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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
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... ..."
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...
Chu spaces: Complementarity and Uncertainty in Rational Mechanics
, 1994
"... this paper will be realizations. The category of Boolean operations and their propertypreserving renamings is not selfdual since nonT 0 Chu spaces transpose to nonextensional ones. By the same reasoning the full subcategory consisting of T 0 operations, those with no properties a j b for distinct ..."
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Cited by 9 (0 self)
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this paper will be realizations. The category of Boolean operations and their propertypreserving renamings is not selfdual since nonT 0 Chu spaces transpose to nonextensional ones. By the same reasoning the full subcategory consisting of T 0 operations, those with no properties a j b for distinct variables a; b, is selfdual. This is a very important fact: it means that to every full subcategory C of this selfdual category we may associate its dual as the image of C under the selfduality. This associates sets to complete atomic Boolean algebras, Boolean algebras to Stone spaces, distributive lattices to StonePriestley posets, semilattices to algebraic lattices, complete semilattices to themselves, and so on for many other familiar [Joh82] and not so familiar (selfduality of finitedimensional vector spaces over GF (2)) instances of Stone duality We now illustrate the general idea with some examples.
Chu Spaces: Automata with quantum aspects
 In Proc. Workshop on Physics and Computation (PhysCompâ€™94
, 1994
"... Chu spaces are a recently developed model of concurrent computation extending automata theory to express branching time and true concurrency. They exhibit in a primitive form the quantum mechanical phenomena of complementarity and uncertainty. The complementarity arises as the duality of information ..."
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Cited by 8 (3 self)
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Chu spaces are a recently developed model of concurrent computation extending automata theory to express branching time and true concurrency. They exhibit in a primitive form the quantum mechanical phenomena of complementarity and uncertainty. The complementarity arises as the duality of information and time, automata and schedules, and states and events. Uncertainty arises when we define a measurement to be a morphism and notice that increasing structure in the observed object reduces clarity of observation. For a Chu space this uncertainty can be calculated numerically in an attractively simple way directly from its form factor to yield the usual Heisenberg uncertainty relation. Chu spaces correspond to wavefunctions as vectors of Hilbert space, whose inner product operation is realized for Chu spaces as right residuation and whose quantum logic becomes Girard's linear logic. 1 Introduction 1.1 Prospects for Chu Spaces The automaton model of this paper, Chu spaces, is an outgrowth ...
Time and Information in Sequential and Concurrent Computation
 In Proc. Theory and Practice of Parallel Programming
, 1994
"... Time can be understood as dual to information in extant models of both sequential and concurrent computation. The basis for this duality is phase space, coordinatized by time and information, whose axes are oriented respectively horizontally and vertically. We fit various basic phenomena of computat ..."
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Cited by 5 (1 self)
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Time can be understood as dual to information in extant models of both sequential and concurrent computation. The basis for this duality is phase space, coordinatized by time and information, whose axes are oriented respectively horizontally and vertically. We fit various basic phenomena of computation, and of behavior in general, to the phase space perspective. The extant twodimensional logics of sequential behavior, the van Glabbeek map of branching time and true concurrency, eventstate duality and scheduleautomaton duality, and Chu spaces, all fit the phase space perspective well, in every case confirming our choice of orientation. 1 Introduction Our recent research has emphasized a basic duality between time and information in concurrent computation. In this paper we return to our earlier work on sequential computation and point out that a very similar duality is present there also. Our main goal here will be to compare concurrent and sequential computation in terms of this dua...
Types as Processes, via Chu spaces
 EXRESS'97 Proceedings
, 1997
"... We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces ..."
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Cited by 2 (0 self)
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We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces and their transformational logic. Beyond this point the connection appears to break down; we pose the question of whether the failures of the corrrespondence are intrinsic or cultural. 1 Introduction Typesasprocesses modernizes dataasprograms. It is the CurryHoward propositionsastypes correspondence with propositions replaced by processes. To the extent that types and processes are both part of the working programmer 's toolkit, even more than propositions, the typesasprocesses correspondence is more central to the practice of programming than propositionsastypes. Moreover the connection works out very well mathematically, at least up to a point. The similarities and differences ...