We introduce the notion of super-state automata ocnstructed from other automata. This construction i used to solve an open question about enumerative sequences in ratioal trees. We prove that any IN-rational sequene s=(s sub n)>0 of nonnegative integers satisfying the Kraft inequality sigma n >0 s sub n K sup -n less than or equal to 1 is the enumerative sequence of leaves by height of a k-ary rational tree. This result had bee nconjectured and was known only in the case of strict inequality. We also give a new proof of a result about enumerative sequences of nodes in k-ary rational trees.
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机译:我们介绍了由其他自动机构成的超状态自动机的概念。我曾经用这种结构来解决关于比例树中枚举序列的开放性问题。我们证明,满足卡夫不等式sigma n> 0 s sub n K sup -n小于或等于1的非负整数的IN有理序列s =(s sub n)> 0是叶子的枚举序列,高度为一元有理树。这个结果是不可预知的,只有在严格不平等的情况下才知道。我们还给出了关于k元有理树中节点的枚举序列的结果的新证明。
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