Maze recognizing automata (Extended Abstract)

In [2], computations of nondeterministic machines are shown to correspond to threadings of certain mazes. We briefly summarize these results and then obtain some new extentions of them. A new device called a maze-recognizing automaton is introduced. This is a type of finite-state device that crawls through mazes. The following statements are proven equivalent. (i) There is a maze-recognizing automaton which recognizes the threadable mazes. (ii) Every nondeterministic L(n) tape-bounded Turing machine is equivalent to some deterministic L(n) tape-bounded Turing machine, provided L(n) ≥ log2n.