A sharp threshold for k-colorability
Random Structures & Algorithms
Random graphs
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Generalized satisfiability problems: minimal elements and phase transitions
Theoretical Computer Science
Phase transition for random quantified XOR-formulas
Journal of Artificial Intelligence Research
Low-density graph codes that are optimal for binning and coding with side information
IEEE Transactions on Information Theory
Lossy source compression using low-density generator matrix codes: analysis and algorithms
IEEE Transactions on Information Theory
On the phase transitions of random k-constraint satisfaction problems
Artificial Intelligence
| Hi-index | 0.12 |
In this paper we study random linear systems with $k 3$ variables per equation over the finite field GF(2), or equivalently k-XOR-CNF formulas. In a previous paper Creignou and Daudé proved that there exists a phase transition exhibiting a sharp threshold, for the consistency (satisfiability) of such systems (formulas). The control parameter for this transition is the ratio of the number of equations to the number of variables, and the scale for which the transition occurs remains somewhat elusive. In this paper we establish, for any $k 3$, non-trivial lower and upper estimates of the value of the control ratio for which the phase transition occurs. For $k=3$ we get 0.89 and 0.93, respectively. Moreover, we give experimental results for $k=3$ suggesting that the critical ratio is about 0.92. Our estimates are clearly close to the critical ratio.