On the Complexity of Szilard Languages of Regulated Grammars

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 lowlevel complexity classes such as NC1 and NC2. 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 UE*-uniform NC1 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 NC2. Moreover, we give results on SZLs of RCGs with phrase-structure rules and present several applications on SZLs of other regulated rewriting grammars.

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