836 research outputs found
On the Expressiveness of QCTL
QCTL extends the temporal logic CTL with quantification over atomic propositions. While the algorithmic questions for QCTL and its fragments with limited quantification depth are well-understood (e.g. satisfiability of QkCTL, with at most k nested blocks of quantifiers, is (k+1)-EXPTIME-complete), very few results are known about the expressiveness of this logic.
We address such expressiveness questions in this paper. We first consider the distinguishing power of these logics (i.e., their ability to separate models), their relationship with behavioural equivalences, and their ability to capture the behaviours of finite Kripke structures with so-called characteristic formulas. We then consider their expressive power (i.e., their ability to express a property), showing that in terms of expressiveness the hierarchy QkCTL collapses at level 2 (in other terms, any QCTL formula can be expressed using at most two nested blocks of quantifiers)
Generalized Strong Preservation by Abstract Interpretation
Standard abstract model checking relies on abstract Kripke structures which
approximate concrete models by gluing together indistinguishable states, namely
by a partition of the concrete state space. Strong preservation for a
specification language L encodes the equivalence of concrete and abstract model
checking of formulas in L. We show how abstract interpretation can be used to
design abstract models that are more general than abstract Kripke structures.
Accordingly, strong preservation is generalized to abstract
interpretation-based models and precisely related to the concept of
completeness in abstract interpretation. The problem of minimally refining an
abstract model in order to make it strongly preserving for some language L can
be formulated as a minimal domain refinement in abstract interpretation in
order to get completeness w.r.t. the logical/temporal operators of L. It turns
out that this refined strongly preserving abstract model always exists and can
be characterized as a greatest fixed point. As a consequence, some well-known
behavioural equivalences, like bisimulation, simulation and stuttering, and
their corresponding partition refinement algorithms can be elegantly
characterized in abstract interpretation as completeness properties and
refinements
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