How (and when) can you fit examples to logic-based hypothesis classes over infinite structures?
Year: 2026
Type: preprint
Abstract: We study fitting problems, sometimes called ``training problems'', where we have a finite sample consisting of inputs and outputs, and we want to know whether there is a function in a certain class that could produce these outputs, exactly or approximately, on the given inputs. We focus on the computational and descriptive complexity of fitting for logically-defined classes in common decidable structures, like the real ordered field and Presburger arithmetic, and also for broader classes defined via combinatorial or model-theoretic properties. We isolate the complexity of these fitting problems, with particular attention to cases where we can use queries in a natural query language over the sample to determine whether a sample is fittable.
Source: arXiv (Cornell University)
Authors: Benedikt, Michael, Mansutti, Alessio
Institution: IMDEA Software Institute
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163194350
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