3,540 research outputs found
Expected-Delay-Summing Weak Bisimilarity for Markov Automata
A new weak bisimulation semantics is defined for Markov automata that, in
addition to abstracting from internal actions, sums up the expected values of
consecutive exponentially distributed delays possibly intertwined with internal
actions. The resulting equivalence is shown to be a congruence with respect to
parallel composition for Markov automata. Moreover, it turns out to be
comparable with weak bisimilarity for timed labeled transition systems, thus
constituting a step towards reconciling the semantics for stochastic time and
deterministic time.Comment: In Proceedings QAPL 2015, arXiv:1509.0816
Disjunctive Probabilistic Modal Logic is Enough for Bisimilarity on Reactive Probabilistic Systems
Larsen and Skou characterized probabilistic bisimilarity over reactive
probabilistic systems with a logic including true, negation, conjunction, and a
diamond modality decorated with a probabilistic lower bound. Later on,
Desharnais, Edalat, and Panangaden showed that negation is not necessary to
characterize the same equivalence. In this paper, we prove that the logical
characterization holds also when conjunction is replaced by disjunction, with
negation still being not necessary. To this end, we introduce reactive
probabilistic trees, a fully abstract model for reactive probabilistic systems
that allows us to demonstrate expressiveness of the disjunctive probabilistic
modal logic, as well as of the previously mentioned logics, by means of a
compactness argument.Comment: Aligned content with version accepted at ICTCS 2016: fixed minor
typos, added reference, improved definitions in Section 3. Still 10 pages in
sigplanconf forma
Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes
We have recently defined a weak Markovian bisimulation equivalence in an
integrated-time setting, which reduces sequences of exponentially timed
internal actions to individual exponentially timed internal actions having the
same average duration and execution probability as the corresponding sequences.
This weak Markovian bisimulation equivalence is a congruence for sequential
processes with abstraction and turns out to induce an exact CTMC-level
aggregation at steady state for all the considered processes. However, it is
not a congruence with respect to parallel composition. In this paper, we show
how to generalize the equivalence in a way that a reasonable tradeoff among
abstraction, compositionality, and exactness is achieved for concurrent
processes. We will see that, by enhancing the abstraction capability in the
presence of concurrent computations, it is possible to retrieve the congruence
property with respect to parallel composition, with the resulting CTMC-level
aggregation being exact at steady state only for a certain subset of the
considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055
The Spectrum of Strong Behavioral Equivalences for Nondeterministic and Probabilistic Processes
We present a spectrum of trace-based, testing, and bisimulation equivalences
for nondeterministic and probabilistic processes whose activities are all
observable. For every equivalence under study, we examine the discriminating
power of three variants stemming from three approaches that differ for the way
probabilities of events are compared when nondeterministic choices are resolved
via deterministic schedulers. We show that the first approach - which compares
two resolutions relatively to the probability distributions of all considered
events - results in a fragment of the spectrum compatible with the spectrum of
behavioral equivalences for fully probabilistic processes. In contrast, the
second approach - which compares the probabilities of the events of a
resolution with the probabilities of the same events in possibly different
resolutions - gives rise to another fragment composed of coarser equivalences
that exhibits several analogies with the spectrum of behavioral equivalences
for fully nondeterministic processes. Finally, the third approach - which only
compares the extremal probabilities of each event stemming from the different
resolutions - yields even coarser equivalences that, however, give rise to a
hierarchy similar to that stemming from the second approach.Comment: In Proceedings QAPL 2013, arXiv:1306.241
Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi
Labeled transition systems are typically used to represent the behavior of
nondeterministic processes, with labeled transitions defining a one-step state
to-state reachability relation. This model has been recently made more general
by modifying the transition relation in such a way that it associates with any
source state and transition label a reachability distribution, i.e., a function
mapping each possible target state to a value of some domain that expresses the
degree of one-step reachability of that target state. In this extended
abstract, we show how the resulting model, called ULTraS from Uniform Labeled
Transition System, can be naturally used to give semantics to a fully
nondeterministic, a fully probabilistic, and a fully stochastic variant of a
CSP-like process language.Comment: In Proceedings PACO 2011, arXiv:1108.145
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
Observer design for piecewise smooth and switched systems via contraction theory
The aim of this paper is to present the application of an approach to study
contraction theory recently developed for piecewise smooth and switched
systems. The approach that can be used to analyze incremental stability
properties of so-called Filippov systems (or variable structure systems) is
based on the use of regularization, a procedure to make the vector field of
interest differentiable before analyzing its properties. We show that by using
this extension of contraction theory to nondifferentiable vector fields, it is
possible to design observers for a large class of piecewise smooth systems
using not only Euclidean norms, as also done in previous literature, but also
non-Euclidean norms. This allows greater flexibility in the design and
encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear)
systems. The theoretical methodology is illustrated via a set of representative
examples.Comment: Preprint accepted to IFAC World Congress 201
Revisiting bisimilarity and its modal logic for nondeterministic and probabilistic processes
We consider PML, the probabilistic version of Hennessy-Milner logic introduced by Larsen and Skou to characterize bisimilarity over probabilistic processes without internal
nondeterminism.We provide two different interpretations for PML by considering nondeterministic and probabilistic processes as models, and we exhibit two new bisimulation-based equivalences that are in full agreement with those interpretations. Our new equivalences include
as coarsest congruences the two bisimilarities for nondeterministic and probabilistic processes proposed by Segala and Lynch. The latter equivalences are instead in agreement with two versions of Hennessy-Milner logic extended with an additional probabilistic operator
interpreted over state distributions rather than over individual states. Thus, our new interpretations of PML and the corresponding new bisimilarities offer a uniform framework for reasoning on processes that are purely nondeterministic or reactive probabilistic or are mixing nondeterminism and probability in an alternating/non-alternating way
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