Deciding Hyperproperties
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by
Bernd Finkbeiner, Christopher Hahn
2016
Abstract
Hyperproperties, like observational determinism or symmetry, cannot be
expressed as properties of individual computation traces, because they describe
a relation between multiple computation traces. HyperLTL is a temporal logic
that captures such relations through trace variables, which are introduced
through existential and universal trace quantifiers and can be used to refer to
multiple computations at the same time. In this paper, we study the
satisfiability problem of HyperLTL. We show that the problem is PSPACE-complete
for alternation-free formulas (and, hence, no more expensive than LTL
satisfiability), EXPSPACE-complete for exists-forall-formulas, and undecidable
for forall-exists-formulas. Many practical hyperproperties can be expressed as
alternation-free formulas. Our results show that both satisfiability and
implication are decidable for such properties.
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