Katsushi Inoue

A note on two-dimensional probabilistic Turing machines

This paper introduces two-dimensional probabilistic Turing machines (2-ptms), and investigates several properties of them. We first investigate a relationship between two-dimensional alternating finite automata (2-afas) and 2-ptms with error probability less than 12 and with sublogarithmic space, and show that there is a set of square tapes accepted by 2-afa, but not recognized by any o(log-n) space-bounded 2-ptm with error probability less than 12. This partially solves an open problem in Okazaki et al. (Inform. Sci., to appear). We next investigate a space hierarchy of 2-ptms with error probability less than 12 and with sublogarithmic space, and show that if L(n) is space-constructible by a two-dimensional Turing machine, there is a set of square tapes accepted by a strongly L(n) space-bounded two-dimensional deterministic Turing machine, but not recognized by any L(n) space-bounded 2-ptm with error probability less than 12.