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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.19266 |
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- We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where constraint languages and instances are specified by finite automata. The $AutCSP$ captures infinite yet finitely describable sets of relations, enabling concise representations of complex constraints. Studying the complexity of the $AutCSP$s illustrates the interplay between classical CSPs, automata, and logic, sharpening the boundary between tractable and intractable constraints. We show that checking whether an operation is a polymorphism of such a language can be done in polynomial time. Building on this, we establish several complexity classification results for the $AutCSP$. In particular, we prove that Schaefer's Dichotomy Theorem extends to the $AutCSP$ over the Boolean domain, and we provide algorithms that decide tractability of some classes of $AutCSP$s over arbitrary finite domains via automatic polymorphisms. An important part of our work is that our polynomial-time algorithms run on $AutCSP$ instances that can be exponentially more succinct than their standard CSP counterparts.