On two families of forests
An alphabetic cone is a family of forests stable under alphabetic tree transductions, whereas we call REC-closed each family of forests closed under the operations of union, top-catenation, \(a\)-product and \(a\)-star; the sheaves are families having both the above properties. For a given sheaf of forests \(\mathcal F\), both the families of languages \(\text{Br}({\mathcal F})\) and \(\text{yield}({\mathcal F})\) (of branches and yields of \(\mathcal F\), respectively) constitute full AFL's. Further, we show the family K-REC of forests supporting recognizable formal power series on trees is a sheaf and so is the family OCF of behaviors of one-counter tree-automata. On the contrary, restricted on- counter forests (ROCF) constitute an alphabetic cone which fails to be a sheaf; \(\text{ROCF}_ N\) (restricted one-counter forests over alphabets with degree \(\leq N\)) is alphabetically principal generated by the Łukasiewicz forest of rank \(N\).
scientific article; zbMATH DE number 567338
scientific article