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Multihead two-way probabilistic finite automata

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LATIN '95: Theoretical Informatics (LATIN 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 911))

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Abstract

We present properties of multihead two-way probabilistic finite automata that parallel those of their deterministic and nondeterministic counterparts. We define multihead probabilistic finite automata with “log-space constructible” transition probabilities, and we describe a simple technique to simulate these automata by standard log-space probabilistic Turing machines. Next, we represent log-space probabilistic complexity classes as proper hierarchies based on corresponding multihead two-way probabilistic finite automata, and we show their (deterministic log-space) reducibility to the second levels of these hierarchies. We relate the number of heads of a multihead probabilistic finite automaton to the bandwidth of its configuration transition matrix for an input string; partially based on this relation, we find a simpler log-space complete problem for PL (the class of languages recognized by log-space unbounded-error probabilistic Turing machines), and we discuss possibilities for space-efficient deterministic simulations of probabilistic automata.

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References

  1. Borodin, A., Cook, S., and Pippenger, N. Parallel computation for wellendowed rings and space-bounded probabilistic machines, Information and Control 48, 1983, pp. 113–136.

    Article  Google Scholar 

  2. Dijkstra, E. W. Making a fair roulette from a possibly biased coin, Information Processing Letters 36, 1990, pp. 193–193.

    Article  Google Scholar 

  3. Dwork, C., and Stockmeyer, L. Finite state verifiers I: the power of interaction, J. ACM, Vol. 39, 1992, pp. 800–828.

    Article  Google Scholar 

  4. Freivalds, R., and Karpinski, M. Lower Space Bounds for Randomized Computation, Proceedings ICALP 94, LNCS 820, 1994, pp. 580–592.

    Google Scholar 

  5. Freivalds, R. Probabilistic two-way machines, Proceedings MFCS'81, LNCS 118, 1981, pp. 33–45.

    Google Scholar 

  6. Freivalds, R. Complexity of probabilistic versus deterministic automata, Baltic Computer Science, Selected Papers, LNCS 502, 1991, pp. 565–613.

    Google Scholar 

  7. Gill, J. Computational complexity of probabilistic Turing machines, SIAM J. Comput. 6, 1977, pp. 675–695.

    Article  Google Scholar 

  8. Hartmanis, J. On Non-Determinancy in Simple Computing Devices, Acta Informatica 1, 1972, pp. 336–344.

    Google Scholar 

  9. Ibarra, O. H. One two-way multihead automata, J. Comp. and System Sc. 7, 1973, pp. 28–36.

    Google Scholar 

  10. Immerman, N. Nondeterministic space is closed under complementation, SIAM J. Comput. Vol 17, 1988, pp. 935–938.

    Article  Google Scholar 

  11. Jones, N.D. Space-bounded reducibility among combinatorial problems, J. Comp. and System Sc. 11, 1975, pp. 68–75.

    Google Scholar 

  12. Jung, H. Relationships between probabilistic and deterministic tape complexity, Proceedings MFCS'81, LNCS 118, 1981, pp. 339–346.

    Google Scholar 

  13. Jung, H. On probabilistic tape complexity and fast circuits for matrix inversion problems, Proceedings ICALP 84, LNCS 172, 1984, pp. 281–291.

    Google Scholar 

  14. Jung, H. On probabilistic time and space, Proceedings ICALP 85, LNCS 194, 1985, pp. 310–317.

    Google Scholar 

  15. Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata, Diskretnaya Matematika, 1989, vol. 1, no 4, pp. 63–77 (Russian).

    Google Scholar 

  16. Kaneps, J. Regularity of one-letter languages acceptable by 2-way finite probabilistic automata, Proceedings FCT'91, LNCS 529, 1991, pp. 287–296.

