Unambiguity and Fewness for Logarithmic Space

We consider various types of unambiguity and fewness for log space bounded Turing machines and polynomial time bounded log space auxiliary pushdown automata. In particular, we introduce the notions of (general), reach, and strong unambiguity and fewness. We demonstrate that closure under complement of unambiguous classes implies equivalence of unambiguity and “unambiguous fewness”. This, as we will show, applies in the cases of reach and strong unambiguity for log space. Among the many relations we exhibit, we show that the unambiguous linear contextfree languages, which are not known to be contained in deterministic log space, nevertheless are contained in strongly unambiguous log space, and, consequently, are log space reducible to deterministic contextfree languages.

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