Majority Boolean networks classifying density: structural characterization and complexity
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917274564165632 |
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| author | Perrot, Kévin Rolland, Marius |
| author_facet | Perrot, Kévin Rolland, Marius |
| contents | Given a set of entities each holding a Boolean state, the Density Classification Task (DCT) asks them to converge to the most represented state. Given a directed graph of entities where each node synchronously updates to the local majority among its in-neighbors, we characterize in terms of three forbidden patterns when it solves DCT, and show that discovering these patterns is complete for NP and PSPACE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13511 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Majority Boolean networks classifying density: structural characterization and complexity Perrot, Kévin Rolland, Marius Discrete Mathematics Given a set of entities each holding a Boolean state, the Density Classification Task (DCT) asks them to converge to the most represented state. Given a directed graph of entities where each node synchronously updates to the local majority among its in-neighbors, we characterize in terms of three forbidden patterns when it solves DCT, and show that discovering these patterns is complete for NP and PSPACE. |
| title | Majority Boolean networks classifying density: structural characterization and complexity |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2602.13511 |