Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A threshold for unsatisfiability
Journal of Computer and System Sciences
The scaling window of the 2-SAT transition
Random Structures & Algorithms
On the critical exponents of random k-SAT
Random Structures & Algorithms
Subclasses of Quantified Boolean Formulas
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
New results on the phase transition for random quantified Boolean formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
A framework for the specification of random SAT and QSAT formulas
TAP'12 Proceedings of the 6th international conference on Tests and Proofs
Hi-index | 0.00 |
We explore random Boolean quantified CNF formulas of the form *** X *** Y φ (X ,Y ), where X has $m=\lfloor \alpha \log n\rfloor$ variables (*** 0), Y has n variables and each clause in φ has one literal from X and two from Y . These (1,2)-QCNF-formulas, which can be seen as quantified extended 2-CNF formulas, were introduced in SAT'08. It was proved that the threshold phenomenon associated to the satisfiability of such random formulas, (1,2)-QSAT, is controlled by the ratio c between the number of clauses and the number n of existential variables. In this paper, we prove that the threshold is sharp. For any value of *** , we give the exact location of the associated critical ratio, a (*** ). At this ratio, our study highlights the sudden emergence of unsatisfiable formulas with a very specific shape. From the experimental point of view (1,2)-QSAT is challenging. Indeed, while for small values of m the critical ratio can be observed experimentally, it is not anymore the case for bigger values of m . For small values of m we give precise numerical estimates of the probability of satisfiability for critical (1,2)-QCNF-formulas. These experiments give evidence that the asymptotical regime is difficult to reach and provide some indication on the behavior of random instances. Moreover, experiments show that the computational effort, which is increasing with m , is maximized within the phase transition.