SIAM Journal on Computing
A general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Information Processing Letters
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Combinatorial sharpness criterion and phase transition classification for random CSPs
Information and Computation
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Discrete Applied Mathematics
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The sensitivity set of a Boolean function at a particular input is the set of input positions where changing that one bit changes the output. Analogously we define the sensitivity set of a Boolean formula in a conjunctive normal form at a particular truth assignment, it is the set of positions where changing that one bit of the truth assignment changes the evaluation of at least one of the conjunct in the formula. We consider Boolean formulas in a generalized conjunctive normal form. Given a set @? of Boolean functions, an @?-constraint is an application of a function from @? to a tuple of literals built upon distinct variables, an @?-formula is then a conjunction of @?-constraints. In this framework, given a truth assignment I and a set of positions S, we are able to enumerate all @?-formulas that are satisfied by I and that have S as the sensitivity set at I. We prove that this number depends on the cardinality of S only, and can be expressed according to the sensitivity of the Boolean functions in @?.