NC2NC2. The paper is a survey of the most important complexity results in the field, but it also brings several new insights into the parallel complexity of Szilard languages of grammar systems. We focus on parallel communicating grammar systems (PCGSs) with context-free components, and we prove that the class of Szilard languages of centralized (returning or non-returning) PCGSs is included in NC1NC1.