On the Complexity of Szilard Languages of Regulated Grammars

Abstract

We investigate computational resources used by alternating Turing machines (ATMs) to accept Szilard languages (SZLs) of regulated rewriting grammars. The main goal is to relate these languages to low-level complexity classes such as $\cal N$ $\cal C$ ¹ and $\cal N$ $\cal C$ ². We focus on the derivation process in random context grammars (RCGs) with context-free rules. We prove that unrestricted SZLs and leftmost-1 SZLs of RCGs can be accepted by ATMs in logarithmic time and space. Hence, these languages belong to the $U_{E^*}$-uniform $\cal N$ $\cal C$ ¹ class. Leftmost-i SZLs, i ∈ {2,3}, of RCGs can be accepted by ATMs in logarithmic space and square logarithmic time. Consequently, these languages belong to $\cal N$ $\cal C$ ². Moreover, we give results on SZLs of RCGs with phrase-structure rules and present several applications on SZLs of other regulated rewriting grammars.