Fairneß, Randomisierung und Konspiration in verteilten Algorithmen

Fairneß (d.h. faire Konfliktlösung), Randomisierung (d.h. Münzwürfe) und partielle Synchronie sind verschiedene Konzepte, die häufig zur Lösung zentraler Synchronisations- und Koordinationsprobleme in verteilten Systemen verwendet werden. Beispiele für solche Probleme sind das Problem des wechselseitigen Ausschlusses (kurz: Mutex-Problem) sowie das Konsens-Problem. Für einige solcher Probleme wurde bewiesen, daß ohne die oben genannten Konzepte keine Lösung für das betrachtete Problem existiert. Unmöglichkeitsresultate dieser Art verbessern unser Verständnis der Wirkungsweise verteilter Algorithmen sowie das Verständnis des Trade-offs zwischen einem leicht analysierbaren und einem ausdrucksstarken Modell für verteiltes Rechnen. In dieser Arbeit stellen wir zwei neue Unmöglichkeitsresultate vor. Darüberhinaus beleuchten wir ihre Hintergründe. Wir betrachten dabei Modelle, die Randomisierung einbeziehen, da bisher wenig über die Grenzen der Ausdrucksstärke von Randomisierung bekannt ist. Mit einer Lösung eines Problems durch Randomisierung meinen wir, daß das betrachtete Problem mit Wahrscheinlichkeit 1 gelöst wird. Im ersten Teil der Arbeit untersuchen wir die Beziehung von Fairneß und Randomisierung. Einerseits ist bekannt, daß einige Probleme (z.B. das Konsens- Problem) durch Randomisierung nicht aber durch Fairneß lösbar sind. Wir zeigen nun, daß es andererseits auch Probleme gibt (nämlich das Mutex-Problem), die durch Fairneß, nicht aber durch Randomisierung lösbar sind. Daraus folgt, daß Fairneß nicht durch Randomisierung implementiert werden kann. Im zweiten Teil der Arbeit verwenden wir ein Modell, das Fairneß und Randomisierung vereint. Ein solches Modell ist relativ ausdrucksstark: Es erlaubt Lösungen für das Mutex-Problem, das Konsens-Problem, sowie eine Lösung für das allgemeine Mutex-Problem. Beim allgemeinen Mutex-Problem (auch bekannt als Problem der speisenden Philosophen) ist eine Nachbarschaftsrelation auf den Agenten gegeben und ein Algorithmus gesucht, der das Mutex-Problem für jedes Paar von Nachbarn simultan löst. Schließlich betrachten wir das ausfalltolerante allgemeine Mutex-Problem -- eine Variante des allgemeinen Mutex-Problems, bei der Agenten ausfallen können. Wir zeigen, daß sogar die Verbindung von Fairneß und Randomisierung nicht genügt, um eine Lösung für das ausfalltolerante allgemeine Mutex-Problem zu konstruieren. Ein Hintergrund für dieses Unmöglichkeitsresultat ist ein unerwünschtes Phänomen, für das in der Literatur der Begriff Konspiration geprägt wurde. Konspiration wurde bisher nicht adäquat charakterisiert. Wir charakterisieren Konspiration auf der Grundlage nicht-sequentieller Abläufe. Desweiteren zeigen wir, daß Konspiration für eine große Klasse von Systemen durch die zusätzliche Annahme von partieller Synchronie verhindert werden kann, d.h. ein konspirationsbehaftetes System kann zu einem randomisierten System verfeinert werden, das unter Fairneß und partieller Synchronie mit Wahrscheinlichkeit 1 konspirationsfrei ist. Partielle Synchronie fordert, daß alle relativen Geschwindigkeiten im System durch eine Konstante beschränkt sind, die jedoch den Agenten nicht bekannt ist. Die Darstellung der Unmöglichkeitsresultate und die Charakterisierung von Konspiration wird erst durch die Verwendung nicht-sequentieller Abläufe möglich. Ein nicht-sequentieller Ablauf repräsentiert im Gegensatz zu einem sequentiellen Ablauf kausale Ordnung und nicht zeitliche Ordnung von Ereignissen. Wir entwickeln in dieser Arbeit eine nicht-sequentielle Semantik für randomisierte verteilte Algorithmen, da es bisher keine in der Literatur gibt. In dieser Semantik wird kausale Unabhängigkeit durch stochastische Unabhängigkeit widergespiegelt.Concepts such as fairness (i.e., fair conflict resolution), randomization (i.e., coin flips), and partial synchrony are frequently used to solve fundamental synchronization- and coordination-problems in distributed systems such as the mutual exclusion problem (mutex problem for short) and the consensus problem. For some problems it is proven that, without such concepts, no solution to the particular problem exists. Impossibilty results of that kind improve our understanding of the way distributed algorithms work. They also improve our understanding of the trade-off between a tractable model and a powerful model of distributed computation. In this thesis, we prove two new impossibility results and we investigate their reasons. We are in particular concerned with models for randomized distributed algorithms since little is yet known about the limitations of randomization with respect to the solvability of problems in distributed systems. By a solution through randomization we mean that the problem under consideration is solved with probability 1. In the first part of the thesis, we investigate the relationship between fairness and randomization. On the one hand, it is known that to some problems (e.g. to the consensus problem), randomization admits a solution where fairness does not admit a solution. On the other hand, we show that there are problems (viz. the mutex problem) to which randomization does not admit a solution where fairness does admit a solution. These results imply that fairness cannot be implemented by coin flips. In the second part of the thesis, we consider a model which combines fairness and randomization. Such a model is quite powerful, allowing solutions to the mutex problem, the consensus problem, and a solution to the generalized mutex problem. In the generalized mutex problem (a.k.a. the dining philosophers problem), a neighborhood relation is given and mutual exclusion must be achieved for each pair of neighbors. We finally consider the crash-tolerant generalized mutex problem where every hungry agent eventually becomes critical provided that neither itself nor one of its neighbors crashes. We prove that even the combination of fairness and randomization does not admit a solution to the crash-tolerant generalized mutex problem. We argue that the reason for this impossibility is the inherent occurrence of an undesirable phenomenon known as conspiracy. Conspiracy was not yet properly characterized. We characterize conspiracy on the basis of non-sequential runs, and we show that conspiracy can be prevented by help of the additional assumption of partial synchrony, i.e., we show that every conspiracy-prone system can be refined to a randomized system which is, with probability 1, conspiracy-free under the assumptions of partial synchrony and fairness. Partial synchrony means that each event consumes a bounded amount of time where, however, the bound is not known. We use a non-sequential semantics for distributed algorithms which is essential to some parts of the thesis. In particular, we develop a non-sequential semantics for randomized distributed algorithms since there is no such semantics in the literature. In this non-sequential semantics, causal independence is reflected by stochastic independence

