LTL ∩ PCTL is decidable because an LTL formula defines a PCTL-expressible tree language iff its word language is DBW-recognizable, via a new HWTcf automata characterization of PCTL.
Two-Way Unary Temporal Logic over Trees
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abstract
We consider a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EF\phi, which says "in some proper descendant \phi holds", and F^-1\phi, which says "in some proper ancestor \phi holds". 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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Deciding the Common Fragment of CTL with Past and LTL
LTL ∩ PCTL is decidable because an LTL formula defines a PCTL-expressible tree language iff its word language is DBW-recognizable, via a new HWTcf automata characterization of PCTL.