16 research outputs found
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
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
Conflict vs causality in event structures
Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting
Principles of Markov automata
A substantial amount of today's engineering problems revolve around systems that are concurrent and stochastic by their nature. Solution approaches attacking these problems often rely on the availability of formal mathematical models that reflect such systems as comprehensively as possible. In this thesis, we develop a compositional model, Markov automata, that integrates concurrency, and probabilistic and timed stochastic behaviour. This is achieved by blending two well-studied constituent models, probabilistic automata and interactive Markov chains. A range of strong and weak bisimilarity notions are introduced and evaluated as candidate relations for a natural behavioural equivalence between systems. Among them, weak distribution bisimilarity stands out as a natural notion being more oblivious to the probabilistic branching structure than prior notions. We discuss compositionality, axiomatizations, decision and minimization algorithms, state-based characterizations and normal forms for weak distribution bisimilarity. In addition, we detail how Markov automata and weak distribution bisimilarity can be employed as a semantic basis for generalized stochastic Petri nets, in such a way that known shortcomings of their classical semantics are ironed out in their entirety.Ein beträchtlicher Teil gegenwärtiger ingenieurwissenschafter Probleme erstreckt sich auf Sys- teme, die ihrer Natur nach sowohl stochastisch als auch nebenläufig sind. Lösungsansätze fußen hierbei häufig auf der Verfügbarkeit formaler mathematischer Modelle, die es erlauben, die Spez- ifika jener Systeme möglichst erschöpfend zu erfassen. In dieser Dissertation entwickeln wir ein kompositionelles Modell namens Markov-Automaten, das Nebenläufigkeit mit probabilistis- chen und stochastischen Prozessen integriert. Dies wird durch die Verschmelzung der zweier bekannter Modellklassen erreicht, und zwar die der probabilistischen Automaten und die der interaktiven Markovketten. Wir entwickeln dabei ein Spektrum verschiedener, starker und schwacher Bisimulationsrelationen und beurteilen sie im Hinblick auf ihre Eignung als natür- liche Verhaltensäquivalenz zwischen Systemen. Die schwache Wahrscheinlichkeitsverteilungs- bisimulation sticht dabei als natürliche Wahl hervor, da sie die probabilistische Verzwei- gungsstruktur treffender abstrahiert als bisher bekannte Bisimulationsrelationen. Wir betra- chten des Weiteren Kompositionalitätseigenschaften, Axiomatisierungen, Entscheidungs- und Minimierungsalgorithmen, sowie zustandsbasierte Charakterisierungen und Normalformen für die schwache Wahrscheinlichkeitsverteilungsbisimulation. Abschließend legen wir dar, dass Markov-Automaten und die schwacheWahrscheinlichkeitsverteilungsbisimulation als Grundlage für eine verbesserte Semantik von verallgemeinerten stochastischen Petrinetzen dienen kann, welche bekannte Mängel der klassischen Semantik vollständig behebt
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science