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I actually started to read complexity classes of problems. and I know that NP class include P class problems and even more problems call NP-complete ...

as many books define NP class as well But I still dont understand what is the clear definition of NP problems...

According to these books (here I mean Sipser chapter 7 complexity https://www.u-cursos.cl/usuario/777719ab2ddbbdb16d99df29431d3036/mi_blog/r/Introduction_to_the_Theory_of_Computation_by_Michael_Sipser_Third_Edition_Course_Technology.pdf )

NP problems are such problems that algorithms that found for them are nondeterministic or in one other definition these problem have at least one verifier that verifies some nondeterministic answer in polynomial time.

My question is specialy about first definition:

"NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine."

which is highly related to nondeterministic algorithms.

How could them find an answer if it really is in an accepted algorithm I mean if a string is accepted in that algorithm it is absolutly one of the problem answer but if the algorithm guess wrong that doesn't mean the string doesn't lead to accept.

how could we fix that error ?? What is the point of nondeterministic algorithm if its not says the truth??

https://www.google.nl/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwjdjMqRpJrNAhWHrRoKHQa6C90QFggmMAI&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FNondeterministic_algorithm&usg=AFQjCNHmrxGbdoikisJBHhHNtIpAUHoZ2Q

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Niloo
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    The definition of acceptance for nondeterministic algorithms is that the algorithm accepts if any possible execution of the algorithm accepts. – David Richerby Jun 09 '16 at 07:44
  • The order of the nondeterministic algorithm is polynomial....and my another question is because of that definition the time order is exponential ...??? because we must use brute force to understadn the input will accept or not....how its possible we don't know how many running nondeterministic algorithm lead us to checking all possible execution of that algorithm...

    Thanks in advance

     – Niloo Jun 10 '16 at 05:11
  • @DavidRicherby previous cm was for you. – Niloo Jun 10 '16 at 05:12
  • We don't know how to efficiently simulate a nondeterministic machine on a deterministic one. But the definition of nondeterministic machine is what it is and, yes, it's not "realistic". I suggest you refer to your textbook, which should explain the operation of nondeterministic machines. – David Richerby Jun 10 '16 at 07:30

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