关于CNF精确学习的新进展
New Steps on the Exact Learning of CNF
摘要：
计算学习理论中的一个主要问题是合取范式（CNF）中的公式类是否可有效学习。虽然已知该类不能单独使用成员资格或等价查询进行多项式学习，但CNF是否可以使用这两种类型的查询进行多项式学习是开放的。关于类CNF的限制的最重要的结果之一是，命题霍恩公式是多项式时间学习的成员和等价查询的Angluin的精确学习模型。在这项工作中，我们推动这一边界，并表明，类的多值依赖公式（MVDF）是多项式学习的解释。然后，我们提供了一个概念，减少学习问题之间的Angluin的模型，表明该算法的转换足以有效地学习多值数据库依赖关系的数据。我们还表明，通过减少，我们的主要结果扩展了众所周知的以前的结果，并允许我们找到替代解决方案。
英文摘要：
A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or equivalence queries alone, it is open whether CNF can be polynomially learned using both types of queries. One of the most important results concerning a restriction of the class CNF is that propositional Horn formulas are polynomial time learnable in Angluin's exact learning model with membership and equivalence queries. In this work we push this boundary and show that the class of multivalued dependency formulas (MVDF) is polynomially learnable from interpretations. We then provide a notion of reduction between learning problems in Angluin's model, showing that a transformation of the algorithm suffices to efficiently learn multivalued database dependencies from data relations. We also show via reductions that our main result extends well known previous results and allows us to find alternative solutions for them.
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