On space-bounded synchronized alternating turing machines

  • Oscar H. Ibarra
  • Nicholas Q. Trân
Commanications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)

Abstract

We continue the study of the computational power of synchronized alternating Turing machines (SATM), introduced in [Hro86, Slo87, Slo88a, Slo88b] to allow communication via synchronization among processes of alternating Turing machines. We compare the classes of languages accepted by the four main classes of space-bounded synchronized alternating Turing machines obtained by adding or removing off-line capability and nondeterminism (1SUTM(S(n)), SUTM(S(n)), 1SATM(S(n)), and SATM(S(n))). We show various strict inclusions, equalities, and incomparabilities between these classes and those accepted by plain and modified alternating Turing machines.

For deterministic synchronized alternating finite automata with at most k processes (1DSA(k)FA and DSA(k)FA) we establish a tight hierarchy on the number of processes for the one-way case, namely \(\mathcal{L}(1DSA(n)FA) \subset \mathcal{L}(1DSA(n + 1)FA)\) for all n>0, and show that \(\mathcal{L}(1DFA(2)) - \cup _{k = 1}^\infty \mathcal{L}(DSA(k)FA) \ne \not 0\), where DFA(k) denotes deterministic k-head finite automata. Finally we investigate closure properties under Boolean operations for some of these classes of languages.

Keywords

Turing Machine Binary String Computation Tree Finite Automaton Kolmogorov Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [CIR87]
    J. H. Chang, O. H. Ibarra, and B. Ravikumar, Some observations concerning alternating Turing machines using small space, IPL, 25 (1987), pp. 1–9.Google Scholar
  2. [CKS81]
    A. K. Chandra, D. K. Kozen, and J. Stockmeyer, Alternation, J. ACM, 28 (1981), pp. 114–133.Google Scholar
  3. [DHK+89]
    [DHK+89] J. Dassow, J. Hromkovič, J. Karhumäki, B. Rovan, and A. Slobodová, On the power of synchronization in parallel computations, in Proc. 14th MFCS'89, Lecture Notes in Computer Science 379, Springer-Verlag, 1989, pp. 196–206.Google Scholar
  4. [HKRS89]
    J. Hromkovič, J. Karhumäki, B. Rovan, and A. Slobodová, On the power of synchronization in parallel computations, tech. report, Comenius University, Bratislava, Czechoslovakia, Department of Theoretical Cybernetics and Institute of Computer Science, 1989.Google Scholar
  5. [Hro86]
    J. Hromkovič, How to organize the communication among parallel processes in alternating computations. Manuscript, January 1986.Google Scholar
  6. [IIT87]
    A. Ito, K. Inoue, and I. Takanami, A note on alternating Turing machines using small space, Trans. IECE Japan E, 70 (1987), pp. 990–996.Google Scholar
  7. [IIT89]
    K. Inoue, A. Ito, and I. Takanami, Alternating Turing machines with modified accepting structure, tech. report, Yamaguchi University, Ube, 755 Japan, Department of Electronics, 1989.Google Scholar
  8. [Imm88]
    N. Immerman, Nondeterministic space is closed under complementation, in Proc. 3rd IEEE Structure in Complexity Theory Conference, 1988, pp. 112–115.Google Scholar
  9. [ITV85]
    K. Inoue, I. Takanami, and R. Vollmar, Alternating on-line Turing machines with only universal states and small space bounds, Theoret. Comp. Sci, 41 (1985), pp. 331–339.Google Scholar
  10. [Kin81]
    K. N. King, Alternating finite automata, PhD thesis, University of California, Berkeley, 1981.Google Scholar
  11. [LV88]
    M. Li and P. M. B. Vitányi, Two decades of applied Kolmogorov complexity in memoriam Andrei Nikolaevich Kolmogorov 1903–1987, in Proc. 3rd IEEE Structure in Complexity Theory Conference, 1988, pp. 80–101.Google Scholar
  12. [PSS81]
    W. J. Paul, J. I. Seiferas, and J. Simon, An information-theoretic approach to time bounds for on-line computation, JCSS, 23 (1981), pp. 108–126.Google Scholar
  13. [Slo87]
    A. Slobodová, On the power of communication in alternating computations. Student Research Papers Competition, Section Computer Science (in Slovac), Comenius University, Bratislava, Czechoslovakia, April 1987.Google Scholar
  14. [Slo88a]
    , On the power of communication in alternating machines, in Proc. 13th MFCS'88, Lecture Notes in Computer Science 324, Springer-Verlag, 1988, pp. 518–528.Google Scholar
  15. [Slo88b]
    , Some properties of space-bounded synchronized alternating Turing machines with only universal states, in Proc. 5th IMYCS'88, Lecture Notes in Computer Science 381, Springer-Verlag, 1988, pp. 102–113.Google Scholar
  16. [Wie87]
    J. Wiedermann, On the power of synchronization, tech. report, VUSEI-AR, Bratislava, Czechoslovakia, 1987.Google Scholar
  17. [YR78]
    A. C. C. Yao and R. L. Rivest, k + 1 heads are better than k, JACM, 25 (1978), pp. 337–340.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Nicholas Q. Trân
    • 1
  1. 1.Department of Computer ScienceUniversity of California at Santa BarbaraSanta Barbara

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