Jakub Rydval

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cs.LO2026

Deciding Amalgamation Beyond Arity Two: The Semantic Horn Case

Jakub Rydval

We study the amalgamation decision problem: given a universal first-order sentence $Φ$ , decide whether the class $fm (Φ)$ of its finite models has the amalgamation property…

cs.LO2026

The Polynomial Hierarchy and $I ¨ $ -categorical CSPs

Santiago GuzmÃ¡n Pro, Jakub Rydval

In 2008, Bodirsky and Grohe showed that for every $I^_{n}^{P}$ -level of the Polynomial Hierarchy (PH) there are $I ¨ $ -categorical Constraint Satisfaction Problems (CSPs) comp…

cs.LO2026

The Golden Path to Guarded Monotone Strict NP

Alexey Barsukov, Michael Pinsker, Jakub Rydval

Guarded Monotone Strict NP (GMSNP) extends Monotone Monadic Strict NP (MMSNP) by guarded existentially quantified predicates of arbitrary arities. We prove that the containment and…

cs.LO2025

Finitely Bounded Homogeneity Turned Inside-Out

Jakub Rydval

Deciding the amalgamation property for a given class of finite structures is an important subroutine in classifying countable finitely homogeneous structures. We study the computat…

Deciding Amalgamation Beyond Arity Two: The Semantic Horn Case

The Polynomial Hierarchy and I¨-categorical CSPs

The Golden Path to Guarded Monotone Strict NP

Finitely Bounded Homogeneity Turned Inside-Out

The Polynomial Hierarchy and $I ¨ $ -categorical CSPs