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What is a complexity class explain NP class of computational complexity using suitable examples?
In computational complexity theory, a complexity class is a set of computational problems of related resource-based complexity. The two most commonly analyzed resources are time and memory. For instance, the class P is the set of decision problems solvable by a deterministic Turing machine in polynomial time.
Why is computational complexity theory important?
Complexity theory helps computer scientists relate and group problems together into complexity classes. Sometimes, if one problem can be solved, it opens a way to solve other problems in its complexity class. An algorithm can be analyzed in terms of its complexity, this is often described in big-O notation.
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 do you mean by NP-hard and NP complete?
A problem is in the class NPC if it is in NP and is as hard as any problem in NP. A problem is NP-hard if all problems in NP are polynomial time reducible to it, even though it may not be in NP itself. These problems are called NP-complete.
What is computational complexity theory?
Computational complexity theory is a subfield of theoretical computer science one of whose primary goals is to classify and compare the practical difficulty of solving problems about finite combinatorial objects – e.g. given two natural numbers n and m, are they relatively prime?
What is the history of computability theory?
In many ways Computability Theory, and its daughter field Complexity Theory, began with proof of the incompleteness of axiomatic systems in 1931. The proof is a tremendously important result in meta-mathematics stating: no recursively axiomatized mathematical system can be both complete and consistent.
Does P ⊊ NP?
A famous conjecture – often regarded as the most fundamental in all of theoretical computer science – states that P is also properly contained in NP – i.e. P ⊊ NP. Demonstrating the non-coincidence of these and other complexity classes remain important open problems in complexity theory.
What is a complexity class?
A complexity class typically refers to a bound on the amount time or space needed to solve the problem in the worst case. Thus, complexity classes describe how difficult a problem is to solve in general.