A space lower bound of two-dimensional probabilistic turing machines

Authors:
Yuji Sasaki;Katsushi Inoue;Akira Ito;Yue Wang
Affiliations:
Chitose Factory, Hitachi Kokusai Electronocs, Chitose, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Japan;Media and Information Technology Center, Yamaguchi University, Ube, Japan
Venue:
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Year:
2002

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Abstract

This paper shows a sublogarithmic space lower bound for two-dimensional probabilistic Turing machines (2-ptm's) over square tapes with bounded error, and shows, using this space lower bound theorem, that a specific set is not recognized by any o(log n) space-bounded 2- ptm. Furthermore, the paper investigates a relationship between 2-ptm's and two-dimensional Turing machines with both nondeterministic and probabilistic states, which we call "two-dimensional stochastic Turing machines (2-stm's)", and shows that for any loglog n ≤ = L(n) = o(log n), L(n) space-bounded 2-ptm's with bounded error are less powerful than L(n) space-bounded 2-stm's with bounded error which start in nondeterministic mode, and make only one alternation between nondeterministic and probabilistic modes.