A Dichotomy for First-Order Reducts of Unary Structures

Abstract

Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite domains. Our first result is a general polynomial-time reduction from such infinite-domain CSPs to finite-domain CSPs. We use this reduction to obtain new powerful polynomial-time tractability conditions that can be expressed in terms of the topological polymorphism clone of $\mathbb{A}$. Moreover, we study the subclass $\mathcal{C}$ of CSPs for structures $\mathbb{A}$ that are reducts of a structure with a unary language. Also this class $\mathcal{C}$ properly extends the class of all finite-domain CSPs. We apply our new tractability conditions to prove the general tractability conjecture of Bodirsky and Pinsker for reducts of finitely bounded homogeneous structures for the class $\mathcal{C}$.

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• Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics
• A complexity dichotomy for poset constraint satisfaction
• Canonical Functions: a proof via topological dynamics
• Constraint Satisfaction and Semilinear Expansions of Addition over the Rationals and the Reals

Cited by in corpus (2)

• Canonical Functions: a proof via topological dynamics
• Structures with Small Orbit Growth