What is the definition of the complexity class NP hard of decision problems?

(definition) Definition: The complexity class of decision problems that are intrinsically harder than those that can be solved by a nondeterministic Turing machine in polynomial time.

What is NP complexity class?

The class NP-Complete (NPC): class of the “hardest” problems in NP. • this class has property that if any NPC problem can. be solved in polynomial time, then all problems in NP can be solved in polynomial-time.

What is formal complexity class?

Complexity classes are sets of related computational problems. They are defined in terms of the computational difficulty of solving the problems contained within them with respect to particular computational resources like time or memory.

What is the meaning of NP-hard problems?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

What is meant by P and NP class of problems explain in detail?

Step 1 − If a problem is in class P, it is nothing but we can find a solution to that type of problem in polynomial time. Step 2 − If a problem is in class NP, it is nothing but that we can verify a possible solution in polynomial time.

What is meant by P and NP class of problems?

P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

What is the relationship among the NP NP hard NP-complete and P problems explain?

All other problems in class NP can be reduced to problem p in polynomial time. NP-hard problems are partly similar but more difficult problems than NP complete problems. They don’t themselves belong to class NP (or if they do, nobody has invented it, yet), but all problems in class NP can be reduced to them.