Paper
The satisfiability threshold and solution space of random uniquely extendable constraint satisfaction problems
Authors
Pu Gao, Theodore Morrison
Abstract
We study the satisfiability threshold and solution-space geometry of random constraint satisfaction problems defined over uniquely extendable (UE) constraints. Motivated by a conjecture of Connamacher and Molloy, we consider random -ary UE-SAT instances in which each constraint function is drawn, according to a certain distribution , from a specified subset of uniquely extendable constraints over an -spin set. We introduce a flexible model that allows arbitrary distributions on constraint types, encompassing both random linear systems and previously studied UE-SAT models. Our main result determines the satisfiability threshold for a wide family of distributions . Under natural reducibility or symmetry conditions on , we prove that the satisfiability threshold of coincides with the classical -XORSAT threshold.