Theory of one-tape linear-time Turing machines

• Published in: Theoretical computer science Vol. 411; no. 1; pp. 22 - 43
• Main Authors: Tadaki, Kohtaro, Yamakami, Tomoyuki, Lin, Jack C.H.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 2010; Elsevier
• Subjects: Advice; Applied sciences; Automata. Abstract machines. Turing machines; Computer science; control theory; systems; Crossing sequence; Exact sciences and technology; Finite state automaton; Low set; Many-one reducibility; Miscellaneous; One-tape Turing machine; One-way function; Regular language; Theoretical computing; One-way function; Finite state automaton; Low set; Crossing sequence; One-tape Turing machine; Regular language; Advice; Many-one reducibility; Reducibility; Computer theory; Turing machine; Resource; Linear time; Complexity; Polynomial time; Linear theory; Counting
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2009.08.031

A theory of one-tape two-way one-head off-line linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in linear time, where the running time of a machine is defined as the length of any longest computation path. We explore structural properties of one-tape linear-time Turing machines and clarify how the machines’ resources affect their computational patterns and power.