Fitting and Learning Basis-Restricted Propositional Formulas

Abstract:For a finite set $O$ of Boolean functions, we consider the class of propositional formulas built using the functions in $O$ as connectives. We determine, for each possible choice of $O$, the complexity of various fitting and learning problems. These include: finding a formula that fits a given labeled sample, finding a small one (an Occam algorithm), minimizing the number of misclassified examples when the sample is not realizable (empirical risk minimization), and several forms of PAC learning. Our results apply both to formulas (represented as trees) and to circuits. We also briefly discuss the status of the same questions for other kinds of propositional fragments.

Logic in Computer Science (cs.LO); Machine Learning (cs.LG)

arXiv:2609.08961 [cs.LO]

(or arXiv:2609.08961v1 [cs.LO] for this version)

https://doi.org/10.48550/arXiv.2609.08961 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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