Percolation of unsatisfiability in finite dimensions
The optimization of two-dimensional Boolean formulas is studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition as the constraint density is varied, although there is a logical connectivity transition....
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| Published in: | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 70; no. 3 Pt 2; p. 035103 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01-09-2004
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| Online Access: | Get full text |
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| Summary: | The optimization of two-dimensional Boolean formulas is studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition as the constraint density is varied, although there is a logical connectivity transition. In the disconnected phase, there is a transition in the solution time. The thermodynamic ground state for this NP-hard optimization problem is unique; local solutions can be adjoined to find the global ground state. These results have implications for the computational study of disordered materials. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1539-3755 1550-2376 |
| DOI: | 10.1103/PhysRevE.70.035103 |