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Learning Expressions over Monoids

机译:学习表达式

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摘要

We study the problem of learning an unknown function represented as an expression over a known finite monoid. As in other areas of computational complexity where programs over algebras have been used, the goal is to relate the computational complexity of the learning problem with the algebraic complexity of the finite monoid. Indeed, our results indicate a close connection between both kinds of complexity. We focus on monoids which are either groups or aperiodic, and on the learning model of exact learning from queries. For a group G, we prove that expressions over G are easily learnable if G is nilpotent and impossible to learn efficiently (under cryptographic assumptions) if G is nonsolvable. We present some partial results for solvable groups, and point out a connection between their efficient learnability and the existence of lower bounds on their computational power in the program model. For aperiodic monoids, our results seem to indicate that the monoid class known as DA captures exactly learnability of expressions by polynomially many Evaluation queries.
机译:我们研究了学习一个未知函数,表示作为已知有限大块的表达的未知功能。与已经使用代数的程序的计算复杂性的其他领域一样,目标是将学习问题的计算复杂性与有限元的数量复杂性相关。实际上,我们的结果表明两种复杂性之间的密切连接。我们专注于群体或非周期性,以及查询的精确学习模型。对于组G,我们证明,如果G是NOLPOTENT,如果G是无能为止,则可以轻松学习,如果g是不可溶解的话,则可以轻松学习。我们为可溶性组提供了一些部分结果,并指出了他们有效的可读性与下界对程序模型的计算能力之间的连接。对于非周期性的,我们的结果似乎表明称为DA的单个级别通过多项式许多评估查询捕获表达的学报。

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