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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines
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by Wolfgang Maass PDF
Trans. Amer. Math. Soc. 292 (1985), 675-693 Request permission


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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 675-693
  • MSC: Primary 03D15; Secondary 03D10, 68Q15, 94A17
  • DOI:
  • MathSciNet review: 808746