Scale-Free Random SAT Instances
Abstract
:1. Introduction
2. Generation of Scale-Free Graphs
3. Scale-Free Random Formulas
3.1. Some Properties of the Model
3.2. Implementation of the Generator
Algorithm 1: Scale-free random k-SAT formula generator. |
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4. Industrial SAT Instances
5. Phase Transition in Scale-Free Random 2-SAT Formulas
- when , i.e., , a random graph almost surely has no connected component larger than ;
- when , i.e., a largest component of size almost surely emerges;
- when , i.e., , the graph almost surely contains a unique giant component with a fraction of the nodes and no other component contains more than nodes.
5.1. A Criterion for Phase Transition in 2-SAT
Algorithm 2: Algorithm for finding literals implied by x. |
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- (case A), if and ;
- (case B), if ;
- (case C), if and .
5.2. Classical 2-SAT Formulas
5.3. Scale-Free 2-SAT Formulas
6. Unsatisfiability by Small Cores
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Ansótegui , C.; Bonet, M.L.; Levy, J. Scale-Free Random SAT Instances. Algorithms 2022, 15, 219. https://doi.org/10.3390/a15060219
Ansótegui C, Bonet ML, Levy J. Scale-Free Random SAT Instances. Algorithms. 2022; 15(6):219. https://doi.org/10.3390/a15060219
Chicago/Turabian StyleAnsótegui , Carlos, Maria Luisa Bonet, and Jordi Levy. 2022. "Scale-Free Random SAT Instances" Algorithms 15, no. 6: 219. https://doi.org/10.3390/a15060219