We develop a coherent model in order to study specific random constraint satisfaction problems. Our framework includes all the generalized satisfiability problems defined by Schaefer. For such… (More)

The Gaussian algorithm for lattice reduction in dimension 2 is analysed under its standard version. It is found that, when applied to random inputs in a continuous model, the complexity is constant… (More)

The aim of this paper is to study the threshold behavior for the satisfiability property of a random k-XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with k… (More)

We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable is there exist two SAT assignments differing in Nx… (More)

The QSAT problem is the quantified version of the SAT problem. We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified extended… (More)

The QXOR-SAT problem is the quantified version of the satisfiability problem XOR-SAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated… (More)