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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.”
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...
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 ..."
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Cited by 32 (16 self)
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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
Relationships between Models of Concurrency
, 1994
"... . Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The ..."
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Cited by 25 (4 self)
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. Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalized through the medium of category theory. Keywords. Semantics, Concurrency, Models for Concurrency, Categories. Contents 1 Preliminaries 431 2 Deterministic Transition Systems 433 3 Noninterleaving vs. Interleaving Models 436 Synchronization Trees and Labelled Event Structures : : : : : : : : : : : : : : 438 Transition Systems with Independence : : : : : : : : : : : : : : : : : : : : : : 439 4 Behavioural, Linear Time, Noninterleaving Models 441 Semilanguages and Event Structures : : : : : : : : : : : : : : : : : : : : : : : 443 Trace Languages and Event Structures : : : : : : : : : : : : : : : : : : : : : : 446 5 Transition Systems with Independence and Lab...
Event Spaces and Their Linear Logic
 In AMAST’91: Algebraic Methodology and Software Technology, Workshops in Computing
, 1991
"... Boolean logic treats disjunction and conjunction symmetrically and algebraically. The corresponding operations for computation are respectively nondeterminism (choice) and concurrency. Petri nets treat these symmetrically but not algebraically, while event structures treat them algebraically but not ..."
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Cited by 22 (9 self)
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Boolean logic treats disjunction and conjunction symmetrically and algebraically. The corresponding operations for computation are respectively nondeterminism (choice) and concurrency. Petri nets treat these symmetrically but not algebraically, while event structures treat them algebraically but not symmetrically. Here we achieve both via the notion of an event space as a poset with all nonempty joins representing concurrence and a top representing the unreachable event. The symmetry is with the dual notion of state space, a poset with all nonempty meets representing choice and a bottom representing the start state. The algebra is that of a parallel programming language expanded to the language of full linear logic, Girard's axiomatization of which is satisfied by the event space interpretation of this language. Event spaces resemble finite dimensional vector spaces in distinguishing tensor product from direct product and in being isomorphic to their double dual, but differ from them i...
Action Refinement
 Handbook of Proacess Algebra
, 2000
"... S. All local authors can be reached via email at the address lastname@cs.unibo.it. Questions and comments should be addressed to tradmin@cs.unibo.it. Recent Titles from the UBLCS Technical Report Series 974 An Algebra of Actors, M. Gaspari, G. Zavattaro, May 1997. 975 On the Turing Equivalen ..."
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Cited by 18 (3 self)
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S. All local authors can be reached via email at the address lastname@cs.unibo.it. Questions and comments should be addressed to tradmin@cs.unibo.it. Recent Titles from the UBLCS Technical Report Series 974 An Algebra of Actors, M. Gaspari, G. Zavattaro, May 1997. 975 On the Turing Equivalence of Linda Coordination Primitives, N. Busi, R. Gorrieri, G. Zavattaro, May 1997 (Revised October 1998). 976 A Process Algebraic View of Linda Coordination Primitives, N. Busi, R. Gorrieri, G. Zavattaro, May 1997. 977 Validating a Software Architecture with respect to an Architectural Style, P. Ciancarini, W. Penzo, July 1997. 978 System Support for PartitionAware Network Applications, O. Babaoglu, R. Davoli, A. Montresor, R. Segala, October 1997. 979 Generalized SemiMarkovian Process Algebra, M. Bravetti, M. Bernardo, R. Gorrieri, October 1997. 981 Group Communication in Partitionable Systems: Specification and Algorithms, O. Babao glu, R. Davoli, A. Montresor, April 1998. 982...
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... ..."
Algebraic recognizability of languages
 In Proc. 29th Int. Symp. Math. Found. of Comp. Sci. (MFCS’04
, 2004
"... Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those ..."
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Cited by 11 (3 self)
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Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finiteindex congruences, rational expressions, monadic second
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 ..."
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Cited by 10 (0 self)
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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...
Deterministic Behavioural Models for Concurrency (Extended Abstract)
 Mathematical Foundations of Computer Science
, 1993
"... This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled ev ..."
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Cited by 9 (5 self)
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This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled event structures, generalized trace languages in which the independence relation is contextdependent, and deterministic languages of pomsets. Introduction Models for concurrency can be classified according to whether they can represent the structure of systems or just their behaviours (Behaviour or System model); whether they can faithfully take into account the difference between concurrency and nondeterminism (Interleaving or Noninterleaving model); and, finally, whether they can represent the branching structure of processes, i.e., the points in which choices are taken, or not (Linear or Branching Time model). In [9], the authors studied a range of models based on such a classificatio...