Question text is in black, my answers in blue.
There are two relevant typos in [AB], pointed out on the course main page -- the more important one is also referred to below.
My question concerns the definition you corrected, where "B ≤r C" is defined to mean that some PTM M takes a string x to a string M(x), such that Pr[C(M(x)) = B(x)] ≥ 2/3. Doesn't Definition 7.1 say that a PTM has to output a single bit, not a string?
Pretty clearly [AB] mean to extend that definition so that a PTM produces a string taken from a probability distribution on strings -- it's pretty clear that a coin-flipping machine can do this so that we can talk about Pr[M(x) = y] as the sum of all path probabilities for M running on x such that y is on the output tape when M halts.
Last modified 15 April 2010