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Lower bounds by kolmogorov-complexity

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Automata, Languages and Programming (ICALP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

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Abstract

Using Kolmogorov-complexity, we obtain the following new lower bounds.

For on-line nondeterministic Turing machines,

  1. (1)

    simulating 2 pushdown stores by 1 tape requries Ω(n 1.5/logn) time; together with a newly proved O(n 1.5√logn) upper bound [L3], this basically settled the open problem 1 in [DGPR] for 1 tape vs. 2 pushdown case (the case of 1 tape vs 2 tapes was basically settled by [M]);

  2. (2)

    simulating 1 queue by 1 tape requires Ω(n 4/3/logn) time; this brings us closer to a newly proved O(n 1.5√logn) upper bound [L3];

  3. (3)

    simulating 2 tapes by 1 tape requires Ω(n 2/lognloglogn) time; this is a minor improvement of [M]'s Ω(n 2/log 2 nloglogn) lower bound; it is also claimed (full proof contained in [L3]) that the actual languages used in [M] (also here) and [F] do not yield Ω(n 2) lower bound.

To cope with an open question of [GS] of whether a k-head 1-way DFA (k-DFA) can do string matching, we develop a set of techniques and show that 3-DFA cannot do string matching, settling the case k=3. Some other related lower bounds are also presented.

extended abstract

This work was supported in part by an NSF grant DCR-8301766.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853, Ithaca, New York

    Ming Li

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  1. Ming Li
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Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Li, M. (1985). Lower bounds by kolmogorov-complexity. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015764

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  • DOI: https://doi.org/10.1007/BFb0015764

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  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

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