Connections among space-bounded and multihead probabilistic automata

Abstract

We show that the heads of multihead unbounded-error or bounded-error or one-sided-error probabilistic finite automata are equivalent alternatives to the storage tapes of the corresponding probabilistic Turing machines (Theorem 1). These results parallel the classic ones concerning deterministic and nondeterministic automata. Several important properties of logarithmic-space (nondeterministic and probabilistic) Turing machines follow trivially (Observations 1--3) from the more refined versions that we prove in the setting of multihead finite automata (Theorems 2--4)