    Google Scholar 

  17. King, K.N. Alternating multihead finite automata, Theoretical Computer Science, Vol. 61, 1988, pp. 149–174.

    Google Scholar 

  18. Kuklin, Yu. I. Two-way probabilistic automata, Avtomatika i vycislitelnaja tekhnika, No 5, 1973, pp. 35–36. (Russian)

    Google Scholar 

  19. Lewis II, P.M., Stearn, R., and Hartmanis, J. Memory bounds for recognition of context-free and context-sensitive languages, IEEE Conference Record on Switching Circuit Theory and Logical Design, 1965, pp. 191–202.

    Google Scholar 

  20. Macarie, I.I. Space-efficient deterministic simulations of probabilistic automata, Proceedings STACS'94, LNCS 775, 1994, pp. 109–122.

    Google Scholar 

  21. Macarie, I.I. Decreasing the bandwidth of a configuration transition matrix, To appear in Information Processing Letters.

    Google Scholar 

  22. Monien, B. Transformational Methods and their Application to Complexity Problems, Acta Informatica 6, 1976, pp. 95–108.

    Google Scholar 

  23. Monien, B. Two-way Multihead Automata over a one-letter alphabet, R.A.I.R.O. Informatique theoretique/Theoretical Informatics 14, No. 1, 1980, pp. 67–82.

    Google Scholar 

  24. John von Neumann. Various techniques used in connection with random digits, in John von Neumann, Collected Works, Vol. V, Pergamon, Oxford, 1963 pp. 768–770.

    Google Scholar 

  25. Paz, A. Introduction to Probabilistic Automata, Academic Press, New York, London, 1971.

    Google Scholar 

  26. Ravikumar, B. Some Observations on 2-way Probabilistic Finite Automata, TR92-208, May 1992, Dept. of Comp. Science and Statistics, Univ. of Rhode Island.

    Google Scholar 

  27. Ruzzo, W., Simon, J., and Tompa, M. Space-bounded hierarchies and probabilistic computation, Proceedings STOC'82, 1982 pp. 215–223.

    Google Scholar 

  28. Santos, E. Computability by probabilistic Turing machines, Trans. Amer. Math. Soc. 159, 1971, pp. 165–184.

    Google Scholar 

  29. Savitch, W.J. Relationships between nondeterministic and deterministic tape complexity, J. Comp. and System Sc. 4, 1970, pp. 177–192.

    Google Scholar 

  30. Seiferas, J. I. Relating Refined Space Complexity Classes, J. Comp. and System Sc. 14, 1977, pp. 100–129.

    Google Scholar 

  31. Seiferas, J.I. Techniques for Separating Space Complexity Classes, J. Comp. and System Sc. 14, 1977, pp. 73–99.

    Google Scholar 

  32. Simon, J. On the difference between one and many, Proceedings, ICALP'77, LNCS 52, 1977, pp. 480–491.

    Google Scholar 

  33. Simon, J. Space-bounded probabilistic Turing machine complexity classes are closed under complement, Proceedings STOC'81, 1981, pp. 158–167.

    Google Scholar 

  34. Sudborough, I.H. On Tape-Bounded Complexity Classes and Multihead Finite Automata, J. Comp. and System Sc. 10, 1975, pp. 62–76.

    Google Scholar 

  35. Szelepcsenyi, R. The method of forced enumeration for nondeterministic automata, Acta Informatica, 1988, pp. 279–284.

    Google Scholar 

  36. Turakainen, P. On languages representable in rational probabilistic automata, Ann. Acad. Sci. Fenn. AI 439.

    Google Scholar 

  37. Yao, A.C. and Rivest, R.L. K+1 heads are better than K, J. ACM, Vol. 25, 1978, pp. 337–340.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Rochester, USA

    Ioan I. Macarie

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  1. Ioan I. Macarie
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Ricardo Baeza-Yates Eric Goles Patricio V. Poblete

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© 1995 Springer-Verlag Berlin Heidelberg

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Macarie, I.I. (1995). Multihead two-way probabilistic finite automata. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_103

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  • DOI: https://doi.org/10.1007/3-540-59175-3_103

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  • Print ISBN: 978-3-540-59175-7

  • Online ISBN: 978-3-540-49220-7

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