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Modelling Concurrency with Partial Orders
, 1986
"... Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a n ..."
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Cited by 236 (18 self)
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Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets or pomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. Th...
Associative Broadcast And The Communication Semantics Of Naming In Concurrent Systems
, 1993
"... ..."
On The Specification Of Concurrent Systems
, 1991
"... In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by ..."
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Cited by 9 (0 self)
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In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by that of a set with a metric which takes values in a given ordered monoid. Partial orders are the simple case of a monoid whose two elements represent the presence or absence of a constraint. An ordered monoid can be seen as a monoidal category, and schedules based on it are categories enriched in the monoid. Algebraic operations on schedules can then be defined as constructions in the category of schedules. These definitions rely on certain properties of a category of schedules, such as closure and completeness. To simplify proofs of these properties, two constructions are defined. The first creates a category of unlabeled schedules from a system of constraints. The second adds labels to unl...
An Analytical Taxonomy of Naming Systems
 Univ. of Texas Dept. of CS
, 1992
"... A naming system consists of the mechanisms that govern the definition, binding, and access to the names upon which communication among active objects in a parallel or distributed system depends. A concurrent algorithm may require certain patterns of communication among objects. Naming systems differ ..."
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Cited by 5 (2 self)
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A naming system consists of the mechanisms that govern the definition, binding, and access to the names upon which communication among active objects in a parallel or distributed system depends. A concurrent algorithm may require certain patterns of communication among objects. Naming systems differ significantly in the patterns of communication that they support, and this diversity suggests the existence of efficiency tradeoffs and specialization among the various approaches. To enable the impact of these differences upon the structure of concurrent computations to be examined systematically, we present a taxonomy of naming systems that isolates a small set of fundamental naming system properties, and ranks naming systems in (partial) order of the expressiveness they derive from their properties. We compare the properties of the naming systems that underlie several representative concurrent programming systems, and give examples of algorithms that require specific naming system proper...
Parsing Partially Ordered Multisets
, 1997
"... A partially ordered multiset or pomset is a generalization of a string in which the total order has been relaxed to a partial order. Strings are often used as a model for sequential computation; pomsets are a natural model for parallel and distributed computation. By viewing pomsets as a generalizat ..."
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Cited by 4 (1 self)
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A partially ordered multiset or pomset is a generalization of a string in which the total order has been relaxed to a partial order. Strings are often used as a model for sequential computation; pomsets are a natural model for parallel and distributed computation. By viewing pomsets as a generalization of strings, the question is raised whether concepts from language theory can be generalized to pomsets. An important area in the theory of languages is parsing theory. This paper develops the fundamentals of a parsing theory for pomsets, called PLR parsing. It is based on the LRparsing technique, which is the most powerful deterministic parsing technique in language theory. The basic algorithm in the class of PLR parsing algorithms, the PLR(0) algorithm is explained in detail. Keywords: partial orders  partially ordered multisets  pomset languages  pomset grammars  LR parsing  PLR parsing  concurrency theory 1. Introduction Gischer introduces partially ordered multisets o...
The Validity Problem for Extended Regular Expressions
 M. Sc. thesis, MIT
, 1996
"... The study of regular expressions, possibly extended with operators other than the usual union, concatenation and star, has traditionally focused on closed expressions, i.e. expressions not containing free language variables. In this thesis we consider open expressions (i.e. expressions that may cont ..."
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Cited by 3 (0 self)
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The study of regular expressions, possibly extended with operators other than the usual union, concatenation and star, has traditionally focused on closed expressions, i.e. expressions not containing free language variables. In this thesis we consider open expressions (i.e. expressions that may contain language variables) and the problem of deciding valid equations between them. In particular, we study constantfree shuffleintersection regular expressions, that is, expressions containing only language variables and using the shuffle and intersection operators in addition to the usual union, concatenation and star. We prove the decidability of valid equations and inequations between such expressions. This result is achieved introducing a new semantics for constantfree shuffleintersection regular expressions. We prove that our semantics is correct and fully abstract. We then reduce the problem of deciding if two expressions have the same semantics to the equivalence problem of finite ...
Modular Completeness For Communication Closed Layers
 CONCUR '93: 4TH INTERNATIONAL CONFERENCE ON CONCURRENCY THEORY
, 1993
"... The Communication Closed Layers law is shown to be modular complete for a model related to that of Mazurkiewicz. It is shown that in a modular style of program development the CCL rule cannot be derived from simpler ones. Within a nonmodular setup the CCL rule can be derived however from a simp ..."
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The Communication Closed Layers law is shown to be modular complete for a model related to that of Mazurkiewicz. It is shown that in a modular style of program development the CCL rule cannot be derived from simpler ones. Within a nonmodular setup the CCL rule can be derived however from a simpler independence rule and an analog of the expansion rule for process algebras.
Twenty years on: Reflections on the CEDISYS project. Combining true concurrency with
"... process algebra. ..."
Mathematics of Multisets Apostolos Syropoulos
 In Multiset Processing
, 2001
"... This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their ..."
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This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their operations. Finally, we present partially ordered multisets. 1
Concurrent Kleene Algebra and its Foundations <
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: