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Chapter 7: Q22P (page 324)

Let DOUBLE-SAT={}has at least two satisfying assignments}. Show thatDOUBLE-SATisNP- complete

Short Answer

Expert verified

TheDOUBLE-SAT鈥�is鈥�NP-complete.

Step by step solution

01

To proof DOUBLE-SAT∈NP.

DOUBLE - SAT鈭�NP

NTM N can decide double-SAT as follows:

Non-deteministicallyguess two Boolean assignments t1鈥�and鈥�t2which are different from each other.

If both t1鈥�and鈥�t2satisfies then accept otherwise, reject.

Hence,DOUBLE-SAT鈭�NP.

02

Step 2:To Explain DOUBLE-SAT

SAT猢�pDOUBLE-SAT

The function f which maps an instance D O U B L E-S A T work as follows:

蠒'=蠒鈭�x1鈭�x2

Where x1鈥�and鈥�x2re new variables. They do not occur in $\phi$.

Thus, theDOUBLE-SAT is NP - complete.

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