# negation of a nid-assignment to φ

negation of a nid-assignment to φ

Let φ be a 3cnf formula. A non-identical assignment, or nid-assignment, to the variables of φ is an assignment where each clause of φ contains two literals with different truth values, i.e., there cannot be a clause with the 3 true literals. Thus, a nid-assignment satisfies φ without assigning true to the 3 literals of any of the clauses.

(a) Show that the negation of a nid-assignment to φ is also a nid-assignment to φ.

(b) Let SATnid be the collection of 3cnf formulas that have a nid-assignment. Show that it is possible to obtain a polynomial-time reduction from 3SAT to SATnid by replacing each ci clause of the form (y1 ∨ y2 ∨ y3) by two clauses (y1 ∨ y2 ∨ zi) and (zi ∨ y3 ∨ b) where zi is a new variable for each ci clause, and b is a single additional new variable.

(c) Conclude that SATnid is NP-complete.

## How do you place an order?

It takes a few steps to place an order with Us:

• The first step is to place your order. You will need to provide us with some basic information about your project.
• Once you have placed your order, you will be taken to our secure payment page.
• Once we receive your order, we will carefully review it and match you with a writer who has the skills and experience.
• Stay in contact with the writer and discuss vital details of research.
• Your completed proposal will be delivered via email within the specified deadline.

### You are secure when using our service

It's critical for each client to feel secure. As a result, we at Research Proposal Writing take precautions to secure your data.

Financial security You may securely pay for your purchase using a variety of secure payment methods.
Personal security The personal information of our clients is secure. Nobody else will have access to it.
Academic security We use a specialized program to check every completed paper to ensure that we deliver no-plagiarism samples.
Web security This website is safe from unauthorized breaches. We maintain our privacy management in line with the latest laws and regulations.