Abstract
Using Kolmogorov-complexity, we obtain the following new lower bounds.
For on-line nondeterministic Turing machines,
-
(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]);
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(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];
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(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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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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