Probabilistic event structures and domains

Varacca, Daniele; Völzer, Hagen; Winskel, Glynn

doi:10.1016/j.tcs.2006.01.015

Cited by 47 publications

(36 citation statements)

References 14 publications

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“…This is a particular case of a general observation which we take into account in our approach, namely, the observation that probability spaces characterizing initial segments of random behaviours can be established only on confluence-free sets of processes (cf. [25] for a similar observation and the respective conclusions).…”

Section: Random Behaviours a Peculiarity Of Behaviours With Concurrensupporting

confidence: 78%

An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive Presentation

Winkowski

2009

Fundamenta Informaticae

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The paper is the first part of a two-part paper that contributes with a concept of a process viewed as a model of a run of a phenomenon (discrete, continuous, or of a mixed type), with operations allowing to define complex processes in terms of their components, with the respective algebras, and with the idea of using the formal tools thus obtained to describe the behaviours of concurrent systems.A process may have an initial state (a source), a final state (a target), or both. A process can be represented by a partially ordered multiset. Processes of which one can be a continuation of the other can be composed sequentially. Independent processes, i.e. processes which do not disturb each other, can be composed in parallel. Processes may be prefixes, i.e. independent components of initial segments of other processes.Processes in a universe of objects and operations on such processes form a partial algebra, called algebra of processes. Algebras of processes are partial categories with respect to the sequential composition, and partial monoids with respect to the parallel composition.Algebras of processes can be used to define behaviours of concurrent systems. The behaviour of a system can be defined as the set of possible processes of this system with a structure on this set. Such a set is prefix-closed. The structure on this set reflects the prefix order and, possibly, specific features of the behaviour like observability, the relation to flow of real time, etc.Algebras of processes can also be used to define behaviours, to define operations on behaviours similar to those in the existing calculi of behaviours, and to define random behaviours.The first part of the whole paper investigates algebras of processes and their applications to describing behaviours of systems. In the second part the properties of algebras of processes described in the first part are regarded as axioms defining a class of abstract partial algebras, called behaviouroriented algebras, and they initiate a theory of such algebras. Partial ordersGiven a partial order ≤ on a set X, i.e. a binary relation which is reflexive, anti-symmetric and transitive, we call P = (X, ≤) a partially ordered set, or briefly a poset, by the strict partial order corresponding to ≤ we mean <, where x < y iff x ≤ y and x = y, by a chain we mean a subset Y ⊆ X such that x ≤ y or y ≤ x for all x, y ∈ Y , and by an antichain we mean a subset Z ⊆ X such that x < y does not hold for any x, y ∈ Z.2.1. Definition. Given a poset P = (X, ≤), by a strong cross-section of P we mean a maximal antichain Z of P that has an element in every maximal chain of P . By a weak cross-section, or briefly a crosssection, of P we mean a maximal antichain Z of P such that, for every x, y ∈ X for which x ≤ y and x ≤ z ′ and z ′′ ≤ y with some z ′ , z ′′ ∈ Z, there exists z ∈ Z such that x ≤ z ≤ y. ♯ Definition.We say that a partial order ≤ on X (and the poset P = (X, ≤)) is strongly K-dense (resp.: weakly K-dense) iff every maximal antichain of P is a strong (resp.: a weak) cross-section of P...

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Section: Random Behaviours a Peculiarity Of Behaviours With Concurrensupporting

confidence: 78%

An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive Presentation

Winkowski

2009

Fundamenta Informaticae

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“…5) Extensions: Games, such as those of [8], [13], allowing copying are being systematized through the use of monads and comonads [11], work now feasible on event structures with symmetry [12]. Nondeterministic strategies can potentially support probability as probabilistic or stochastic event structures [14] to become probabilistic or stochastic strategies.…”

Section: ) Stable Spans Profunctors and Stable Functionsmentioning

confidence: 99%

Concurrent Strategies

Rideau

Winskel

2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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131

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“…This is a topic worthwhile to be pursued since event structures with a probability dimension are currently under study (see [269]). …”

Section: Normative Knowledge Representationmentioning

confidence: 99%

Analysis and Synthesis of Logics

Gabbay

Carnieli²,

Coniglio³

et al. 2008

Applied Logic Series

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SCOPE OF THE SERIESLogic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Springer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing so demonstrates the underlying unity and applicability of logic.The titles published in this series are listed at the end of this volume. Library of Congress Control Number: 2008920294ISBN 978-1-4020-6781-5 (HB) ISBN 978-1-4020-6782-2 (e-book)Published by Springer,

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Probabilistic event structures and domains

Cited by 47 publications

References 14 publications

An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive Presentation

An Algebraic Framework for Defining Behaviours of Concurrent Systems. Part 1: The Constructive Presentation

Concurrent Strategies

Analysis and Synthesis of Logics

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