Abstract
Ruzzo [Tree-size bounded alternation, J. Comput. Syst. Sci. 21] introduced the notion of tree-size for alternating Turing machines (ATMs) and showed that it is a reasonable measure for classification of complexity classes. We establish in this paper that computations by tree-size and space simultaneously bounded ATMs roughly correspond to computations by time and space simultaneously bounded nondeterministic TMs (NTMs).
We also show that not every polynomial time bounded and sublinear space simultaneously bounded NTM can be simulated by any deterministic TM with a slightly increased time bound and a slightly decreased space bound simultaneously.
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References
Bruss, A.R., Meyer, A.R.: On time-space classes and their relation to the theory of addition. Theor. Comput. Sci.11, 59–69 (1980)
Fischer, M.J., Rosenberg, A.L.: Real-time solutions of the origin-crossing problem. Math. Syst. Theory2, 257–263 (1968)
Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages, and computation. Reading, MA: Addison-Wesley 1979
Kannan, R.: Alternation and the power of nondeterminism. Proceedings 15th Annual ACM Symposium on Theor. of Comput., pp. 344–346 (1983)
Kannan, R.: Towards separating nondeterminism from determinism. Math. Syst. Theory17, 29–45 (1984)
Monien, B., Sudborough, I.H.: Bandwidth constrained NP-complete problems. Theor. Comput. Sci.41, 141–168 (1985)
Moriya, E., Iwata, S., Kasai, T.: A note on some simultaneous relations among time, space, and reversal for single worktape offline Turing machines. Inf. Contr.70, 179–185 (1986)
Paul, W.J., Pippenger, N., Szemerédi, E., Trotter, W.T.: On determinism versus nondeterminism and related problems. Proceedings 24th Annual Symposium on Foundation of Computer Science, pp. 429–438 (1983)
Pippenger, N., Fischer, M.: Relations among complexity measures. J. Assoc. Comput. Mach.26, 361–381 (1979)
Ruzzo, W.L.: Tree-size bounded alternation. J. Comput. Syst. Sci.21, 218–235 (1980)
Ruzzo, W.L.: On uniform circuit complexity. J. Comput. Syst. Sci.22, 365–383 (1981)
Seiferas, J.I., Fischer, M.J., Meyer, A.R.: Separating nondeterministic time complexity classes. J. Assoc. Comput. Mach.25, 146–167 (1978)
Sudborough, I.H.: A note on tape bounded complexity classes and linear context-free languages. J. Assoc. Comput. Mach.22, 499–500 (1975)
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Iwata, S., Kasai, T. & Moriya, E. Relations among simultaneous complexity classes of nondeterministic and alternating Turing machines. Acta Informatica 30, 267–278 (1993). https://doi.org/10.1007/BF01179374
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DOI: https://doi.org/10.1007/BF01179374