Two-Way Unary Temporal Logic over Trees

preprint2009arXivOpen access

Abstract

We consider a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EFϕ, which says "in some proper descendant ϕholds", and F^-1ϕ, which says "in some proper ancestor ϕholds". We present an algorithm for deciding if a regular language of unranked finite trees can be expressed in EF+F^-1. The algorithm uses a characterization expressed in terms of forest algebras.

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