343 research outputs found
Coalgebraic Behavioral Metrics
We study different behavioral metrics, such as those arising from both
branching and linear-time semantics, in a coalgebraic setting. Given a
coalgebra for a functor , we define a framework for deriving pseudometrics on which
measure the behavioral distance of states.
A crucial step is the lifting of the functor on to a
functor on the category of pseudometric spaces.
We present two different approaches which can be viewed as generalizations of
the Kantorovich and Wasserstein pseudometrics for probability measures. We show
that the pseudometrics provided by the two approaches coincide on several
natural examples, but in general they differ.
If has a final coalgebra, every lifting yields in a
canonical way a behavioral distance which is usually branching-time, i.e., it
generalizes bisimilarity. In order to model linear-time metrics (generalizing
trace equivalences), we show sufficient conditions for lifting distributive
laws and monads. These results enable us to employ the generalized powerset
construction
Compositional bisimulation metric reasoning with Probabilistic Process Calculi
We study which standard operators of probabilistic process calculi allow for
compositional reasoning with respect to bisimulation metric semantics. We argue
that uniform continuity (generalizing the earlier proposed property of
non-expansiveness) captures the essential nature of compositional reasoning and
allows now also to reason compositionally about recursive processes. We
characterize the distance between probabilistic processes composed by standard
process algebra operators. Combining these results, we demonstrate how
compositional reasoning about systems specified by continuous process algebra
operators allows for metric assume-guarantee like performance validation
Probabilistic Semantics: Metric and Logical Character\ua8ations for Nondeterministic Probabilistic Processes
In this thesis we focus on processes with nondeterminism and probability in the PTS model, and we propose novel techniques to study their semantics, in terms of both classic behavioral relations and the more recent behavioral metrics.
Firstly, we propose a method for decomposing modal formulae in a probabilistic extension of the Hennessy-Milner logic. This decomposition method allows us to derive the compositional properties of probabilistic (bi)simulations.
Then, we propose original notions of metrics measuring the disparities in the behavior of processes with respect to (decorated) trace and testing semantics.
To capture the differences in the expressive power of the metrics we order them by the relation `makes processes further than'.
Thus, we obtain the first spectrum of behavioral metrics on the PTS model.
From this spectrum we derive an analogous one for the kernels of the metrics, ordered by the relation `makes strictly less identification than'.
Finally, we introduce a novel technique for the logical characterization of both behavioral metrics and their kernels, based on the notions of mimicking formula and distance on formulae.
This kind of characterization allows us to obtain the first example of a spectrum of distances on processes obtained directly from logics.
Moreover, we show that the kernels of the metrics can be characterized by simply comparing the mimicking formulae of processes
Probabilistic Semantics: Metric and Logical Character¨ations for Nondeterministic Probabilistic Processes
In this thesis we focus on processes with nondeterminism and probability in the PTS model, and we propose novel techniques to study their semantics, in terms of both classic behavioral relations and the more recent behavioral metrics.
Firstly, we propose a method for decomposing modal formulae in a probabilistic extension of the Hennessy-Milner logic. This decomposition method allows us to derive the compositional properties of probabilistic (bi)simulations.
Then, we propose original notions of metrics measuring the disparities in the behavior of processes with respect to (decorated) trace and testing semantics.
To capture the differences in the expressive power of the metrics we order them by the relation `makes processes further than'.
Thus, we obtain the first spectrum of behavioral metrics on the PTS model.
From this spectrum we derive an analogous one for the kernels of the metrics, ordered by the relation `makes strictly less identification than'.
Finally, we introduce a novel technique for the logical characterization of both behavioral metrics and their kernels, based on the notions of mimicking formula and distance on formulae.
This kind of characterization allows us to obtain the first example of a spectrum of distances on processes obtained directly from logics.
Moreover, we show that the kernels of the metrics can be characterized by simply comparing the mimicking formulae of processes
Towards Trace Metrics via Functor Lifting
We investigate the possibility of deriving metric trace semantics in a
coalgebraic framework. First, we generalize a technique for systematically
lifting functors from the category Set of sets to the category PMet of
pseudometric spaces, showing under which conditions also natural
transformations, monads and distributive laws can be lifted. By exploiting some
recent work on an abstract determinization, these results enable the derivation
of trace metrics starting from coalgebras in Set. More precisely, for a
coalgebra on Set we determinize it, thus obtaining a coalgebra in the
Eilenberg-Moore category of a monad. When the monad can be lifted to PMet, we
can equip the final coalgebra with a behavioral distance. The trace distance
between two states of the original coalgebra is the distance between their
images in the determinized coalgebra through the unit of the monad. We show how
our framework applies to nondeterministic automata and probabilistic automata
Fixed-point Characterization of Compositionality Properties of Probabilistic Processes Combinators
Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences
Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully
probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing
single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing
equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models
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