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On deterministic context-free languages, multihead automata, and the power of an auxiliary pushdown store

Ivan Hal Sudborough

Abstract

A deterministic context-free language L0 is described which is log(n)-complete for the family of languages recognized by deterministic log(n)- tape bounded auxiliary pushdown automata in polynomial time. It follows that L0 is a “hardest” deterministic context-free language (DCFL), since all DCFL's are recognized in polynomial time by deterministic pushdown automata. L0 is, moreover, a simple precedence language and a simple LL(1) language. Thus the tape complexities of these proper subfamilies are essentially the same as the tape complexity of all DCFL's.

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Key concepts: Deterministic pushdown automaton, Pushdown automaton, Embedded pushdown automaton, Context-free language, Deterministic context-free grammar, Computer science, Nested word, Time complexity