5 research outputs found
Positive Hennessy-Milner Logic for Branching Bisimulation
Labelled transitions systems can be studied in terms of modal logic and in
terms of bisimulation. These two notions are connected by Hennessy-Milner
theorems, that show that two states are bisimilar precisely when they satisfy
the same modal logic formulas. Recently, apartness has been studied as a dual
to bisimulation, which also gives rise to a dual version of the Hennessy-Milner
theorem: two states are apart precisely when there is a modal formula that
distinguishes them.
In this paper, we introduce ``directed'' versions of Hennessy-Milner theorems
that characterize when the theory of one state is included in the other. For
this we introduce ``positive modal logics'' that only allow a limited use of
negation. Furthermore, we introduce directed notions of bisimulation and
apartness, and then show that, for this positive modal logic, the theory of
is included in the theory of precisely when is directed bisimilar to
. Or, in terms of apartness, we show that is directed apart from
precisely when the theory of is not included in the theory of . From the
directed version of the Hennessy-Milner theorem, the original result follows.
In particular, we study the case of branching bisimulation and
Hennessy-Milner Logic with Until (HMLU) as a modal logic. We introduce
``directed branching bisimulation'' (and directed branching apartness) and
``Positive Hennessy-Milner Logic with Until'' (PHMLU) and we show the directed
version of the Hennessy-Milner theorems. In the process, we show that every
HMLU formula is equivalent to a Boolean combination of Positive HMLU formulas,
which is a very non-trivial result. This gives rise to a sublogic of HMLU that
is equally expressive but easier to reason about.Comment: 19 pages + appendices (28 pages total
Fixpoints and relative precompleteness
We study relative precompleteness in the context of the theory of numberings,
and relate this to a notion of lowness. We introduce a notion of divisibility
for numberings, and use it to show that for the class of divisible numberings,
lowness and relative precompleteness coincide with being computable.
We also study the complexity of Skolem functions arising from Arslanov's
completeness criterion with parameters. We show that for suitably divisible
numberings, these Skolem functions have the maximal possible Turing degree. In
particular this holds for the standard numberings of the partial computable
functions and the c.e. sets.Comment: 12 page
Magnetization switching in bistable nanomagnets by picosecond pulses of surface acoustic waves
International audienceWe perform a theoretical investigation of the magnetization switching in polycrystalline Ni nanoparticles induced by ultrashort pulses of surface acoustic waves via magnetoelastic interactions. In our numerical simulations, a Ni nanoparticle is modeled as an ellipsoidal disk deposited on a dielectric substrate. The in-plane external magnetic field breaks the symmetry and allows us to adjust the height of the energy barrier between two metastable magnetization states of the free-energy density and dramatically lower the amplitude of elastic strain pulses required for magnetization switching. The switching threshold is shown to depend on the duration of an acoustic pulse, the magnetic shape anisotropy of an elliptical nanoparticle, the amplitude of the external magnetic field, and the magnetostriction coefficient. We introduce the magnetoelastic switching diagram, allowing for the simultaneous visualization of the switching threshold and its characteristic timescale as a function of various physical parameters