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Remarks on languages acceptable in log log n space. (English) Zbl 0652.68055

A language is acceptable in the strong sense by a two-way nondeterministic Turing machine when all computation paths on every input stop and satisfy the space bound. The following main theorem is established. There exists a language which is acceptable in the strong sense by a two-way nondeterministic Turing machine in log log n space such that: if the language is not decidable by any two-way deterministic Turing machine in log log n space, then \(L\neq NL\).
Reviewer: Lih Ko-Wei

MSC:

68Q25 Analysis of algorithms and problem complexity
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
68Q45 Formal languages and automata
Full Text: DOI

References:

[1] Alberts, M., Space complexity of alternating Turing machines, (Budach, L., Fundamentals of Computing Theory, FCT’85 Conf., Vol. 199 (1985), Springer: Springer Berlin), 1-7, Lecture Notes in Computer Science · Zbl 0574.68040
[2] Freivalds, R., On time complexity of deterministic and nondeterministic Turing machines, Latvian Mathematics, 23, 158-165 (1979), (in Russian) · Zbl 0462.68028
[3] Lewis, P. M.; Stearns, R. E.; Hartmanis, J., Memory bounds for recognition of context-free and context-sensitive languages, IEEE Conf. Rec. on Switching Circuit Theory and Logic Design, 191-202 (1965) · Zbl 0272.68054
[4] Sierpiński, W., Elementary Theory of Numbers, Monografie Matematyczne, Vol. 42 (1964), PWN: PWN Warszawa · Zbl 0638.10001
[5] Stearns, R. E.; Hartmanis, J.; Lewis, P. M., Hierarchies of memory limited computations, IEEE Conf. Rec. on Switching Circuit Theory and Logic Design, 179-190 (1965) · Zbl 0229.02033
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