Typical random 3-SAT formulae and the satisfiability threshold

: k-SAT is one of the best known among a wide class of random constraint satisfaction problems believed to exhibit a threshold phenomenon where the control parameter is the ratio, number of constraints to number of variables. There has been a large amount of work towards estimating the 3-SAT threshold. We present a new structural (or syntactic) approach aimed at narrowing the gap between the exact threshold and upper bounds obtained by the first moment method. This is based on the notion of typicity, specific definitions of which may vary so as to encompass any purely formal property of a random formula which holds with high probability. The idea is that the formulae responsible for the gap tend to be atypical, hence restriction to typical formulae will give a better bound. In this paper, the method is carried through using an uncomplicated definition in terms of the numbers of signed occurrences of variables. We demonstrate its ability to combine with previous techniques (locally extr...

• Type: Conference
• Year: 2000
• Where: SODA
• Authors: Olivier Dubois, Yacine Boufkhad, Jacques Mandler
• Keywords: Algorithms, Random Constraint Satisfaction, SODA 2000, Threshold Phenomenon, Upper Bound