Adding Priority to Event Structures

Event Structures (ESs) are mainly concerned with the representation of causal relationships between events, usually accompanied by other event relations capturing conflicts and disabling. Among the most prominent variants of ESs are Prime ESs, Bundle ESs, Stable ESs, and Dual ESs, which differ in their causality models and event relations. Yet, some application domains require further kinds of relations between events. Here, we add the possibility to express priority relationships among events. We exemplify our approach on Prime, Bundle, Extended Bundle, and Dual ESs. Technically, we enhance these variants in the same way. For each variant, we then study the interference between priority and the other event relations. From this, we extract the redundant priority pairs-notably differing for the types of ESs-that enable us to provide a comparison between the extensions. We also exhibit that priority considerably complicates the definition of partial orders in ESs.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Generalized event structures and probabilities

For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also consistently suppose predictions and probabilities which are neither classical nor quantum, but which are subject to subclassicality; that is, the additivity of probabilities for mutually exclusive, co-measurable observables, as formalized by admissibility rules and frame functions.Comment: 10 pages, 10 figures in Information and Complexity, World Scientific Series in Information Studies: Volume 6, ed. by Mark Burgin and Cristian S Calude, Chapter 11, pp. 276-300, (World Scientific, Singapore, 2016

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

Event structures for Petri nets with persistence

Event structures are a well-accepted model of concurrency. In a seminal paper by Nielsen, Plotkin and Winskel, they are used to establish a bridge between the theory of domains and the approach to concurrency proposed by Petri. A basic role is played by an unfolding construction that maps (safe) Petri nets into a subclass of event structures, called prime event structures, where each event has a uniquely determined set of causes. Prime event structures, in turn, can be identified with their domain of configurations. At a categorical level, this is nicely formalised by Winskel as a chain of coreflections. Contrary to prime event structures, general event structures allow for the presence of disjunctive causes, i.e., events can be enabled by distinct minimal sets of events. In this paper, we extend the connection between Petri nets and event structures in order to include disjunctive causes. In particular, we show that, at the level of nets, disjunctive causes are well accounted for by persistent places. These are places where tokens, once generated, can be used several times without being consumed and where multiple tokens are interpreted collectively, i.e., their histories are inessential. Generalising the work on ordinary nets, Petri nets with persistence are related to a new subclass of general event structures, called locally connected, by means of a chain of coreflections relying on an unfolding construction

Language and tool support for event refinement structures in Event-B

Event-B is a formal method for modelling and verifying the consistency of chains of model refinements. The event refinement structure (ERS) approach augments Event-B with a graphical notation which is capable of explicit representation of control flows and refinement relationships. In previous work, the ERS approach has been evaluated manually in the development of two large case studies, a multimedia protocol and a spacecraft sub-system. The evaluation results helped us to extend the ERS constructors, to develop a systematic definition of ERS, and to develop a tool supporting ERS. We propose the ERS language which systematically defines the semantics of the ERS graphical notation including the constructors. The ERS tool supports automatic construction of the Event-B models in terms of control flows and refinement relationships. In this paper we outline the systematic definition of ERS including the presentation of constructors, the tool that supports it and evaluate the contribution that ERS and its tool make. Also we present how the systematic definition of ERS and the corresponding tool can ensure a consistent encoding of the ERS diagrams in the Event-B models

A Nice Labelling for Tree-Like Event Structures of Degree 3 (Extended Version)

We address the problem of finding nice labellings for event structures of degree 3. We develop a minimum theory by which we prove that the labelling number of an event structure of degree 3 is bounded by a linear function of the height. The main theorem we present in this paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors. Finally, we exemplify how to use this theorem to construct upper bounds for the labelling number of other event structures of degree 3