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Languages Simultaneously Complete for One-Way and Two-Way Log-Tape Automata

Author
Hartmanis, Juris; Mahaney, Stephen R.
Abstract
In this paper we study languages accepted by nondeterministic $\log n$-tape automata which scan their input only once and relate their computational power to two-way, $\log n$-tape automata. We show that for the one-way, $\log n$-tape automata the nondeterministic model (1-NL) is computationally much more powerful than the deterministic model (1-L); that under one-way, $\log n$-tape reductions there exist natural complete languages for these automata and that the complete languages cannot be sparse. Furthermore, we show that any language complete for nondeterministic one-way $\log n$-tape automata (under 1-L reductions) is also complete for the computationally more powerful nondeterministic two-way, $\log n$-tape reductions. Therefore, for all bounds $T(n),T(n \geq \log n$, the deterministic and nondeterministic $T(n)$-tape bounded computations collapse if the nondeterministic one-way $\log n$-tape computations can be carried out by two-way deterministic $\log n$-tape automata.
Date Issued
1980-02Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR80-413
Type
technical report