# CMPSCI 601: Theory of Computation

### David Mix Barrington

### Spring, 2010

# Questions and Answers on Homework Assignment #7

#### HW#7 is due on paper in discussion class or to the main
office by 4:00 p.m., Friday, 23 April 2010.

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.

**Question 7.1, posted 15 April 2010:**
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