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Solutions to Problem Set 4
Fall, 2013
Due: Monday, December 2, beginning of lecture
1. Show that if k is any positive integer there is function h : cfw_0, 1 cfw_0, 1 which is
computable in log space and satises
|h(x)| = |x|k
Note we may assume tha
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Solutions to Problem Set 2
Fall, 2013
Due: Friday, October 18, beginning of tutorial
1. Let P AL be the set of even length palindromes. Thus
P AL = cfw_wwR | w cfw_0, 1
Let
A = cfw_ M | M is a TM and L(M ) P AL
Is A semi-decidable?
Is A semi-deci
CSC463S
Problem Set 2
Winter, 2016
Due: Friday, February 12, beginning of tutorial
NOTE: Each problem set counts 15% of your mark, and it is important to do your own
work. You may consult with others concerning the general approach for solving problems on
CSC463S
Problem Set 1
Winter, 2016
Due: Friday, January 29, beginning of tutorial
NOTE: Each problem set counts 15% of your mark, and it is important to do your own
work. You may consult with others concerning the general approach for solving problems on
CSC 364S Notes
University of Toronto
Spring, 2003
Computability and Noncomputability
Up to now, we have been concerned with how eciently various problems can be computed.
Now we will address the issue of which problems can be computed at all, even when we
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Last Name
Midterm Test
October 25, 2013
First Name & Initial
Student No.
NO AIDS ALLOWED. Answer ALL questions on test paper. Use backs of sheets for scratch work.
Total Marks: 40
[10]
1. Let B be a decidable set. For each y let
By = cfw_x | x, y
CSC 364S
Notes
Spring, 2003
Turing Machines and Reductions
So far, we have discussed a number of problems for which we were able to come up with
polynomial time algorithms, and some for which we were not able to nd a polynomial time
algorithm. We never ri
CSC 463F
Solutions to Midterm Test
Last Name
October 25, 2013
First Name & Initial
Student No.
NO AIDS ALLOWED. Answer ALL questions on test paper. Use backs of sheets for scratch work.
Total Marks: 40
[10]
1. Let B be a decidable set. For each y let
By =
CSC 463F
Supplementary Notes
Fall, 2012
CFLs and Noncomputability
These brief notes are intended to supplement the text Introduction to the Theory of
Computation by Michael Sipser, Third Edition.
We are especially interested in the proof of Theorem 5.13 (
CSC 364S Notes
University of Toronto, Spring, 2003
NP and NP-Completeness
NP
NP is a class of languages that contains all of P, but which most people think also contains
many languages that arent in P. Informally, a language L is in NP if there is a guess
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Markers Comments for Problem Set 4
Mika Gs
Problem 1
The crux of the problem was to show how a log-space algorithm can count up to nk where
n is the size of the input. Simply k nested for loops would have done the trick, but most
students were eag
CSC463F
Solutions to Problem Set 1
Fall, 2013
Due: Friday, September 27, beginning of tutorial
1. Let
A = cfw_w cfw_0, 1 | w has equally many 0s and 1s
Give a Turing machine M such that L(M ) = A, and M is a decider (i.e. halts on all
inputs). Your TM mus
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Solutions to Problem Set 3
Fall, 2013
Due: Friday, November 15, beginning of tutorial
1. Motivation: Let COM P OSIT ES = cfw_x | x = yz for integers y, z > 1. It is easy
to see that COM P OSIT ES NP, because the pair y, z is a certicate for x
COM
CSC463S
Solutions to Problem Set 1
Winter, 2016
Due: Friday, January 29, beginning of tutorial
1. Give a Turing machine which copies over its input string. That is, if the input is a string
w over the alphabet cfw_0, 1, then the machine should halt with t