Assignment Help - homework help

  Problems in NP-complete, Complexity P & NP

Hundreds of well-known problems are NP-complete:

3-CNF SAT is the beginning point of chains of trouble reduction theorems to exhibit that hundreds of other well known decision troubles are NP complete. The problem CLIQUE is an illustration: Given a graph G and an integer k, does G comprise a clique of size ≥ k?

Theorem: CLIQUE is NP-complete

Proof: Show that the 3-CNF ≤p CLIQUE. Given 3-CNF expression F, build a graph G = (V, E) and an integer k in such a way that F is satisfiable if and only if G consists of a k-clique.

Suppose F = (z11 ∨ z12 ∨ z13) ∧ (z21 ∨ z22 ∨ z23) ∧ ... ∧ (zm1 ∨ zm2 ∨ zm3), where each zij is the literal.

To each of the occurrence of literal we assign a vertex, that is, V = {(1,1), (1,2), (1,3), ... , (m, 1), (m, 2), (m, 3)}

We introduce an edge ((i, j) (p, q)) if and only if i ≠ p (that is, the two literals are in distinct clauses) and zij ≠ ¬zpq (that is, the 2 literals don’t clash, that is, both can be made true beneath similar assignment).

Lastly, suppose k, the desired clique size, be = m, the number of clauses.

With this construction of G we examine that F is satisfiable through an assignment A

If and only if 1) All clause includes a literal which is true beneath A, state z1, j1, z2, j2, ... ,  zm, jm
If and only if 2) there are literals z1, j1,  z2, j2, ... , zm, jm no two of which are negations of one other
If and only if 3) there are vertices (1, j1), (2, j2), ... , (m, jm) which are pair-wise joined by an edge
If and only if 4) G consists of a k-clique.

Latest technology based Theory of Computation Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Theory of Computation help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Theory of Computation, project ideas and tutorials. We provide email based Theory of Computation help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Theory of Computation. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Theory of Computation Homework help and assignment help services. They use their experience, as they have solved thousands of the Theory of Computation assignments, which may help you to solve your complex issues of Theory of Computation. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
Home | Company Overview | Services | Discover Q&A | Sitemap | Contact Us | T & C | Refund Policy | Copyright Policy | Blog | Q&A | Directory

©TutorsGlobe All rights reserved 2022-2023.