Title: Strategies and Timing for Aligning Examples with Logic-Driven Hypothesis Classes on Infinite Domains

Abstract: This research investigates "fitting problems," frequently referred to as "training problems," which involve a finite dataset of input-output pairs. The central question is whether a function from a specified class can generate these outputs—either precisely or with some approximation—when applied to the provided inputs. We concentrate on the descriptive and computational complexities associated with fitting logically defined classes within standard decidable structures, such as Presburger arithmetic and the ordered field of real numbers. Additionally, we examine broader classes characterized by combinatorial or model-theoretic attributes. Our analysis isolates the complexity of these fitting tasks, paying special attention to scenarios where the fittability of a sample can be determined by utilizing queries within a natural query language defined over the sample itself.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC