Some Properties of Multihead Automata on Four-Dimensional Input Tapes

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The comparative study of the computational powers of deterministic and nondeterministic computations is one of the central tasks of complexity theory. This paper investigates the computational power of nondeterministic computing devices with restricted nondeterminism. There are only few results measuring the computational power of restricted nondeterminism. In general, there are three possibilities to measure the amount of nondeterminism in computation. In this paper, we consider the possibility to count the number of different nondeterministic computation paths on any input. In particular, we deal with seven-way four-dimensional finite automata with multiple input heads operating on four-dimensional input tapes.
2009-09-30