Deciding according to the shortest computations

Authors:
Florin Manea
Affiliations:
Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, Magdeburg, Germany and Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

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Abstract

In this paper we propose, and analyze from the computational complexity point of view, a new variant of nondeterministic Turing machines. Such a machine accepts a given input word if and only if one of its shortest possible computations on that word is accepting; on the other hand, the machine rejects the input word when all the shortest computations performed by the machine on that word are rejecting. Our main results are two new characterizations of PNP[log] and PNP in terms of the time complexity classes defined for such machines.