Question

Show that P is closed under homomorphism iff P = NP.

Short answer

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Step-by-step solution

Homomorphism

The class P includes problems that can be solved in polynomial time. Problems that can be verified in polynomial time are classified as NP.

With the use of a little extra knowledge, it is possible to check the accuracy of a claimed answer in the NP class of decision problems.Homomorphism is defined as a function f that has the property $f\left(x,y\right)=f\left(x\right)f\left(y\right)$on a string.

To Explain the homomorphic image of the language

Let $L\in NP$. Let L be the homomorphic image of language that V accepts. On the inputs . From a to 0 and b to 1, there is a mapping. L' is a language with the alphabet localid="1663225637929" ${\left\{a,b,0,1\right\}}^{*}$. This demonstrates that homomorphism closes the language L.