scholarly journals Models for Concurrency

1992 ◽  
Vol 21 (429) ◽  
Author(s):  
Glynn Winskel ◽  
Mogens Nielsen
Keyword(s):  
Category Theory ◽  
Parallel Composition ◽  
Transition Systems ◽  
Basic Category ◽  
Oxford University ◽  
Event Structures ◽  
Causal Independence ◽  
Draft Version ◽  
Use Category ◽  
Mazurkiewicz Traces

This is a draft version of a chapter for the Handbook of Logic and the Foundations of Computer Science, Oxford University Press. The final draft can be found as DAIMI PB 463. <br /> It surveys a range of models for parallel computation to include interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like Petri nets, asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. It is still a draft at present. In particular, the ''Notes'' surveying related work are incomplete and the appendix on fibred categories needs to be overhauled in the light of some slick proofs, provided by Bart Jacobs. It is ragged in other places too. Constructive comments and corrections will be appreciated. <p>A knowledge of basic category theory is assumed, up to an acquaintance with the notion of adjunction.</p>

scholarly journals Models for Concurrency

1993 ◽  
Vol 22 (463) ◽  
Author(s):  
Glynn Winskel ◽  
Mogens Nielsen
Keyword(s):  
Category Theory ◽  
Parallel Composition ◽  
Transition Systems ◽  
Basic Category ◽  
Final Version ◽  
Oxford University ◽  
Event Structures ◽  
Causal Independence ◽  
Use Category ◽  
Mazurkiewicz Traces

<p>Revised version of DAIMI PB-429</p><p> </p><p>This is, we believe, the final version of a chapter for the Handbook of Logic and the Foundations of Computer Science, vol. IV, Oxford University Press.</p><p>It surveys a range of models for parallel computation to include interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like Petri nets, asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence.</p><p>The presentation is unified by casting the models in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. A knowledge of basic category theory is assumed, up to an acquaintance with the notion of adjunction.</p>

scholarly journals Models for Concurrency

1994 ◽  
Vol 1 (12) ◽  
Author(s):  
Glynn Winskel ◽  
Mogens Nielsen
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Category Theory ◽  
Parallel Composition ◽  
Transition Systems ◽  
Basic Category ◽  
Event Structures ◽  
Causal Independence ◽  
Use Category ◽  
Mazurkiewicz Traces

This report surveys a range of models for parallel computation to include interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like Petri nets, asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models.<br /> <br />A knowledge of basic category theory is assumed, up to an acquaintance with the notion of adjunction.

scholarly journals A Compositional Proof System on a Category of Labelled Transition Systems

1989 ◽  
Vol 18 (294) ◽  
Author(s):  
Glynn Winskel
Keyword(s):  
Category Theory ◽  
Proof System ◽  
Parallel Composition ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Proof Systems ◽  
Categorical Logic ◽  
Parallel Processes ◽  
System A ◽  
Categorical Constructions

This paper presents an attempt to cast labelled transition systems, and other models of parallel computation, in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. Another aim is to exploit the framework of categorical logic to systematise specification languages and the derivation of proof systems for parallel processes. After presenting a category of labelled transition systems, its categorical constructions are used to establish a compositional proof system. A category of properties of transition systems indexed by the category of labelled transition systems is used in forrning the proof system.

Modelling Nondeterministic Concurrent Processes with Event Structures

1991 ◽  
Vol 14 (1) ◽  
pp. 39-73
Author(s):  
Rita Loogen ◽  
Ursula Goltz
Keyword(s):  
Dynamic Behaviour ◽  
Partially Ordered Sets ◽  
Parallel Composition ◽  
Ordered Sets ◽  
Communicating Sequential Processes ◽  
Partially Ordered ◽  
Event Structures ◽  
Transition Relation ◽  
Concurrent Processes ◽  
Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

scholarly journals Transition-Systems, Event Structures, and Unfoldings

1995 ◽  
Vol 118 (2) ◽  
pp. 191-207 ◽  
Author(s):  
M. Nielsen ◽  
G. Rozenberg ◽  
P.S. Thiagarajan
Keyword(s):  
Transition Systems ◽  
Event Structures

scholarly journals Bisimulation from Open Maps

1994 ◽  
Vol 1 (7) ◽  
Author(s):  
André Joyal ◽  
Mogens Nielsen ◽  
Glynn Winskel
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Transition Systems ◽  
New Model ◽  
Event Structures ◽  
Uniform Definition ◽  
Refinement Operators ◽  
Definition Of ◽  
Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

Linking Business and Application Architectures

2013 ◽  
pp. 209-228
Author(s):  
Suresh Kamath
Keyword(s):  
Information Technology ◽  
Category Theory ◽  
Information Architecture ◽  
Common Language ◽  
It Strategy ◽  
It Investments ◽  
Business Architecture ◽  
It Architecture ◽  
Application Architecture ◽  
Use Category

The development of an IT strategy and ensuring that it is the best possible one for business is a key problem many organizations face. This problem is that of linking business architecture to IT architecture in general and application architecture specifically. Without this linkage it is difficult to manage the changes needed by the business and maximize the benefits from the information technology (IT) investments. Linking the two domains requires defining the two architectures using a “common language.” While the application architecture domain has developed tools and processes to define and represent the architecture, the business architecture domain, however, lacks such processes and tools to be useful for linking of the two. The chapter addresses several questions dealing with the linking of the business and the application architectures. The author proposes to use category theory related constructs and notions to represent the business and information architecture and the linkages.

SPECIFICATION OF SOFTWARE ARCHITECTURE

2000 ◽  
Vol 10 (01) ◽  
pp. 69-95 ◽  
Author(s):  
MARK J. GERKEN
Keyword(s):  
Software Architecture ◽  
Category Theory ◽  
Formal Definition ◽  
The Past ◽  
Algebraic Specifications ◽  
Software Specifications ◽  
Architecture Theory ◽  
Definition Of ◽  
Semantic Compatibility ◽  
Use Category

Over the past several years, software architecture representation and analysis has become an active area of research. However, most approaches to software architecture representation and analysis have been informal. We postulate that through formality, the term "architecture" can be precisely defined and important properties of systems, such as semantic compatibility between connected entities, can be investigated with precision. In this paper, we use category theory and algebraic specifications to develop a formal definition of architecture and show how architecture theory can be used in the construction of software specifications.

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