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47
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 ..."
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Cited by 263 (33 self)
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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.”
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 239 (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...
Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 231 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
On Interprocess Communication
, 1985
"... A formalism, not based upon atomic actions, for specifying and reasoning about concurrent systems is defined. It is used to specify several classes of interprocess communication mechanisms and to prove the correctness of algorithms for implementing them. ..."
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Cited by 145 (6 self)
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A formalism, not based upon atomic actions, for specifying and reasoning about concurrent systems is defined. It is used to specify several classes of interprocess communication mechanisms and to prove the correctness of algorithms for implementing them.
Modeling Concurrency with Geometry
, 1991
"... The phenomena of branching time and true or noninterleaving concurrency find their respective homes in automata and schedules. But these two models of computation are formally equivalent via Birkhoff duality, an equivalence we expound on here in tutorial detail. So why should these phenomena prefer ..."
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Cited by 125 (13 self)
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The phenomena of branching time and true or noninterleaving concurrency find their respective homes in automata and schedules. But these two models of computation are formally equivalent via Birkhoff duality, an equivalence we expound on here in tutorial detail. So why should these phenomena prefer one home over the other? We identify dimension as the culprit: 1dimensional automata are skeletons permitting only interleaving concurrency, whereas true nfold concurrency resides in transitions of dimension n. The truly concurrent automaton dual to a schedule is not a skeletal distributive lattice but a solid one. We introduce true nondeterminism and define it as monoidal homotopy; from this perspective nondeterminism in ordinary automata arises from forking and joining creating nontrivial homotopy. The automaton dual to a poset schedule is simply connected whereas that dual to an event structure schedule need not be, according to monoidal homotopy though not to group homotopy. We conclude...
The Equational Theory of Pomsets
, 1988
"... Pomsets have been introduced as a mode2 of concurrency. Since a pomset is a string in which the total order has been relaxed to be a partial order, in this paper we view them as a generalization cf Strings, and investigate their algebraic properties. In particular, we investigate the axiomatic prope ..."
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Cited by 49 (0 self)
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Pomsets have been introduced as a mode2 of concurrency. Since a pomset is a string in which the total order has been relaxed to be a partial order, in this paper we view them as a generalization cf Strings, and investigate their algebraic properties. In particular, we investigate the axiomatic properties of pornsets, sets of pomsets and ideals of pornsets, under such operations as concatenation, parallel composition, union and their associated closure operations. We find that the equational theory of sets, pomsets under concatenation, parallel composition and union is finitely axiomatizable, whereas the theory of languages under the analogous operations is not. A similar result is obtained for ideals of pornsets, which incorporate the notion of subsumption which is also known as auaentation. Finally, we show that the addition of any closure operation (parallel or serial) Ieads to nonfinite axiomatizability of the resulting equational theory.
Hereditary History Preserving Bisimulations or What is the Power of the Future Perfect in Program Logics
 Polish Academy of Sciences
, 1991
"... Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations ..."
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Cited by 36 (0 self)
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Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Relations Between History Preserving Bisimulations . . . . . . . . . . . . . . . . 5 2 History Preserving Bisimulations and Refinement 7 2.1 Refinement of Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 History Preserving Bisimulations vs Refinement . . . . . . . . . . . . . . . . . . . 8 3 Back and Forth Bisimulation on Sequential Systems 8 3.1 Unfolding transition systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Unfolding versus BackandForth Bisimulation . . . . . . . . . . . . . . . . . . . 12 3.3 The Power of the Future Pe
Local Specification of Distributed Families of Sequential Objects
 Recent Trends in Data Types Specification, Proc. 10th Workshop on Specification of Abstract Data Types joint with the 5th COMPASS Workshop, S.Margherita, Italy, May/June 1994, Selected papers
, 1995
"... . Fully concurrent models of distributed object systems are specified using linear temporal logic that does not per se cope with concurrency. This is achieved by employing the principle of local sequentiality: we specify from local viewpoints assuming that there is no intraobject concurrency but ful ..."
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Cited by 28 (11 self)
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. Fully concurrent models of distributed object systems are specified using linear temporal logic that does not per se cope with concurrency. This is achieved by employing the principle of local sequentiality: we specify from local viewpoints assuming that there is no intraobject concurrency but full interobject concurrency. Local formulae are labelled by identity terms. For interaction, objects may refer to actions of other objects, e.g., calling them to happen synchronously. A locality predicate allows for making local statements about other objects. The interpretation structures are global webs of local life cycles, glued together at shared communication events. These interpretation structures are embedded in an interpretation frame that is a labelled locally sequential event structure. Two initiality results are presented: the category of labelled locally sequential event structures has initial elements, and so has the full subcategory of those satisfying given temporal axioms. As...
Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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Cited by 23 (0 self)
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...
Projecting Sequential Algorithms on Strongly Stable Functions
 Annals of Pure and Applied Logic
, 1993
"... We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the ..."
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Cited by 22 (2 self)
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We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the "extensional projections" of some sequential algorithms. We define a model of PCF where morphisms are "extensional" sequential algorithms and prove that any equation between PCF terms which holds in this model also holds in the strongly stable model.