Non-deterministic Polynomial Time (NP) refers to a class of decision problems for which a solution can be verified in polynomial time by a deterministic Turing machine, but it is unknown whether they can be solved in polynomial time. The concept is central to computational complexity theory, particularly in understanding the P vs NP problem, which questions whether every problem whose solution can be quickly verified can also be quickly solved.

Non-deterministic Polynomial Time

Decision problems are questions with a yes or no answer, often used in computational complexity to determine whether a given problem can be solved within certain resource constraints. They are fundamental in distinguishing between different complexity classes, such as P, NP, and NP-complete, which help in understanding the efficiency of algorithms.

decision problems

Solution verification is the process of ensuring that a solution meets predefined requirements and specifications, confirming its accuracy and reliability. It involves systematic checks and validation techniques to ensure that the solution performs as intended in all expected scenarios.

Solution Verification

deterministic Turing machine

Polynomial time refers to the class of computational problems for which the time required to solve the problem using an algorithm is a polynomial function of the size of the input. This is significant in computer science because problems solvable in polynomial time are considered efficiently solvable or 'tractable'.

Polynomial Time

Computational Complexity Theory is a branch of theoretical computer science that focuses on classifying computational problems based on their inherent difficulty and quantifying the resources needed to solve them. It provides a framework to understand the efficiency of algorithms and the limitations of what can be computed in a reasonable amount of time and space.

computational complexity theory

The P vs NP Problem is a fundamental question in computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Solving this problem would have profound implications for fields such as cryptography, algorithm design, and computational complexity theory.

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