### give two examples about the attempts to solve p versus np problem.

In this paper, you are required to provide two examples about the attempts to solve p versus np problem. You are guided to combine between discrete math field and computer science and follow the basic research steps.

1) the subject should combine between discrete math field and computer science .

2) at the end of the research give two examples about the attempts to solve p versus np problem.

3)follow the basic research steps(in the body of the research don’t forget to discuss p versus np problem).

4) plagiarism shouldn’t exceed 15% , because our college uses the LMS and its really accurate.

The P = NP question is largely considered one of the most imperative and in-depth questions in modern-day mathematics and computer science. Its origin appears to date back to a letter written to John Von Neumann by Kurt Gὄdel in 1956. In the letter, Gὄdel asked whether a particular NP-complete problem could be solved in linear or quadratic time (Deolalikar 1). In 1971, Stephen cook introduced the precise statement of the P versus NP problem in his seminal white paper – “The complexity of theorem proving procedures.” If the P ≠ NP, the problem could never be solved efficiently. On the other hand, if P = NP, the outcomes would be even more stunning, – since each of these problems would have a polynomial time answer (Deolalikar 1). The impact of this on applications, for instance, on cryptography, as well as on the philosophical question of whether human creativity could be automated, would be profound. This is considered by scores of people to be the most essential open problem in the field.

Additionally, the P = NP question is singular in the series of approaches presented over the years. From the original question in logic, the focus shifted to complexity theory where early works employed diagnalization along with relativization techniques (Sipser). However, Baker et, al. proved that these techniques were perhaps inadequate in resolving P =? NP by displaying relativized worlds where P _ NP along with others where P ≠ NP (Deolalikar 3). This consequently shifted the focus to techniques using circuit complexity and for a long time this practice was considered one of the most likely to resolve the question…………………