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

A Threat to the Occident? Comparing Human Values of Muslim Immigrants, Christian, and Non-religious Natives in Western Europe

With a growing Muslim population, many European countries need to integrate Muslims into their societies. One aspect that can hinder successful integration are substantial differences in human values. This is because such values are consequential for attitudes as well as behavior. We compare basic human values between Muslim immigrants and non-Muslim natives in four European countries with distinct immigration histories and integration politics: Belgium, France, Germany, and Sweden. For most insightful comparisons, we contrast values of Muslim immigrants with those of Christian natives as well as those of non-religious natives. We employ data of more than 50,000 individuals based on the first eight waves of the European Social Survey. Our findings reveal significant differences in value priorities between Muslims, Christians and non-religious individuals in all four countries. Amongst other things, Muslim immigrants score particularly high in conservation values (security and tradition/conformity). At the same time, they also score higher in self-transcendence values (benevolence as well as universalism). While many of these findings are in line with theory and previous research, the higher score in universalism is unexpected. A potential explanation is the combination of religious traditionalism and discrimination experiences. In other words, religious traditions are associated with more conservative views, but being subject to marginalization can still result in an appreciation of equal opportunities. We find only limited support for differences in hedonism. Religiosity correlates with values of tradition/conformity for Muslim immigrants as well as for Christian natives. Thus, accounting for religiosity renders differences in these values between Muslims and other groups statistically insignificant. While most of these findings hold in all countries, differences are most pronounced in Sweden and lower in the other three countries, which is also true after accounting for differences in socio-economic status and religiosity between the three groups. This suggests that a combination of a country's history of diversity and national integration policies either encourages the convergence of values or leads to a solidification of value differences between groups. We discuss these political and social implications of our findings

A threat to the occident? Comparing human values of muslim immigrants, christian, and non-religious natives in Western Europe

With a growing Muslim population, many European countries need to integrate Muslims into their societies. One aspect that can hinder successful integration are substantial differences in human values. This is because such values are consequential for attitudes as well as behavior. We compare basic human values between Muslim immigrants and non-Muslim natives in four European countries with distinct immigration histories and integration politics: Belgium, France, Germany, and Sweden. For most insightful comparisons, we contrast values of Muslim immigrants with those of Christian natives as well as those of non-religious natives. We employ data of more than 50,000 individuals based on the first eight waves of the European Social Survey. Our findings reveal significant differences in value priorities between Muslims, Christians and non-religious individuals in all four countries. Amongst other things, Muslim immigrants score particularly high in conservation values (security and tradition/conformity). At the same time, they also score higher in self-transcendence values (benevolence as well as universalism). While many of these findings are in line with theory and previous research, the higher score in universalism is unexpected. A potential explanation is the combination of religious traditionalism and discrimination experiences. In other words, religious traditions are associated with more conservative views, but being subject to marginalization can still result in an appreciation of equal opportunities. We find only limited support for differences in hedonism. Religiosity correlates with values of tradition/conformity for Muslim immigrants as well as for Christian natives. Thus, accounting for religiosity renders differences in these values between Muslims and other groups statistically insignificant. While most of these findings hold in all countries, differences are most pronounced in Sweden and lower in the other three countries, which is also true after accounting for differences in socio-economic status and religiosity between the three groups. This suggests that a combination of a country's history of diversity and national integration policies either encourages the convergence of values or leads to a solidification of value differences between groups. We discuss these political and social implications of our findings

The Quest for Minimal Quotients for Probabilistic Automata

One of the prevailing ideas in applied concurrency theory and verification is the concept of automata minimization with respect to strong or weak bisimilarity. The minimal automata can be seen as canonical representations of the behaviour modulo the bisimilarity considered. Together with congruence results wrt. process algebraic operators, this can be exploited to alleviate the notorious state space explosion problem. In this paper, we aim at identifying minimal automata and canonical representations for concurrent probabilistic models. We present minimality and canonicity results for probabilistic automata wrt. strong and weak bisimilarity, together with polynomial time minimization algorithms

A semantics for every GSPN

Generalised Stochastic Petri Nets (GSPNs) are a popular modelling formalism for performance and dependability analysis. Their semantics is traditionally associated to continuous-time Markov chains (CTMCs), enabling the use of standard CTMC analysis algorithms and software tools. Due to ambiguities in the semantic interpretation of confused GSPNs, this analysis strand is however restricted to nets that do not exhibit non-determinism, the so-called well-defined nets. This paper defines a simple semantics for every GSPN. No restrictions are imposed on the presence of confusions. Immediate transitions may be weighted but are not required to be. Cycles of immediate transitions are admitted too. The semantics is defined using a non-deterministic variant of CTMCs, referred to as Markov automata. We prove that for well-defined bounded nets, our semantics is weak bisimulation equivalent to the existing CTMC semantics. Finally, we briefly indicate how every bounded GSPN can be quantitatively assessed. © 2013 Springer-Verlag.Generalised Stochastic Petri Nets (GSPNs) are a popular modelling formalism for performance and dependability analysis. Their semantics is traditionally associated to continuous-time Markov chains (CTMCs), enabling the use of standard CTMC analysis algorithms and software tools. Due to ambiguities in the semantic interpretation of confused GSPNs, this analysis strand is however restricted to nets that do not exhibit non-determinism, the so-called well-defined nets. This paper defines a simple semantics for every GSPN. No restrictions are imposed on the presence of confusions. Immediate transitions may be weighted but are not required to be. Cycles of immediate transitions are admitted too. The semantics is defined using a non-deterministic variant of CTMCs, referred to as Markov automata. We prove that for well-defined bounded nets, our semantics is weak bisimulation equivalent to the existing CTMC semantics. Finally, we briefly indicate how every bounded GSPN can be quantitatively assessed. © 2013 Springer-Verlag