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Compact Metric Spaces as MinimalLimit Sets in Domains of Bottomed Sequences
, 2003
"... It is shown that every compact metric space X is homeomorphically embedded in an !algebraic domain D as the set of minimal limit elements. ..."
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It is shown that every compact metric space X is homeomorphically embedded in an !algebraic domain D as the set of minimal limit elements.
On a Question of Friedman
 Information and Computation
, 1995
"... In this paper we answer a question of Friedman, providing an !separable model M of the fijcalculus. There therefore exists an ffseparable model for any ff 0. The model M permits no nontrivial enrichment as a partial order; neither does it permit an enrichment as a category with an initial ob ..."
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In this paper we answer a question of Friedman, providing an !separable model M of the fijcalculus. There therefore exists an ffseparable model for any ff 0. The model M permits no nontrivial enrichment as a partial order; neither does it permit an enrichment as a category with an initial object. The open term model embeds in M: by way of contrast we provide a model which cannot embed in any nontrivial model separating all pairs of distinct elements. 1 Introduction Separability is a recurring topic in the calculus. It is usually defined syntactically; there is also an interesting modeltheoretic definition. Say that a subset A of an applicative structure (X; \Delta) is separable if any function f : A ! X is realised by some f in X , by which is meant, that for all a in A, f(a) = f \Delta a. This idea first appears in work of Flagg and Myhill [FM]. They termed the concept "discreteness," employing a topological analogy; we prefer to extend the usual calculus terminology....
Information Categories
 Applied Categorical Structures
, 1991
"... \Information systems" have been introduced by Dana Scott as a convenient means of presenting a certain class of domains of computation, usually known as Scott domains. Essentially the same idea has been developed, if less systematically, by various authors in connection with other classes of dom ..."
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\Information systems" have been introduced by Dana Scott as a convenient means of presenting a certain class of domains of computation, usually known as Scott domains. Essentially the same idea has been developed, if less systematically, by various authors in connection with other classes of domains. In previous work, the present authors introduced the notion of an Icategory as an abstraction and enhancement of this idea, with emphasis on the solution of domain equations of the form D = F (D), with F a functor. An important feature of the work is that we are not conned to domains of computation as usually understood; other classes of spaces, more familiar to mathematicians in general, become also accessible. Here we present the idea in terms of what we call information categories, which are concrete Icategories in which the objects are structured sets of \tokens" and morphisms are relations between tokens. This is more in the spirit of information system work, and...
Induction and recursion on the partial real line via biquotients of bifree algebras (extended abstract
 In Proceedings of the Twelveth Annual IEEE Symposium on Logic in Computer Science
, 1997
"... of bifree algebras ..."
Computability on the Interval Space: A Domain Approach
"... The effectively given continuous domains aims characterize the computable functions (as opposed to the merely continuous ones) and the computable elements of types represented by continuous domains. In this paper we show that computability on arbitrary effectively given continuous domain depends str ..."
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The effectively given continuous domains aims characterize the computable functions (as opposed to the merely continuous ones) and the computable elements of types represented by continuous domains. In this paper we show that computability on arbitrary effectively given continuous domain depends strongly upon the ChurchTuring computability (classical computability on countable sets) on a countable base. In order to introduce the notion of computability on the interval space we need the concepts of effectively given continuous domain. In this approach, several desired properties of a computable interval analysis are obtained.
Abstract Interpretation from a Topological Perspective
, 2009
"... We develop abstract interpretation from topological principles by relaxing the definitions of open set and continuity; key results still hold. We study families of closed and open sets and show they generate post and precondition analyses, respectively. Giacobazzi’s forwardsand backwardscomplete ..."
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We develop abstract interpretation from topological principles by relaxing the definitions of open set and continuity; key results still hold. We study families of closed and open sets and show they generate post and precondition analyses, respectively. Giacobazzi’s forwardsand backwardscomplete functions are characterized by the topologically closed and continuous maps, respectively. Finally, we show that Smyth’s upper and lower topologies for powersets induce the overapproximating and underapproximating transition functions used for abstractmodel checking.
Noetherian spaces in verification
 In ICALP’10
, 2010
"... Abstract. Noetherian spaces are a topological concept that generalizes well quasiorderings. We explore applications to infinitestate verification problems, and show how this stimulated the search for infinite procedures à la KarpMiller. 1 ..."
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Abstract. Noetherian spaces are a topological concept that generalizes well quasiorderings. We explore applications to infinitestate verification problems, and show how this stimulated the search for infinite procedures à la KarpMiller. 1
Interactive Computation: Stepping Stone in the Pathway From Classical to Developmental Computation ∗
"... This paper reviews and extends previous work on the domaintheoretic notion of Machine Development. It summarizes the concept of Developmental Computation and shows how Interactive Computation can be understood as a stepping stone in the pathway from Classical to Developmental Computation. A critica ..."
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This paper reviews and extends previous work on the domaintheoretic notion of Machine Development. It summarizes the concept of Developmental Computation and shows how Interactive Computation can be understood as a stepping stone in the pathway from Classical to Developmental Computation. A critical appraisal is given of Classical Computation, showing in which ways its shortcomings tend to restrict the possible evolution of real computers, and how Interactive and Developmental Computation overcome such shortcomings. A formal conceptual framework is sketched, in order to frame the future development of the formal theory of Developmental Computation. Finally, the current frontier of the work on Developmental Computation is briefly exposed. 1
Decomposition of Domains
 University of Pennsylvania
, 1990
"... The problem of decomposing domains into sensible factors is addressed and solved for the case of dIdomains. A decomposition theorem is proved which allows the represention of a large subclass of dIdomains in a product of flat domains. Direct product decompositions of Scottdomains are studied s ..."
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The problem of decomposing domains into sensible factors is addressed and solved for the case of dIdomains. A decomposition theorem is proved which allows the represention of a large subclass of dIdomains in a product of flat domains. Direct product decompositions of Scottdomains are studied separately. 1 Introduction This work was initiated by Peter Buneman's interest in generalizing relational databases, see [6]. He  quite radically  dismissed the idea that a database should be forced into the format of an nary relation. Instead he allowed it to be an arbitrary antichain in a Scottdomain. The reason for this was that advanced concepts in database theory, such as `null values', `nested relations', and `complex objects' force one to augment relations and values with a notion of information order. Following Buneman's general approach, the question arises how to define basic database theoretic concepts such as `functional dependency' for antichains in Scottdomains. For...
Representations Of Complete Uniform Spaces Via Uniform Domains
, 2002
"... In this paper, we show that complete uniform spaces can be represented domaintheoretically. We introduce the notion of a uniform domain, which is an !algebraic domain with some uniform structure on the set K(D) of nite elements of D. It is proved that when (X; ) is a complete uniform space of coun ..."
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In this paper, we show that complete uniform spaces can be represented domaintheoretically. We introduce the notion of a uniform domain, which is an !algebraic domain with some uniform structure on the set K(D) of nite elements of D. It is proved that when (X; ) is a complete uniform space of countable weight, there is a uniform domain D such that X is the retract of the set L(D) of limit elements of D. On the other hand, in every uniform domain D, there exists a minimal subspace M(D) of L(D) on which K(D) induces a uniformity structure. Thus, a uniform domain can be considered as a set with a particular kind of base of a uniformity. Since every in nite increasing sequences in K(D) identi es one element of M(D), through a labelling of edges of K(D), we obtain an admissible representation of a uniform space in a uniform domain. We also show that such a representation is a proper representation.