On the power of nondeterminism and Las Vegas randomization for two-dimensional finite automata

摘要

The goal of this work is to investigate the computational power of nondeterminism and Las Vegas randomization for two-dimensional finite automata. The following three results are the main contribution of this paper: (ⅰ) Las Vegas (three-way) two-dimensional finite automata are more powerful than (three-way) two-dimensional deterministic ones, (ⅱ) Three-way two-dimensional nondeterministic finite automata are more powerful than three-way two-dimensional Las Vegas finite automata, (ⅲ) There is a strong hierarchy based on the number of computations (as measure of the degree of nondeterminism) for three-way two-dimensional finite automata. These results contrast with the situation for one-way and two-way finite automata, where all these computation modes have the same acceptance power, and the differences may occur only in the sizes of automata. Results (ⅰ) and (ⅱ) provide the first such simultaneous acceptance separation between nondeterminism, Las Vegas, and determinism for a computing model.