Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose I'm given a CNF formula with $m$ clauses (and $k$ literals in each clause), with a total of $n$ variables in the formula, where each variable is in at most $c$ clauses, along with a satisfying assignment to this formula. I change the value of each variable to the other possible value (from the one in the given assignment) with constant probability $p \leq \frac{1}{2}$ independently of the other variables. I want to show that with probability at least $1-exp\left(-\frac{p^2n}{2c^2}\right)$, the new assignment satisfies at least $\left(1-\left(c+1\right)p\right)m$ clauses.

It seems I should use here martingales (Azuma's inequality) or large deviation inequalities, however I didn't manage to get any meaningful results using these methods, so that may not be the case.

share|cite|improve this question
Is this homework by any chance? We have a tag for that. – Yuval Filmus Jun 4 '11 at 22:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.