Combining the $k$-CNF and XOR Phase-Transitions
| Autor: | Dudek, Jeffrey M., Meel, Kuldeep S., Vardi, Moshe Y. |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both $k$-CNF and XOR constraints (known as $k$-CNF-XOR formulas), but the behavior of random $k$-CNF-XOR formulas is unexplored in prior work. In this paper, we present the first study of the satisfiability of random $k$-CNF-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a linear trade-off between $k$-CNF and XOR constraints. Furthermore, we prove that a phase-transition for $k$-CNF-XOR formulas exists for $k = 2$ and (when the number of $k$-CNF constraints is small) for $k > 2$. Comment: Presented at The 25th International Joint Conference on Artificial Intelligence (IJCAI-16) |
| Databáze: | arXiv |
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