Computational Complexity of Probabilistic Turing Machines

A probabilistic Turing machine is a Turing machine with the ability to make decisions based on the outcomes of unbiased coin tosses. The partial function computed by a probabilistic machine is defined by assigning to each input the output which occurs with probability greater than 12. With this definition, only partial recursive functions are probabilistically computable. The run time and tape of probabilistic machines are defined. A palindrome-like language is described that can be recognized faster by one-tape probabilistic Turing machines than by one-tape deterministic Turing machines. It is shown that every nondeterministic machine can be simulated in the same space by a probabilistic machine with small error probability. Several classes of languages recognized probabilistically in polynomial time are defined and compared with NP.