Super-state automata and rational trees
We introduce the notion of super-state automata constructed from other automata. This construction is used to solve an open question about enumerative sequences in rational trees. We prove that any IN-rational sequence s=(s n)n≥0 of nonnegative integers satisfying the Kraft inequality σn≥0 s n k −n ≤1 is the enumerative sequence of leaves by height of a k-ary rational tree. This result had been conjectured 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.
KeywordsRational Tree Adjacency Matrix Finite Automaton Outgoing Edge Rational Sequence
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