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# Lec19NPC - April 13th Class Notes Hw 5 will be worth 50...

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April 13 th Class Notes Hw# 5 will be worth 50 points and it will be posted tonight or tomorrow

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Definition of the Class NP 1)Language that can be accepted on a nondeterministic TM in polynomial time. If it isn’t in the language it may not reject in polynomial time 2)Given a certificate, one can verify in polynomial time whether or not an input is in the language
Hampath={<G>|G has a Hamiltonian path} This doesn’t have a Hampath since there are three vertices of degree one and we would need a way in and a way out

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The graph below has a hampath
One Hampath for the diagram is A-B-D-F-E-C This path can be used to represent a certificate. Verifying this path would take less than polynomial time We can also prove that this can NP by checking all path options at once

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Hampath={<G>|Gdoesn’t have a hamiltonion path There is not an easy certificate that can be generated to prove that no path exists This is Co-NP (compliment NP)
Composites ={n|n exists Z+ and there exists a p and q such that n=p*q} Can easily produce a certificate ie if n=143 p=11 and q=13

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Primes={n|there is no way to represent n=p*q, where pa nd q exist in Z+ and P>1 and q>1} This has been shown to be O(n**6) by AKS
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Lec19NPC - April 13th Class Notes Hw 5 will be worth 50...

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