Improved simulation of nondeterministic Turing machines

Authors:
Subrahmanyam Kalyanasundaram;Richard J. Lipton;Kenneth W. Regan;Farbod Shokrieh
Affiliations:
College of Computing, Georgia Tech, Atlanta, GA 30332, United States;College of Computing, Georgia Tech, Atlanta, GA 30332, United States;Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY 14260, United States;School of Electrical and Computer Engineering, Georgia Tech, Atlanta, GA 30332, United States
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

The standard simulation of a nondeterministic Turing machine (NTM) by a deterministic one essentially searches a large bounded-degree graph whose size is exponential in the running time of the NTM. The graph is the natural one defined by the configurations of the NTM. All methods in the literature have required time linear in the size S of this graph. This paper presents a new simulation method that runs in time O@?(S). The search savings exploit the one-dimensional nature of Turing machine tapes. In addition, we remove most of the time dependence on nondeterministic choices of states and tape head movements.