Phase transitions in artificial intelligence systems
Artificial Intelligence
Expected gains from parallelizing constraint solving for hard problems
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Exploiting the deep structure of constraint problems
Artificial Intelligence
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Theoretical analysis of Davis-Putnam procedure and propositional satisfiability
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Which search problems are random?
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Detecting Motifs in a Large Data Set: Applying Probabilistic Insights to Motif Finding
BICoB '09 Proceedings of the 1st International Conference on Bioinformatics and Computational Biology
Model complexity vs. performance in the bayesian optimization algorithm
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Automated testing and debugging of SAT and QBF solvers
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
On the relative merits of simple local search methods for the MAX-SAT problem
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Hi-index | 0.00 |
In the past few years there have been several empirical discoveries of phase transitions in constraint satisfaction problems (CSPs), and a growth of interest in the area among the artificial intelligence community. This paper extends a simple analytical theory of phase transitions in three-satisfiability (3-SAT) problems in two directions. First, a more accurate, problem-dependent calculation leads to a new polynomial time probabilistic estimate of the satisfiability of 3-SAT problems called PE-SAT (Probabilistic Estimate SATisfiability algorithm). PE-SAT empirically classifies 3-SAT problems with about 70% accuracy at the hardest region (the so-called crossover point or 50% satisfiable region) of random 3-SAT space. Furthermore, the estimate has a meaningful magnitude such that extreme estimates are much more likely to be correct. Second, the same estimate is used to improve the running time of a backtracking search for a solution to 3-SAT by pruning unlikely branches of the search. The speed-up is achieved at the expense of accuracy--the search remains sound but is no longer complete. The trade-off between speed-up and accuracy is shown to improve as the size of problems increases.