Matching Business Process Workflows across Abstraction Levels

In Business Process Modeling, several models are defined for the same system, supporting the transition from business requirements to IT implementations. Each of these models targets a different abstraction level and stakeholder perspective. In order to maintain consistency among these models, which has become a major challenge not only in this field, the correspondence between them has to be identified. A correspondence between process models establishes which activities in one model correspond to which activities in another model. This paper presents an algorithm for determining such correspondences. The algorithm is based on an empirical study of process models at a large company in the banking sector, which revealed frequent correspondence patterns between models spanning multiple abstraction levels. The algorithm has two phases, first establishing correspondences based on similarity of model element attributes such as types and names and then refining the result based on the structure of the models. Compared to previous work, our algorithm can recover complex correspondences relating whole process fragments rather than just individual activities. We evaluate the algorithm on 26 pairs of business-technical and technical-IT level models from four real-world projects, achieving overall precision of 93% and recall of 70%. Given the substantial recall and the high precision, the algorithm helps automating significant part of the correspondence recovery for such models.Ministerio de Ciencia e Innovación TIN2008-03107Ministerio de Economía y Competitividad TIN2011-2379

Probabilistic event structures and domains

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AI-augmented Business Process Management Systems (ABPMSs) are an emerging class of process-aware information systems, empowered by trustworthy AI technology. An ABPMS enhances the execution of business processes with the aim of making these processes more adaptable, proactive, explainable, and context-sensitive. This manifesto presents a vision for ABPMSs and discusses research challenges that need to be surmounted to realize this vision. To this end, we define the concept of ABPMS, we outline the lifecycle of processes within an ABPMS, we discuss core characteristics of an ABPMS, and we derive a set of challenges to realize systems with these characteristics

Augmented Business Process Management Systems: A Research Manifesto

Augmented Business Process Management Systems (ABPMSs) are an emerging class of process-aware information systems that draws upon trustworthy AI technology. An ABPMS enhances the execution of business processes with the aim of making these processes more adaptable, proactive, explainable, and context-sensitive. This manifesto presents a vision for ABPMSs and discusses research challenges that need to be surmounted to realize this vision. To this end, we define the concept of ABPMS, we outline the lifecycle of processes within an ABPMS, we discuss core characteristics of an ABPMS, and we derive a set of challenges to realize systems with these characteristics.Comment: 19 pages, 1 figur

Refinement-robust fairness

We motivate and study the robustness of fairness notions under refinement of transitions and places in Petri nets. We show that the classical notions of weak and strong fairness are not robust and we propose a hierarchy of increasingly strong, refinement-robust fairness notions. That hierarchy is based on the conflict structure of transitions, which characterizes the interplay between choice and synchronization in a fairness notion. Our fairness notions are defined on non-sequential runs, but we show that the most important notions can be easily expressed on sequential runs as well. The hierarchy is further motivated by a brief discussion on the computational power of the fairness notions

When a system is fairly correct

characterisation of fairness. We also derive a notion of a fairly correct system and sketch its application

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