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Chapter 0: Q20P (page 1)

We generally believe that PATH is not NP-complete. Explain the reason behind this belief. Show that proving PATH is not NP-complete would prove P 鈮� NP

Short Answer

Expert verified

If PATH is not NP -complete, thenNP鈮�P$.

Step by step solution

01

To assume PATH would ne NP-complete

EveryAisNPis polynomial time reducible toB.

G is a directed graph that has a directed path.

PATH is not NP - complete:

Let us assume that PATH would be NP - complete.

From the definition of NP - completeness,

02

To explain it’s true or not

ThusP=NP which we believe that it is not true.

Hence, PATH is not NP - complete.

Assume thatP=NP and then show that PATH is NP - complete.

So assume P=NP.

So, PATH is NP - complete.

Thus, if PATH is not NP -complete, thenP鈮�NP

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Give an example in the spirit of the recursion theorem of a program in a real programming language (or a reasonable approximation thereof) that prints itself out.

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