NP-Completeness
A brief review of NP-Completeness
`Tractable' problems and `Intractable' problems.
A tractable problem is polynomial-time solvable
on its input size under the computational model of
deterministic Turing machine. For example,
sorting, ma
CS 6743 (Complexity of Computational Problems) Fall 2008
Instructor: Antonina Kolokolova.
Email: (at cs.mun) kol Oce: ER 6011
Lectures: TBA
Instructor oce hours: TBA.
Course Web Site: http:/www.cs.mun.ca/~kol/courses/6743-f07
All announcements will be pos
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CS6743 Assignment 1
due date: Feb. 26, 2014
1. Design a Turing machine to decide the following languages over the alphabet cfw_0, 1. (i.e., to
describe a high-level algorithm for a machine to decide the language.)
(a) L1 = cfw_w w contains an equal number
MUN CS 6743
Oct 11, 2007
Homework Assignment #2
Due: Oct 30, 2007
1. For each of the problems below, state whether you think that the problem is NP-complete. Justify
your answer by either proving it to be NP-complete (the in NP part can be a couple of sen
CS6743 Assignment 2
due date: March. 26, 2014
1. Show P is closed under union, concatenation, and complement.
2. Show N P is closed under union, concatenation, and the star operation.
3. Show that if P = N P , then every language AP except A = and A = , i
CS 6743
1
Lecture 11 1
Fall 2007
More NP-complete problems
1.1
SubsetSum
Theorem 1. SubsetSum is NP-complete
Proof. We already have seen that SubsetSum is in NP (guess S, check that the sum is equal
to t). Now we will show that SubsetSum is NP-complete by
MUN CS 6743
Sep 24, 2007
Homework Assignment #1
Due: Oct 9, 2007
[15]
1. Turing machines: two-way innite tape
Suppose that we change the denition of a Turing machine to have a tape that is innite in both
directions, rather than one. In this case, the inpu
CS6743 Take Home Examination
Due date: 5:00pm, July 9, 2011 (submit your answer in PDF or MS-word le to
[email protected]).
1. Consider the following algorithm for SAT problem: For every instance
of SAT , we try all possible assignments for the n variables. Th
CS6743 Midterm Examination
(Take home examination.)
Due date: 5:00pm, November 16, 2006 (hand in your answer to my oce).
1. Consider the following algorithm for SAT problem: For every instance
of SAT , we try all possible assignments for the n variables.
CS6743 course out-line
Instructor: Cao An Wang
Introduction (An overview of the course).
Turing Machines.
Non-deterministic Turing Machine
Universal Turing Machine
Properties of Algorithmic Computation.
Characteristics of Algorithms
Unsolvable prob
CS 6743
1
Lecture 18 1
Fall 2007
Interactive proof systems and graph non-isomorphism
The interactive protocols (IP) are also protocols between a probabilistic polytime Verier
and an all-powerful Prover, where after a certain number of rounds of communicat