{"ID":2830177,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.11007","arxiv_id":"2512.11007","title":"Uniform winning strategies for the synchronization games on subclasses of finite automata","abstract":"The pseudovariety $\\mathbf{DS}$ consists of all finite monoids whose regular $D$-classes form subsemigroups. We exhibit a uniform winning strategy for Synchronizer in the synchronization game on every synchronizing automaton whose transition monoid lies in $\\mathbf{DS}$, and we prove that $\\mathbf{DS}$ is the largest pseudovariety with this property.","short_abstract":"The pseudovariety $\\mathbf{DS}$ consists of all finite monoids whose regular $D$-classes form subsemigroups. We exhibit a uniform winning strategy for Synchronizer in the synchronization game on every synchronizing automaton whose transition monoid lies in $\\mathbf{DS}$, and we prove that $\\mathbf{DS}$ is the largest p...","url_abs":"https://arxiv.org/abs/2512.11007","url_pdf":"https://arxiv.org/pdf/2512.11007v1","authors":"[\"Henning Fernau\",\"Carolina Haase\",\"Stefan Hoffmann\",\"Mikhail Volkov\"]","published":"2025-12-11T08:37:02Z","proceeding":"cs.FL","tasks":"[\"cs.FL\",\"cs.GT\"]","methods":"[]","has_code":false}