55 research outputs found
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions
In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well
Rooted branching bisimulation as a congruence for probabilistic transition systems
Ponencia presentada en el 13 International Workshop on Quantitative Aspects of Programming Languages and Systems. London, United Kingdom, April 11-12, 2015.We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format.Fil: Lee, Matías David. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: De Vink, Erik P. Eindhoven University of Technology; The Netherlands.Fil: De Vink, Erik P. Centrum Wiskunde & Informatica; The Netherlands.Ciencias de la Computació
On Bisimilarity for Quasi-discrete Closure Spaces
Closure spaces, a generalisation of topological spaces, have shown to be a
convenient theoretical framework for spatial model checking. The closure
operator of closure spaces and quasi-discrete closure spaces induces a notion
of neighborhood akin to that of topological spaces that build on open sets. For
closure models and quasi-discrete closure models, in this paper we present
three notions of bisimilarity that are logically characterised by corresponding
modal logics with spatial modalities: (i) CM-bisimilarity for closure models
(CMs) is shown to generalise Topo-bisimilarity for topological models.
CM-bisimilarity corresponds to equivalence with respect to the infinitary modal
logic IML that includes the modality for ``being near''. (ii)
CMC-bisimilarity, with `CMC' standing for CM-bisimilarity with converse,
refines CM-bisimilarity for quasi-discrete closure spaces, carriers of
quasi-discrete closure models. Quasi-discrete closure models come equipped with
two closure operators, Direct and Converse , stemming from
the binary relation underlying closure and its converse. CMC-bisimilarity, is
captured by the infinitary modal logic IMLC including two modalities, Direct
and Converse , corresponding to the two closure operators.
(iii) CoPa-bisimilarity on quasi-discrete closure models, which is weaker than
CMC-bisimilarity, is based on the notion of compatible paths. The logical
counterpart of CoPa-bisimilarity is the infinitary modal logic ICRL with
modalities Direct and Converse , whose semantics relies on
forward and backward paths, respectively. It is shown that CoPa-bisimilarity
for quasi-discrete closure models relates to divergence-blind stuttering
equivalence for Kripke structures.Comment: 32 pages, 14 figure
Modelling and analysing software in mCRL2
Model checking is an effective way to design correct software.Making behavioural models of software, formulating correctness properties using modal formulas, and verifying these using finite state analysis techniques, is a very efficient way to obtain the required insight in the software. We illustrate this on four common but tricky examples
Lowerbounds for Bisimulation by Partition Refinement
We provide time lower bounds for sequential and parallel algorithms deciding
bisimulation on labeled transition systems that use partition refinement. For
sequential algorithms this is and for parallel algorithms this is , where
is the number of states and is the number of transitions. The lowerbounds
are obtained by analysing families of deterministic transition systems,
ultimately with two actions in the sequential case, and one action for parallel
algorithms. For deterministic transition systems with one action, bisimilarity
can be decided sequentially with fundamentally different techniques than
partition refinement. In particular, Paige, Tarjan, and Bonic give a linear
algorithm for this specific situation. We show, exploiting the concept of an
oracle, that this approach is not of help to develop a faster generic algorithm
for deciding bisimilarity. For parallel algorithms there is a similar situation
where these techniques may be applied, too
Multiple verification in computational modeling of bone pathologies
We introduce a model checking approach to diagnose the emerging of bone
pathologies. The implementation of a new model of bone remodeling in PRISM has
led to an interesting characterization of osteoporosis as a defective bone
remodeling dynamics with respect to other bone pathologies. Our approach allows
to derive three types of model checking-based diagnostic estimators. The first
diagnostic measure focuses on the level of bone mineral density, which is
currently used in medical practice. In addition, we have introduced a novel
diagnostic estimator which uses the full patient clinical record, here
simulated using the modeling framework. This estimator detects rapid (months)
negative changes in bone mineral density. Independently of the actual bone
mineral density, when the decrease occurs rapidly it is important to alarm the
patient and monitor him/her more closely to detect insurgence of other bone
co-morbidities. A third estimator takes into account the variance of the bone
density, which could address the investigation of metabolic syndromes, diabetes
and cancer. Our implementation could make use of different logical combinations
of these statistical estimators and could incorporate other biomarkers for
other systemic co-morbidities (for example diabetes and thalassemia). We are
delighted to report that the combination of stochastic modeling with formal
methods motivate new diagnostic framework for complex pathologies. In
particular our approach takes into consideration important properties of
biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could
be further expanded, inching towards the complexity of human diseases. Finally,
we briefly introduce self-adaptiveness in formal methods which is a key
property in the regulative mechanisms of biological systems and well known in
other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Programmable models of growth and mutation of cancer-cell populations
In this paper we propose a systematic approach to construct mathematical
models describing populations of cancer-cells at different stages of disease
development. The methodology we propose is based on stochastic Concurrent
Constraint Programming, a flexible stochastic modelling language. The
methodology is tested on (and partially motivated by) the study of prostate
cancer. In particular, we prove how our method is suitable to systematically
reconstruct different mathematical models of prostate cancer growth - together
with interactions with different kinds of hormone therapy - at different levels
of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104
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