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Reversal-bounded and visit-bounded realtime computations

  • Andreas Brandstädt
  • Klaus Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)

Abstract

First it is dealt with the class RBQ (also sometimes called BNP) of all languages acceptable in linear time by reversal-bounded nondeterministic multitape Turing machines.

It has been shown (see /2/) that the RBQ languages can already be accepted by nondeterministic realtime machines having only three pushdown stores and working with at most one reversal per pushdown store. We show that these three pushdown stores can be replaced by two checking stacks each making at most two reversals. In this result "two" cannot be replaced by "one" because of a recent result by HULL (see /7/).

The class RBQ is known to be closed under intersection and the AFL operations except for Kleene star. It is conjectured that RBQ is not closed under Kleene star (see /3/). We show that the least intersection closed AFL containing RBQ (or, equivalently, the least intersection closed semi-AFL containing the set PAL*) coincides with the class VBQ of all languages acceptable in linear time by visit-bounded nondeterministic multitape Turing machines. Furthermore, the VBQ languages can already be accepted by nondeterministic realtime machines having only three pushdown stores and working with at most 3 visits (or, equivalently, having only two checking stacks and working with at most 4 visits). These results cannot be improved unless RBQ=VBQ.

Keywords

Linear Time Relative Minimum Input Length Real Input Pushdown Automaton 
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. /1/.
    Book, R.V., Greibach, S.A., Quasi-Realtime Languages, Math. Syst. Theory 4(1970), 97–111CrossRefGoogle Scholar
  2. /2/.
    Book, R.V., Nivat, M., Paterson, M., Reversal-Bounded Acceptors and Intersections of Linear Languages, SIAM J. Computing 3(1974), 283–295CrossRefGoogle Scholar
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    Book, R.V., Nivat, M., Linear Languages and the Intersection Closures of Classes of Languages, SIAM J. Computing 7(1978), 167–177CrossRefGoogle Scholar
  4. /4/.
    Ginsburg, S., Algebraic and automata theoretic properties of formal languages, North-Holland 1975Google Scholar
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    Greibach, S.A., One way finite visit automata, Theor. Comp. Science 6 (1978), 175–221Google Scholar
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    Greibach, S.A., Checking automata and one-way stack languages, J. Comp. Syst. Sci. 3 (1969), 196–217Google Scholar
  7. /7/.
    Hull, R.B., Containments between intersection families of linear and reset langugges, Ph. D. thesis 1979Google Scholar
  8. /8/.
    Wechsung, G., The oscillation complexity and a hierarchie of context-free languages (extended abstract), Fundamentals of Computation Theory FCT '79, Akademie-Verlag Berlin 1979, 508–515Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  • Klaus Wagner
    • 1
  1. 1.Section of MathematicsFriedrich-Schiller University JenaGerman Democratic Republic

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