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## What would prove that P NP?

One way to prove that P = NP is to **show that the complexity measure TM (n) for some NP problem, like the 3-CNF-SAT problem, cannot be reduced to a polynomial time**. We will show that the 3-CNF-SAT problem behaves as a common safe problem and that its complexity is time dependent.

## What is P and NP?

**P stands for polynomial time.** **NP stands for non-deterministic polynomial time**. Definitions: Polynomial time means that the complexity of the algorithm is O(n^k), where n is the size of your data (e. g. number of elements in a list to be sorted), and k is a constant.

## 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].

## What is NP and P in computational theory?

**The class of questions for which an answer can be verified in polynomial time is NP, which stands for “nondeterministic polynomial time”**. An answer to the P versus NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time.

## Why is P vs NP important?

**If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them**. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.

## What are tractable and intractable problems?

Tractable Problem: **a problem that is solvable by a polynomial-time algorithm.** **The upper bound is polynomial.** **Intractable Problem: a problem that cannot be solved by a polynomial-time al- gorithm**.

## What are deterministic and nondeterministic algorithms?

In deterministic algorithm, for a given particular input, the computer will always produce the same output going through the same states but in case of non-deterministic algorithm, for the same input, the compiler may produce different output in different runs.

## What is deterministic polynomial time problem?

NP is **the set of decision problems for which the problem instances, where the answer is “yes”, have proofs verifiable in polynomial time by a deterministic Turing machine**, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine.

## What is P deterministic polynomial time?

In computational complexity theory, P, also known as PTIME or DTIME(n), is a fundamental complexity class. It **contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time**.

## Why is NP non-deterministic?

Non-deterministic polynomial time (NP) is actually **a marker used to point to a set of problems and bounds of the capability of certain types of computing**. NP refers to the set of problems that can be solved in polynomial time by a non-deterministic Turing machine.

## What is P and NP class in automata?

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.