Turing Machines with Sublogarithmic Space

Andrzej Szepietowski (eds.)3540583556, 9783540583554, 0387583556

This comprehensive monograph investigates the computational power of Turing machines with sublogarithmic space. The studies are devoted to the Turing machine model introduced by Stearns, Hartmanis, and Lewis (1965) with a two-way read-only input tape and a separate two-way read-write work tape. The book presents the key results on space complexity, also as regards the classes of languages acceptable, under the perspective of a sublogarithmic number of cells used during computation. It originates from courses given by the author at the Technical University of Gdansk and Gdansk University in 1991 and 1992. It was finalized in 1994 when the author visited Paderborn University and includes the most recent contributions to the field.

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Table of contents :
Introduction….Pages 1-6
Basic Notions….Pages 7-14
Languages acceptable with logarithmic space….Pages 15-20
Examples of languages acceptable with sublogarithmic space….Pages 21-25
Lower bounds for accepting non-regular languages….Pages 27-36
Space constructible functions….Pages 37-45
Halting property and closure under complement….Pages 47-59
Strong versus weak mode of space complexity….Pages 61-66
Padding….Pages 67-75
Deterministic versus nondeterministic Turing machines….Pages 77-80
Space hierarchy….Pages 81-84
Closure under concatenation….Pages 85-87
Alternating hierarchy….Pages 89-94
Independent complement….Pages 95-97
Other models of Turing machines….Pages 99-110