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

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.