gaqsip.blogg.se - Show that np is closed under union and concatenation.

" Complete" refers to the property of being able to simulate everything in the same complexity class.

Polynomial time refers to an amount of time that is considered "quick" for a deterministic algorithm to check a single solution, or for a nondeterministic Turing machine to perform the whole search. In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. The name "NP-complete" is short for "nondeterministic polynomial-time complete". If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly.

the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct.

it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.

In computational complexity theory, a problem is NP-complete when: Cook and Levin proved that each easy-to-verify problem can be solved as fast as SAT, which is hence NP-complete. While it is easy to verify whether a given assignment renders the formula true, no essentially faster method to find a satisfying assignment is known than to try all assignments in succession. p is sat.The Boolean satisfiability problem (SAT) asks to determine if a propositional formula (example depicted) can be made true by an appropriate assignment of truth values to its variables. Let p be the truth assignment corresponding to literals chosen in variable gadgets. Must include exactly 1 vertex from each variable gadget and 2 from each clause gadget. <= suppose there is a vertex cover of size k = L + 2m.

Every edge in variable and clause pieces covered, and edges between the variable vert and clause vert covered since clause vert are chosen when variable vert are not Add L variable vertices to the cover corresponding to true literals in p.