147 research outputs found
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
A framework to measure the robustness of programs in the unpredictable environment
Due to the diffusion of IoT, modern software systems are often thought to
control and coordinate smart devices in order to manage assets and resources,
and to guarantee efficient behaviours. For this class of systems, which
interact extensively with humans and with their environment, it is thus crucial
to guarantee their correct behaviour in order to avoid unexpected and possibly
dangerous situations. In this paper we will present a framework that allows us
to measure the robustness of systems. This is the ability of a program to
tolerate changes in the environmental conditions and preserving the original
behaviour. In the proposed framework, the interaction of a program with its
environment is represented as a sequence of random variables describing how
both evolve in time. For this reason, the considered measures will be defined
among probability distributions of observed data. The proposed framework will
be then used to define the notions of adaptability and reliability. The former
indicates the ability of a program to absorb perturbation on environmental
conditions after a given amount of time. The latter expresses the ability of a
program to maintain its intended behaviour (up-to some reasonable tolerance)
despite the presence of perturbations in the environment. Moreover, an
algorithm, based on statistical inference, it proposed to evaluate the proposed
metric and the aforementioned properties. Throughout the paper, two case
studies are used to the describe and evaluate the proposed approach
On the Axiomatisation of Branching Bisimulation Congruence over CCS
In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP
On the Axiomatisability of Parallel Composition
This paper studies the existence of finite equational axiomatisations of the
interleaving parallel composition operator modulo the behavioural equivalences
in van Glabbeek's linear time-branching time spectrum. In the setting of the
process algebra BCCSP over a finite set of actions, we provide finite,
ground-complete axiomatisations for various simulation and (decorated) trace
semantics. We also show that no congruence over BCCSP that includes
bisimilarity and is included in possible futures equivalence has a finite,
ground-complete axiomatisation; this negative result applies to all the nested
trace and nested simulation semantics
Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?
Bergstra and Klop have shown that bisimilarity has a finite equational
axiomatisation over ACP/CCS extended with the binary left and communication
merge operators. Moller proved that auxiliary operators are necessary to obtain
a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that
this remains true when Hennessy's merge is added to that language. These
results raise the question of whether there is one auxiliary binary operator
whose addition to CCS leads to a finite axiomatisation of bisimilarity. This
study provides a negative answer to that question based on three reasonable
assumptions
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