论文标题
无上下文的语言和与代数希尔伯特系列的联想代数
Context-free languages and associative algebras with algebraic Hilbert series
论文作者
论文摘要
在本文中，事实证明，同源方法以及理论计算机科学的正式语言理论是确定关联代数的增长和希尔伯特系列的有效工具。也就是说，我们构建了一类与无上下文语言家族有关的有限的联想代数。这使我们能够将这些代数的Hilbert系列与此类语言的生成功能联系起来。特别是，我们获得了具有非理性代数希尔伯特系列的有限分级代数。
In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct a class of finitely presented associative algebras related to a family of context-free languages. This allows us to connect the Hilbert series of these algebras with the generating functions of such languages. In particular, we obtain a class of finitely presented graded algebras with non-rational algebraic Hilbert series.
