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23
A Partial Order on Classical and Quantum States
, 2002
"... We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information ..."
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Cited by 19 (6 self)
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We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same
Nonclassical Techniques for Models of Computation
 Topology Proceedings
, 1999
"... After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem. ..."
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Cited by 8 (4 self)
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After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem.
A domain of spacetime intervals in general relativity
, 2004
"... Beginning from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special c ..."
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Cited by 8 (4 self)
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Beginning from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. 1
Conditional Expectation and the Approximation of Labelled Markov Processes
 IN: CONCUR 2003  CONCURRENCY THEORY, LECTURE NOTES IN COMPUTER SCIENCE 2761 (2003
, 2003
"... We develop a new notion of approximation of labelled Markov processes based on the use of conditional expectations. The key idea is to approximate a system by a coarsegraining of the state space and using averages of the transition probabilities. This is unlike any of the previous notions based ..."
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Cited by 7 (4 self)
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We develop a new notion of approximation of labelled Markov processes based on the use of conditional expectations. The key idea is to approximate a system by a coarsegraining of the state space and using averages of the transition probabilities. This is unlike any of the previous notions based on the use of simulation. The resulting approximations are customizable, more accurate and stay within the world of LMPs. The use of averages and expectations may well also make the approximations more robust. We introduce a novel condition  called "granularity"  which leads to unique conditional expectations and which turns out to be a key concept despite its simplicity.
A fixpoint theory for nonmonotonic parallelism
, 2002
"... This paper studies parallel recursion. The trace specification language used in this paper incorporates sequential,j nondeterminism, reactiveness(inclvenessg,F'k traces), three forms of paral'VgJj (inclVgJjqMkEglglgl fairinterlkEglgl synchronous paralonousg and general recursion. In order to use Ta ..."
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Cited by 7 (5 self)
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This paper studies parallel recursion. The trace specification language used in this paper incorporates sequential,j nondeterminism, reactiveness(inclvenessg,F'k traces), three forms of paral'VgJj (inclVgJjqMkEglglgl fairinterlkEglgl synchronous paralonousg and general recursion. In order to use Tarski's theorem to determine the fixpoints of recursions, we need to identify awelVjgJ,FIq partial order.Several orders are considered,incldered new order calrg the lexical order, which tends tosimulM, the execution of a recursion in asimilk manner as the EglVqgJ,E, order. A theorem of this paper shows that no appropriate order exists for the lhegIIIE Tarski's theoremalor is not enough to determine the fixpoints ofparalVI recursions. Instead of usingTarski's theoremdirectl, we reason about the fixpoints of terminatingand nonterminatingbehavioursseparateli Such reasoningis supported by the leg of a new compositioncalio partition. We propose a fixpoint techniquecalni the partitioned fixpoint, which is thelgqk fixpoint of the nonterminatingbehaviours after the terminatingbehaviours reach their greatest fixpoint. The surprisingresul is thataltg,M, a recursion may not beljV"EgJqVE' monotonic, it must have the partitioned fixpoint, which isequal to thelegj lgjIjI,gJqF' fixpoint. Since the partitioned #xpoint iswel defined in anycompl,q lmpl,q theresulq areappljFMgJ to various semanticmodeli Existing fixpoint techniques simpl becomespecial cases of the partitioned fixpoint. Forexamplj an EglIIqgJq',EFglEFg recursion has itslsgj EglMMFIgJq fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is moregeneral than thelegq EglEEkIgJq fixpoint in that the partitioned fixpoint can be determined even when a recursion is notEglVjjVgJq monotonic.Exampln of nonmonotonic recur...
Topological Games in Domain Theory
 Topology Appl
"... We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet. ..."
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Cited by 5 (0 self)
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We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet.
The Regular Spaces With Countably Based Models
 Theoretical Computer Science
"... The regular spaces which may be realized as the set of maximal elements in an !continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces. ..."
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Cited by 4 (2 self)
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The regular spaces which may be realized as the set of maximal elements in an !continuous dcpo are the Polish spaces. In addition, we give a new and conceptually simple model for complete metric spaces.
The Space of Maximal Elements in a Compact Domain
, 2001
"... In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the max ..."
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Cited by 4 (3 self)
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In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the maximal elements of a Scott domain must be completely metrizable. 1
Entropy as a fixed point
"... We study complexity and information and introduce the idea that while complexity is relative to a given class of processes, information is process independent: Information is complexity relative to the class of all conceivable processes. In essence, the idea is that information is an extension of ..."
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Cited by 4 (2 self)
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We study complexity and information and introduce the idea that while complexity is relative to a given class of processes, information is process independent: Information is complexity relative to the class of all conceivable processes. In essence, the idea is that information is an extension of the concept algorithmic complexity from a class of desirable and concrete processes, such as those represented by binary decision trees, to a class more general that can only in pragmatic terms be regarded as existing in the conception. It is then precisely the fact that information is defined relative to such a large class of processes that it becomes an eective tool for analyzing phenomena in a wide range of disciplines. We test
Ideal Models of Spaces
 Theoretical Computer Science
, 2000
"... Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizab ..."
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Cited by 3 (2 self)
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Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizable spaces.