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Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines

Author: Wolfgang Maass
Journal: Trans. Amer. Math. Soc. 292 (1985), 675-693
MSC: Primary 03D15; Secondary 03D10, 68Q15, 94A17
MathSciNet review: 808746
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Abstract: We introduce new techniques for proving quadratic lower bounds for deterministic and nondeterministic $ 1$-tape Turing machines (all considered Turing machines have an additional one-way input tape). In particular, we derive for the simulation of $ 2$-tape Turing machines by $ 1$-tape Turing machines an optimal quadratic lower bound in the deterministic case and a nearly optimal lower bound in the nondeterministic case. This answers the rather old question whether the computing power of the considered types of Turing machines is significantly increased when more than one tape is used (problem Nos. 1 and 7 in the list of Duris, Galil, Paul, Reischuk [3]). Further, we demonstrate a substantial superiority of nondeterminism over determinism and of co-nondeterminism over nondeterminism for $ 1$-tape Turing machines.

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