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arXiv · 2512.11007

Uniform winning strategies for the synchronization games on subclasses of finite automata

Henning Fernau·Carolina Haase·Stefan Hoffmann·Mikhail Volkov
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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.

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Henning Fernau, Carolina Haase, Stefan Hoffmann, Mikhail Volkov. 2025-12-11. Uniform winning strategies for the synchronization games on subclasses of finite automata. https://arxiv.org/abs/2512.11007

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