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Show that NP is closed under the star operation

Short Answer

Expert verified

Therefore, NP is closed under star operation.

Step by step solution

01

Randomized of P

On such a randomized single cassette Turing machine, P is a class of languages that can be deduced in polynomial time. Let L become the language chosen by the NP machine to demonstrate that is closed under star operation.

To determine L* in non-deterministic polynomial time, we'll use a non-deterministic Turing machine N .

02

Create N

The creation of N is discussed in the phases that follow.

N=Oninputw:

  1. If w=E , accept.
  2. Split wintok parts in an ad hoc manner.

w=w1,w2,w3,wk

  1. Discover the credentials that display non-deterministically for each w1. Check the certifications for authenticity.
  2. Approve if verification has been completed; otherwise, refuse if verification has not been completed.

A non-deterministic Turing machine N that determines L* in non-deterministic polynomial time. For each w1 guess the certificates that determine non deterministically. Verify the certificates.

  • If verification k done then accept ,
  • Else reject if verification fails.

Here, we constructed a non deterministic turing machine NthatdecidesL* in non deterministic polynomial time.

Hence, NP is closed under star operation.

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