hwsol1.3 - CSci 5403, Spring 2010 Brian Berzins Derived...

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Unformatted text preview: CSci 5403, Spring 2010 Brian Berzins Derived with: Stefan Nelson-Lindall, Hannah Jaber Homework 1.3 Solution (a) Show that quadeq is NP-complete. First: We show that quadeq NP by demonstrating that there is a polynomial time verifier for it. One such verifier takes the quadratic sys- tem and a variable assignment ~x { , 1 } n and checks if each quadratic equation in the system evaluates to true. This requires m n 2 (polyno- mial) time. Therefore quadeq NP . Second: We show that quadeq is NP-hard by a reduction from 3sat . Let be a 3sat boolean formula. Construct the reduction as follows: for each clause let the three literals be a , b , and c . Add the following equation to the system of quadratics: az 1 + bz 2 + cz 3 = 1 mod 2 where z 1 , z 2 and z 3 are variables that do not appear in any previous equation in our system. The variables a , b , and c represent the appro- priate literals in the clause and remain consistent across all clauses in . If a negated literal....
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This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.

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hwsol1.3 - CSci 5403, Spring 2010 Brian Berzins Derived...

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