Linear-time Temporal Logic with Team Semantics: Expressivity and Complexity
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We study the expressivity and the model checking problem of linear temporal logic with team semantics (TeamLTL). In contrast to LTL, TeamLTL is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. Logics for hyperproperties have so far been mostly obtained by extending temporal logics like LTL and QPTL with trace quantification, resulting in HyperLTL and HyperQPTL. We study the expressiveness of TeamLTL (and its extensions with downward closed generalised atoms A and connectives such as Boolean disjunction v) in comparison to HyperLTL and HyperQPTL. Thereby, we also obtain a number of model checking results for TeamLTL, a question which is so far an open problem. The two types of logics follow a fundamentally different approach to hyperproperties and are are of incomparable expressiveness. We establish that the universally quantified fragment of HyperLTL subsumes the so-called k-coherent fragment of TeamLTL(A,v). This also implies that the model checking problem is decidable for the fragment. We show decidability of model checking of the so-called "left-flat" fragment of TeamLTL(A,v) via a translation to a decidable fragment of HyperQPTL. Finally, we show that the model checking problem of TeamLTL with Boolean disjunction and inclusion atom is undecidable.
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