Symmetric and Asymmetric Asynchronous Interaction

We investigate classes of systems based on different interaction patterns with the aim of achieving distributability. As our system model we use Petri nets. In Petri nets, an inherent concept of simultaneity is built in, since when a transition has more than one preplace, it can be crucial that tokens are removed instantaneously. When modelling a system which is intended to be implemented in a distributed way by a Petri net, this built-in concept of synchronous interaction may be problematic. To investigate this we consider asynchronous implementations of nets, in which removing tokens from places can no longer be considered as instantaneous. We model this by inserting silent (unobservable) transitions between transitions and some of their preplaces. We investigate three such implementations, differing in the selection of preplaces of a transition from which the removal of a token is considered time consuming, and the possibility of collecting the tokens in a given order. We investigate the effect of these different transformations of instantaneous interaction into asynchronous interaction patterns by comparing the behaviours of nets before and after insertion of the silent transitions. We exhibit for which classes of Petri nets we obtain equivalent behaviour with respect to failures equivalence. It turns out that the resulting hierarchy of Petri net classes can be described by semi-structural properties. For two of the classes we obtain precise characterisations; for the remaining class we obtain lower and upper bounds. We briefly comment on possible applications of our results to Message Sequence Charts.Comment: 27 pages. An extended abstract of this paper was presented at the first Interaction and Concurrency Experience (ICE'08) on Synchronous and Asynchronous Interactions in Concurrent Distributed Systems, and will appear in Electronic Notes in Theoretical Computer Science, Elsevie

Process equivalence in the context of genetic mining

In various application domains there is a desire to compare process models, e.g., to relate an organization-specific process model to a reference model, to find a web service matching some desired service description, or to compare some normative process model with a process model discovered using process mining techniques. Although many researchers have worked on different notions of equivalence (e.g., trace equivalence, bisimulation, branching bisimulation, etc.), most of the existing notions are not very useful in this context. First of all, most equivalence notions result in a binary answer (i.e., two processes are equivalent or not). This is not very helpful, because, in real-life applications, one needs to differentiate between slightly different models and completely different models. Second, not all parts of a process model are equally important. There may be parts of the process model that are rarely activated (i.e., "process veins") while other parts are executed for most process instances (i.e., the "process arteries"). Clearly, differences in some veins of a process are less important than differences in the main artery of a process. To address the problem, this paper proposes a completely new way of comparing process models. Rather than directly comparing two models, the process models are compared with respect to some typical behavior. This way, we are able to avoid the two problems just mentioned. The approach has been implemented and has been used in the context of genetic process mining. Although the results are presented in the context of Petri nets, the approach can be applied to any process modeling language with executable semantics

On Synchronous and Asynchronous Interaction in Distributed Systems

When considering distributed systems, it is a central issue how to deal with interactions between components. In this paper, we investigate the paradigms of synchronous and asynchronous interaction in the context of distributed systems. We investigate to what extent or under which conditions synchronous interaction is a valid concept for specification and implementation of such systems. We choose Petri nets as our system model and consider different notions of distribution by associating locations to elements of nets. First, we investigate the concept of simultaneity which is inherent in the semantics of Petri nets when transitions have multiple input places. We assume that tokens may only be taken instantaneously by transitions on the same location. We exhibit a hierarchy of `asynchronous' Petri net classes by different assumptions on possible distributions. Alternatively, we assume that the synchronisations specified in a Petri net are crucial system properties. Hence transitions and their preplaces may no longer placed on separate locations. We then answer the question which systems may be implemented in a distributed way without restricting concurrency, assuming that locations are inherently sequential. It turns out that in both settings we find semi-structural properties of Petri nets describing exactly the problematic situations for interactions in distributed systems.Comment: 26 pages. An extended abstract of this paper appeared in Proceedings 33rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2008), Torun, Poland, August 2008 (E. Ochmanski & J. Tyszkiewicz, eds.), LNCS 5162, Springer, 2008, pp. 16-3

