Results 1  10
of
11
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
Abstract

Cited by 304 (36 self)
 Add to MetaCart
The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Gates accept concurrent behavior
 In Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci
, 1993
"... We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that ..."
Abstract

Cited by 37 (16 self)
 Add to MetaCart
(Show Context)
We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essentially that of linear logic, with its morphisms being consequencepreserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language. 1
An Event Structure Semantics for General Petri Nets
 Theoretical Computer Science
, 1993
"... In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent stru ..."
Abstract

Cited by 24 (1 self)
 Add to MetaCart
(Show Context)
In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent structures. We propose that ULevent structures are appropriate for capturing the behaviour of general Petri nets. Our answer is a partial one in that in the proposed event structure semantics, autoconcurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a nontrivial and conservative extension of the (prime) event structure semantics of 1safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1safe Petri nets established in a categorical framework in [W3] can be extended to the present setting, provided we restrict our attention to the subclass ...
Causal automata
 THEORETICAL COMPUTER SCIENCE
, 1992
"... We introduce causal automata, a formalism based on a syntactic approach to causality in contrast to conventional approaches based on partial orders. Our main result is the following characterisation of Milner's notion of confluence in CCS:
Confluence = Determinism + {AND;OR} Causality ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
(Show Context)
We introduce causal automata, a formalism based on a syntactic approach to causality in contrast to conventional approaches based on partial orders. Our main result is the following characterisation of Milner's notion of confluence in CCS:
Confluence = Determinism + {AND;OR} Causality
Concurrent Kripke Structures
 In Proceedings of the North American Process Algebra Workshop, Cornell CSTR931369
, 1993
"... We consider a class of Kripke Structures in which the atomic propositions are events. This enables us to represent worlds as sets of events and the transition and satisfaction relations of Kripke structures as the subset and membership relations on sets. We use this class, called event Kripke struct ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
(Show Context)
We consider a class of Kripke Structures in which the atomic propositions are events. This enables us to represent worlds as sets of events and the transition and satisfaction relations of Kripke structures as the subset and membership relations on sets. We use this class, called event Kripke structures, to model concurrency. The obvious semantics for these structures is a true concurrency semantics. We show how several aspects of concurrency can be easily defined, and in addition get distinctions between causality and enabling, and choice and nondeterminism. We define a duality for event Kripke structures, and show how this duality enables us to convert between imperative and declarative views of programs, by treating states and events on the same footing. We provide pictorial representations of both these views, each encoding all the information to convert to the other. We define a process algebra of event Kripke structures, showing how to combine them in the usual waysparallel co...
A Cartesian Closed Category of Event Structures with Quotients
, 2006
"... We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compress ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compression of event structures as an example of quotient: the compression of an event structure E is a minimal event structure with the same space of maximal configurations as E.
A Generalized Event Structure for the Muller Unfolding of a Safe Net
, 1994
"... In 1959, Muller and Bartky published a celebrated paper on "A Theory of Asynchronous Circuits". Among many novel techniques in that paper was the use of lattices resembling the domains of configurations of event structures. In the light of this we present a generalization of Muller's ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
In 1959, Muller and Bartky published a celebrated paper on "A Theory of Asynchronous Circuits". Among many novel techniques in that paper was the use of lattices resembling the domains of configurations of event structures. In the light of this we present a generalization of Muller's construction to safe nets. We find, however, that this "Muller unfolding " cannot be generated as the domain of configurations of any known event structure, not even a General Event structure. (In particular, this unfolding differs from that of Nielsen, Plotkin and Winskel) This paper attempts to fill that gap. We make use of the logical approach to causality, developed in previous work, in which a General Event Structure is interpreted as a logical automation arising from a particular logic of causality. We introduce a new causal logic and associate a corresponding logical automaton to any finite safe Petri net. Our main result is that the domain of configurations of this generalized event structure is isomorphic to the Muller unfolding of the net. The work described here was done as part of
On the Semantics of Place/Transition Nets
 CONCUR'99, LNCS 1664
, 1999
"... Abstract. We present several interpretations of the behavior of P/T nets in terms of traces, event structures, and partial orders. Starting from results of Hoogers, Kleijn and Thiagarajan, we show how Petri nets determine local trace languages; these may be represented by local event structures in m ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We present several interpretations of the behavior of P/T nets in terms of traces, event structures, and partial orders. Starting from results of Hoogers, Kleijn and Thiagarajan, we show how Petri nets determine local trace languages; these may be represented by local event structures in many ways, each method leading to a particular coreflection. One of these semantics is finally proved to be appropriate for the construction of a behavior preserving unfolding of Petri nets. 1
Coherence Spaces As Event Structures And Concrete Data Structures
"... In [ZHA 89] Zhang presents a relation between coherence spaces (that were introduced by Girard [GIR 89] for modelling the system F and to give a semantic for linear logic) and event domains [WIN 81] using theory of categories. In this paper we give a characterization of the relation between coherenc ..."
Abstract
 Add to MetaCart
In [ZHA 89] Zhang presents a relation between coherence spaces (that were introduced by Girard [GIR 89] for modelling the system F and to give a semantic for linear logic) and event domains [WIN 81] using theory of categories. In this paper we give a characterization of the relation between coherence spaces, event domains and concrete domains [KAH 93], as well as a relation between the "concrete counterparts" of these domains: webs of coherence spaces, event structures and concrete data structures (cds). According to Zhang [ZHA 89, p. 156], a coherence space can be seen as a particular case of dIdomains 2 and of event structures too. With respect to the second "characterization" of coherence spaces (related with event structures), we show that the former are related with event domains (the abstract counterpart of the event structures) and not with the event structures as asserts Zhang. The results are presented by twelve propositions and theorems 1