Results 1  10
of
37
Configuration Structures
 Proceedings of 10th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer
, 1995
"... ..."
Chu spaces and their interpretation as concurrent objects
, 2005
"... A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of pa ..."
Abstract

Cited by 34 (0 self)
 Add to MetaCart
A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takes A to be a schedule of events distributed in time, X to be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the =  relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition on X and precedence on A are recovered as respectively the right and left residuals of the heterogeneous binary relation =  with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.
Full completeness of the multiplicative linear logic of chu spaces
 Proc. IEEE Logic in Computer Science 14
, 1999
"... We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on ..."
Abstract

Cited by 27 (8 self)
 Add to MetaCart
We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a twoletter alphabet. This is the online version of the paper of the same title appearing in the LICS’99 proceedings. 1
Chu Spaces From the Representational Viewpoint
 Ann. Pure Appl. Logic
, 1998
"... We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
We give an elementary introduction to Chu spaces viewed as a set of strings all of the same length. This perspective dualizes the alternative view of Chu spaces as generalized topological spaces, and has the advantage of substituting the intuitions of formal language theory for those of topology. 1 Background Chu spaces provide a simple, uniform, and wellstructured approach to the representation of objects that may possess algebraic, relational, or other structure, and that can transform into one another in ways that respect that structure. Chu spaces are simple by virtue of being merely a rectangular array, with no further machinery. They are uniform in the sense that all transformable objects, whether sets, groups, Boolean algebras, vector spaces, or manifolds, are representable by Chu spaces within the same framework, and hence can coexist in a single typeless universe of mathematical objects. And they are wellstructured in that this seemingly featureless universe in fact has a na...
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 ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
(Show Context)
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...
Configuration Structures, Event Structures and Petri Nets
"... In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without selfloops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive powe ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without selfloops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure. A configuration structure can also be considered logically, as a class of propositional models, or—equivalently— as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key
Configuration Structures (Extended Abstract)
 Proceedings 10 th Annual IEEE Symposium on Logic in Computer Science, LICS’95
, 1995
"... Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then subclasses can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for ..."
Abstract

Cited by 10 (7 self)
 Add to MetaCart
Configuration structures provide a model of concurrency generalising the families of configurations of event structures. They can be considered logically, as classes of propositional models; then subclasses can be axiomatised by formulae of simple prescribed forms. Several equivalence relations for event structures are generalised to configuration structures, and also to general Petri nets. Every configuration structure is shown to be STbisimulation equivalent to a prime event structure with binary conflict; this fails for the tighter history preserving bisimulation. Finally, Petri nets without selfloops under the collective token interpretation are shown behaviourally equivalent to configuration structures, in the sense that there are translations in both directions respecting history preserving bisimulation. This fails for nets with selfloops. 1 Introduction The aim of this paper is to connect several models of concurrency, by providing translations between them and studying whi...
Chu Spaces: Automata with quantum aspects
 In Proc. Workshop on Physics and Computation (PhysComp’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 ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
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 ...
Towards Full Completeness for the Linear Logic of Chu Spaces
 IN ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 1997
"... We prove full completeness for a fragment of the linear logic of the selfdual monoidal category of Chu spaces over 2, namely that the proofs between semisimple (conjunctive normal form) formulas of multiplicative linear logic without constants having two occurrences of each variable are in bijec ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
We prove full completeness for a fragment of the linear logic of the selfdual monoidal category of Chu spaces over 2, namely that the proofs between semisimple (conjunctive normal form) formulas of multiplicative linear logic without constants having two occurrences of each variable are in bijection with the dinatural transformations between the corresponding functors. The proof assigns to variables domains having at most four elements, demonstrating a uniform finite model property for this fragment. We define a notion of proof function analogous to the notion of truth function, determining a transformation between functors, and show that the transformation denoted by a proof net is dinatural if and only if the proof net is sound, namely acyclic and connected. Proof functions are of independent interest as a 2valued model of MLL with MIX.