Decidability and coincidence of equivalences for concurrency

There are two fundamental problems concerning equivalence relations in con-currency. One is: for which system classes is a given equivalence decidable? The second is: when do two equivalences coincide? Two well-known equivalences are history preserving bisimilarity (hpb) and hereditary history preserving bisimi-larity (hhpb). These are both ‘independence ’ equivalences: they reflect causal dependencies between events. Hhpb is obtained from hpb by adding a ‘back-tracking ’ requirement. This seemingly small change makes hhpb computationally far harder: hpb is well-known to be decidable for finite-state systems, whereas the decidability of hhpb has been a renowned open problem for several years; only recently it has been shown undecidable. The main aim of this thesis is to gain insights into the decidability problem for hhpb, and to analyse when it coincides with hpb; less technically, we might say, to analyse the power of the interplay between concurrency, causality, and conflict. We first examine the backtracking condition, and see that it has two dimen

Two-dimensional models as testing ground for principles and concepts of local quantum physics

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL(2,Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular Euclideanization'' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J. A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an ``Encyclopedia of Mathematical Physics'' contribution hep-th/0502125.Comment: 55 pages, removal of some typos in section

Factorization Algebras and Functorial Field Theories

Factorization algebras are a new mathematical approach to quantum field theory. They are related to functorial field theories, another approach to quantum field theory. Factorization algebras also figure in current research in manifold topology, homotopy theory and algebraic geometry. The workshop brought together researchers from many different fields to understand and deepen these connections

Algebraic Holography

A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.Comment: 16 pages, 1 figure, v3: new material added in response to referees' reports, v4: a hasty conclusion in v3 rectified + more cosmetic change

Dynamic analysis of repetitive decision-free discreteevent processes: The algebra of timed marked graphs and algorithmic issues

A model to analyze certain classes of discrete event dynamic systems is presented. Previous research on timed marked graphs is reviewed and extended. This model is useful to analyze asynchronous and repetitive production processes. In particular, applications to certain classes of flexible manufacturing systems are provided in a companion paper. Here, an algebraic representation of timed marked graphs in terms of reccurrence equations is provided. These equations are linear in a nonconventional algebra, that is described. Also, an algorithm to properly characterize the periodic behavior of repetitive production processes is descrbed. This model extends the concepts from PERT/CPM analysis to repetitive production processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44155/1/10479_2005_Article_BF02248590.pd

Über Klassen verteilter Petrinetze

This thesis considers -- on a fundamental, and theoretical level -- the question which behaviours respectively algorithms can be realized in a distributed system. It employs Petri nets and various behavioural equivalences to model such systems. Based upon those, it identifies an M-shaped structure as the smallest undistributable Petri net and proves that this identification is stable across a wide swath of the linear-time branching-time spectrum of behavioural equivalences, collected by Glabbeek. It also gives a constructive proof that all Petri nets not containing such a structure are fully distributable. It employs this construction in a prototypical compiler from Petri nets to distributed (via TCP/IP) Linux binaries which was used to test (and fix) said construction. Finally, multiple ways to evade the undistributability theorem's assumptions are discussed, to enable the distributed implementation of necessary behaviours nonetheless.Die Arbeit untersucht -- auf theoretischer und damit fundamentaler Basis -- die Frage welche Verhaltensweisen beziehungsweise Algorithmen durch ein verteiltes System realisiert werden können. Solche Systeme werden dazu durch Petrinetze und verschiedene Verhaltensäquivalenzen modelliert. Innerhalb dieses Modells wird eine M-förmige Struktur als das kleinste unverteilbare Petrinetz identifiziert und gezeigt, dass diese Eigenschaft über einen großen Bereich des durch Glabbeek beschriebenen Linear-Time Branching-Time Spektrums der Verhaltensäquivalenzen stabil bleibt. Die Arbeit enthält weiter einen konstruktiven Beweis, dass alle Petrinetze ohne diese Struktur vollständig verteilbar sind. Die enthaltene Konstruktion wird dann in einem prototypischen Compiler von Petrinetzen nach verteilten (via TCP/IP) Linux-Binaries verwendet, um die Konstruktion zu testen (und zu korrigieren). Schließlich werden verschiedene Wege diskutiert, wie sich die Vorbedingungen des Unverteilbarkeitstheorems umgehen lassen, um notwendige Verhaltensweisen dennoch verteilt implementieren zu können