# Adding noise to an assignment

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.

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