Chapter 7: Q22P (page 324)

Let $D O U B L E - S A T = {}$ has at least two satisfying assignments}. Show that $D O U B L E - S A T i s N P -$ complete

Short Answer

Expert verified

The $D O U B L E - S A T i s N P - c o m p l e t e .$

Step by step solution

To proof DOUBLE-SAT∈NP.

$DOUBLE - SAT \in NP$

NTM N can decide double-SAT as follows:

Non-deteministicallyguess two Boolean assignments $t_{1} a n d t_{2}$ which are different from each other.

If both $t_{1} a n d t_{2}$ satisfies then accept otherwise, reject.

Hence, $D O U B L E - S A T \in N P .$

Step 2:To Explain DOUBLE-SAT

$S A T ⩽_{p} D O U B L E - S A T$

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

$ϕ^{'} = ϕ \land (x_{1} \lor x_{2})$

Where $x_{1} a n d x_{2}$ re new variables. They do not occur in $\phi$.

Thus, the $D O U B L E - S A T$ is NP - complete.

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Let $D O U B L E - S A T = {}$ has at least two satisfying assignments}. Show that $D O U B L E - S A T i s N P -$ complete

Short Answer

Step by step solution

To proof DOUBLE-SAT∈NP.

Step 2:To Explain DOUBLE-SAT

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

Short Answer

Step by step solution

To proof DOUBLE-SAT∈NP.

Step 2:To Explain DOUBLE-SAT

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Computer Systems

Algorithms in Computer Science

Computer Network

Computer Organisation and Architecture

Theory of Computation

Study anywhere. Anytime. Across all devices.

Let $D O U B L E - S A T = {}$ has at least two satisfying assignments}. Show that $D O U B L E - S A T i s N P -$ complete