Computer Science > Formal Languages and Automata Theory
This paper has been withdrawn by Martin Beaudry
[Submitted on 20 May 2021 (v1), last revised 13 Jun 2021 (this version, v2)]
Title:Forest languages defined by counting maximal paths
No PDF available, click to view other formatsAbstract:A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word that belongs to $L$. We look at the class $\mathsf{*D}$ of the languages recognized by iterated wreath products of syntactic algebras of leaf path languages. We prove the existence of an algorithm that, given a regular forest language, returns in finite time a sequence of such algebras; their wreath product is divided by the language's syntactic algebra if, and only if this language belongs to $\mathsf{*D}$, which makes membership in this class a decidable question. The result also applies to the subclasses $\mathsf{PDL}$ and $\mathsf{CTL^*}$.
Submission history
From: Martin Beaudry [view email][v1] Thu, 20 May 2021 18:04:38 UTC (43 KB)
[v2] Sun, 13 Jun 2021 18:50:13 UTC (1 KB) (withdrawn)
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