Can we can prove that Np and P class are the same by finding an efficient polynomial solution for any NP complete problem on a deterministic TM?
The question of whether the classes P and NP are equivalent is one of the most significant and long-standing open problems in the field of computational complexity theory. To address this question, it is essential to understand the definitions and properties of these classes, as well as the implications of finding an efficient polynomial-time solution
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Complexity, Time complexity classes P and NP
Are P and NP actually the same complexity class?
The question of whether P equals NP is one of the most profound and unresolved problems in computer science and mathematics. This problem lies at the heart of computational complexity theory, a field that studies the inherent difficulty of computational problems and classifies them according to the resources needed to solve them. To understand the
Why is it widely believed that P does not equal NP?
In the field of Cybersecurity and Computational Complexity Theory, the question of whether P equals NP has been a topic of great interest and debate for several decades. The prevailing belief among experts is that P does not equal NP. This belief is based on a combination of theoretical and practical considerations, as well as
Describe the process of constructing a polynomial time verifier from a polynomial time non-deterministic Turing machine.
A polynomial time verifier can be constructed from a polynomial time non-deterministic Turing machine (NTM) by following a systematic process. To understand this process, it is essential to have a clear understanding of the concepts of complexity theory, particularly the classes P and NP, and the notion of polynomial verifiability. In computational complexity theory, P