Fitting and Learning Basis-Restricted Propositional Formulas

2026-09-08

AI Summary

研究通过限制命题公式的基，使用不同布尔函数集合作为连接词，解决拟合和学习问题的复杂性。

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.

Problem

• propositional formulas
• complexity
• learning problems
• Occam algorithm
• empirical risk minimization

Innovation

• propositional formulas
• Boolean functions
• Occam algorithm
• empirical risk minimization
• PAC learning