Table of Contents
What does it mean for a problem to be in P?
A problem is in P if we can efficiently find a solution if one exists. (Efficiently, here, has a precise mathematical meaning. Practically, it means that large problems aren’t unreasonably difficult to solve.
What is the meaning of class P?
P-Class. The class P consists of those problems that are solvable in polynomial time, i.e. these problems can be solved in time O(nk) in worst-case, where k is constant. These problems are called tractable, while others are called intractable or superpolynomial.
What makes a problem P?
P is the set of all decision problems which can be solved in polynomial time by a deterministic Turing machine. Since they can be solved in polynomial time, they can also be verified in polynomial time. Therefore P is a subset of NP.
What is P problem example?
An example of a decision problem in P is: Given a list of n integers and an integer k, is there an integer in the list greater than k? Plainly the question can be answered in time linear to n by stepping through the list and checking whether an integer is greater than k.
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.
How do you prove a problem is P?
To prove P=NP, you could construct a polynomial time algorithm for any NP complete problem ( emphasis on complete ). If you could do this, then you could also convert this algorithm in polynomial time to a form that can solve any problem in NP.
What is P and NP class 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 difference between P and NP problems?
P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].
How P class problem is different from NP class problem?
In this theory, the class P consists of all those decision problems (defined below) that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time …