title: Finite-size scaling in random K-satisfiability problems.
abstract: We provide a comprehensive view of various phase transitions in random K-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically important and practically useful in analyzing finite systems. Using the FSS theory of nonequilibrium absorbing phase transitions, we show that the density of unsatisfied clauses clearly indicates the transition from the solvable (absorbing) phase to the unsolvable (active) phase as varying the noise parameter and the density of constraints. Based on the solution clustering (percolation-type) argument, we conjecture two possible values of the FSS exponent, which are confirmed reasonably well in numerical simulations for 2 ≤ K ≤ 3.
authors.affiliation: Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
authors.forename: Sang Hoon
authors.initials: SH
authors.lastname: Lee
authors.forename: Meesoon
authors.initials: M
authors.lastname: Ha
authors.forename: Chanil
authors.initials: C
authors.lastname: Jeon
authors.forename: Hawoong
authors.initials: H
authors.lastname: Jeong
mesh_terms: D008962:Models, Theoretical; D044367:Phase Transition; D013269:Stochastic Processes