Characterizing EF and EX tree logics

Characterizing EF and EX Tree Logics

We describe the expressive power of temporal branching time logics that use the modalities EX and EF. We give a forbidden pattern characterization of the tree languages definable in three logics: EX, EF and EX+EF. The properties in these characterizations can be verified in polynomial time when given a minimal deterministic bottom-up tree automaton. We consider the definability problem for logi...

EF+EX Forest Algebras

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs...

Temporal logics with reference pointers and computation tree logics

A complete axiomatic system CTL rp is introduced for a temporal logic for nitely branching ! +-trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL into CTL rp. In particular, that yields a complete axiomatization for the translations of all valid CTL-formulae. Thus, the temporal ...

Characterizing Definability in Decidable Fixpoint Logics

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as well as effective characterizations. Our algorithms revolve around a finer analysis of the tree-model property and a refinement of the method of moving back...

Decidable Characterizations for Tree Logics