6 research outputs found
Hennessy-Milner Logic with Greatest Fixed Points as a Complete Behavioural Specification Theory
There are two fundamentally different approaches to specifying and verifying
properties of systems. The logical approach makes use of specifications given
as formulae of temporal or modal logics and relies on efficient model checking
algorithms; the behavioural approach exploits various equivalence or refinement
checking methods, provided the specifications are given in the same formalism
as implementations.
In this paper we provide translations between the logical formalism of
Hennessy-Milner logic with greatest fixed points and the behavioural formalism
of disjunctive modal transition systems. We also introduce a new operation of
quotient for the above equivalent formalisms, which is adjoint to structural
composition and allows synthesis of missing specifications from partial
implementations. This is a substantial generalisation of the quotient for
deterministic modal transition systems defined in earlier papers
On Refinements of Boolean and Parametric Modal Transition Systems
We consider the extensions of modal transition systems (MTS), namely Boolean
MTS and parametric MTS and we investigate the refinement problems over both
classes. Firstly, we reduce the problem of modal refinement over both classes
to a problem solvable by a QBF solver and provide experimental results showing
our technique scales well. Secondly, we extend the algorithm for thorough
refinement of MTS providing better complexity then via reductions to previously
studied problems. Finally, we investigate the relationship between modal and
thorough refinement on the two classes and show how the thorough refinement can
be approximated by the modal refinement
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