Algorithmics: theory & practice
Algorithmics: theory & practice
Exploiting the deep structure of constraint problems
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Artificial Intelligence
Local search for statistical counting
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
The constrainedness knife-edge
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
The very particular structure of the very hard instances
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Phase Transitions and Stochastic Local Search in k-Term DNF Learning
ECML '02 Proceedings of the 13th European Conference on Machine Learning
Relational Learning: Hard Problems and Phase Transitions
AI*IA '99 Proceedings of the 6th Congress of the Italian Association for Artificial Intelligence on Advances in Artificial Intelligence
Resampling vs Reweighting in Boosting a Relational Weak Learner
AI*IA 01 Proceedings of the 7th Congress of the Italian Association for Artificial Intelligence on Advances in Artificial Intelligence
A Model to Study Phase Transition and Plateaus in Relational Learning
ILP '08 Proceedings of the 18th international conference on Inductive Logic Programming
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Finding models of a predicate logic formula is a well-known hard problem, whose complexity is exponential in the number of variables. However, even though this number is kept constant, substantial differences in complexity arise when searching for solutions in different problem instances. Such a behavior appears to be quite general, according to recent results reported in the literature; in fact, several classes of hard problems exhibit a narrow phase transition with respect to some order parameter, in correspondence of which the complexity dramatically rises up, still remaining tractable elsewhere. In this paper we provide an extensive experimental study on the emergence of a phase transition in the problem of matching a Horn clause to a universe, searching for a model of the clause or for a proof that no such model exists. As it turns out, phase transition in the matching problem depends in an essential way on two order parameters, one capturing syntactic aspects of the clause structure (intensional aspect), while the other related to the structure of the universe (extensional aspect).