Abstract
This paper investigates some aspects of the accepting powers of deterministic, nondeterministic, and alternating one-pebble Turing machines with spaces between log log n ang log n. We first investigate a relationship between the accepting powers of two-way deterministic one-counter automata and deterministic (or nondeterministic) one-pebble Turing machines, and show that they are incomparable. Then we investigate a relationship between nondeterminism and alternation, and show that there exists a language accepted by a strongly log log n space-bounded alternating one-pebble Turing machine , but not accepted by any weakly o(log n) space-bounded nondeterministic one-pebble Turing machine. Finally, we investigate a space hierarchy, and show that for any one-pebble fully space constructible function L(n) ≤ log n, and any function L′(n)=o(L(n)), there exists a language accepted by a strongly L(n) space-bounded deterministic one-pebble Turing machine, but not accepted by any weakly L′(n) space-bounded nondeterministic one-pebble Turing machine.
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Inoue, A., Ito, A., Inoue, K., Okazaki, T. (2003). Some Properties of One-Pebble Turing Machines with Sublogarithmic Space. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_65
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DOI: https://doi.org/10.1007/978-3-540-24587-2_65
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