Abstract

While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more than a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a coin which lands heads with probability pX it can compute any function recursive in X with arbitrarily high probability. We also show how the assumption of a non-recursive bias can be weakened by using a..