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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 481 (20 self)
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Least fixpoints as meanings of recursive definitions.
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint sol ..."
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Cited by 26 (3 self)
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When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a "free amalgamated product" as a possible solution to the first problem. Subsequently, we define socalled simplycombinable structures (SCstructures). For SCstructures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SCstructures yields the free amalgamated product. The combination technique of [BS92, BaS94a] can be used to combine constraint solvers for (strong) SCstructures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SCstru...
Universal homogeneous causal sets
 Computational Structures for Modelling Space, Time and Causality, Dagstuhl Seminar Proceedings, Internationales Begegnungs und Forschungszentrum (IBFI), Schloss Dagstuhl
, 2006
"... Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete spacetime in quantum gravity. We show that the class C of all countable pastfinite causal sets contains a unique causal set (U, ≤) which is universal (i.e., any member of C can be embedded into ..."
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Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete spacetime in quantum gravity. We show that the class C of all countable pastfinite causal sets contains a unique causal set (U, ≤) which is universal (i.e., any member of C can be embedded into (U, ≤)) and homogeneous (i.e., (U, ≤) has maximal degree of symmetry). Moreover, (U, ≤) can be constructed both probabilistically and explicitly. 1
On an Open Problem of Amadio and Curien: the Finite Antichain Condition 1 Abstract
"... More than a dozen years ago, Amadio [1] (see Amadio and Curien [2] as well) raised the question of whether the category of stable bifinite domains of AmadioDroste [1,6,7] is the largest cartesian closed full subcategory of the category of ωalgebraic meetcpos with stable functions. A solution to ..."
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More than a dozen years ago, Amadio [1] (see Amadio and Curien [2] as well) raised the question of whether the category of stable bifinite domains of AmadioDroste [1,6,7] is the largest cartesian closed full subcategory of the category of ωalgebraic meetcpos with stable functions. A solution to this problem has two major steps: (1) Show that for any ωalgebraic meetcpo D, if all higherorder stable function spaces built from D are ωalgebraic, then D is finitary (i.e., it satisfies the socalled axiom I); (2) Show that for any ωalgebraic meetcpo D, if D violates MI ∞ , then [D → D] violates either M or I. We solve the first part of the problem in this paper, i.e., for any ωalgebraic meetcpo D, if the stable function space [D → D] satisfies M, then D is finitary. Our notion of (mub, meet)closed set, which is introduced for step 1, will also be used for treating some example cases in step 2. 1
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"... this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. Almost every domain is universal ..."
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this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be found at the ENTCS Macro Home Page. Almost every domain is universal
Mediating Secure Information Flow Policies
"... Abstract. In this paper we study secure information flow policies in the sense of Meadows [12] and others for aggregated datasets, collectively. We first present a method for combining different sensitivity levels over a common dataset and investigate its ramifications on information flow policies. ..."
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Abstract. In this paper we study secure information flow policies in the sense of Meadows [12] and others for aggregated datasets, collectively. We first present a method for combining different sensitivity levels over a common dataset and investigate its ramifications on information flow policies. Next, safeflow policies are formulated in full generality using domaintheoretic tools, and systematically derived as closure operators from Scott continuous functions. Maximum safeflow policies correspond to the top element of the lattice of the derived closureoperator collection. We then introduce a categorical framework for information flow, in which amalgamation is used to formulate and characterize informationflow policy merging. Our methods for mediating information flow policies should be of practical interest for information sharing among multiple agencies. Our formulation of safeflow policies as closure operators from Scott continuous functions and its associated categorical formulation of safeflow policy merging provide a sound and general theoretical foundation for the first time for this topic, setting a stage for further development in this area. 1
Domain Theory  Corrected and expanded version
"... bases were introduced in [Smy77] where they are called "Rstructures". Examples of abstract bases are concrete bases of continuous domains, of course, where the relation is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have ..."
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bases were introduced in [Smy77] where they are called "Rstructures". Examples of abstract bases are concrete bases of continuous domains, of course, where the relation is the restriction of the order of approximation. Axiom (INT) is satisfied because of Lemma 2.2.15 and because we have required bases in domains to have directed sets of approximants for each element.
The study of random structures began wi...
"... Abstract In a line of recent development, probabilistic constructions of universal, homogeneous objects have been provided in various categories of ordered structures, such as causal ..."
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Abstract In a line of recent development, probabilistic constructions of universal, homogeneous objects have been provided in various categories of ordered structures, such as causal
This text is based on the chapter Domain Theory in the Handbook for Logic in
"... E. Maibaum, published by Clarendon Press, Oxford in 1994. While the numbering of all theorems and definitions has been kept the same, we have included comments and corrections which we have received over the years. For ease of reading, small typographical errors have simply been corrected. Where we ..."
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E. Maibaum, published by Clarendon Press, Oxford in 1994. While the numbering of all theorems and definitions has been kept the same, we have included comments and corrections which we have received over the years. For ease of reading, small typographical errors have simply been corrected. Where we felt the original text gave a misleading impression, we have included additional explanations, clearly marked as such. If you wish to refer to this text, then please cite the published original version where possible, or otherwise this online version which we try to keep available from the page