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Domains and Processes : Proceedings of the 1st International Symposium on Domain Theory Shanghai, China, October 1999 - Klaus Keimel

Domains and Processes

Proceedings of the 1st International Symposium on Domain Theory Shanghai, China, October 1999

By: Klaus Keimel (Editor), Guo-Qiang Zhang (Editor), Ying Ming Liu (Editor), Yixiang Chen (Editor)

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Published: 31st October 2001
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Domain theory is a rich interdisciplinary area at the intersection of logic, computer science, and mathematics. This volume contains selected papers presented at the International Symposium on Domain Theory which took place in Shanghai in October 1999. Topics of papers range from the encounters between topology and domain theory, sober spaces, Lawson topology, real number computability and continuous functionals to fuzzy modelling, logic programming, and pi-calculi.
This book is a valuable reference for researchers and students interested in this rapidly developing area of theoretical computer science.

Prefacep. ix
Contributing Authorsp. xiii
Encounters Between Topology and Domain Theoryp. 1
Introductionp. 1
Introductory Domain Theoryp. 3
The Scott Topologyp. 7
Locally Compact Spacesp. 10
Spectral Theoryp. 11
Round Ideal Completionsp. 14
Ordered Spacesp. 17
Compact Pospacesp. 18
Spaces of Maximal Pointsp. 19
The Domain of Closed Formal Ballsp. 23
Fixed Point Theoryp. 25
The Probabilistic Power Domainp. 26
Open Problems and Research Directionsp. 28
Topological Appendixp. 29
The Lawson Topology on Quasicontinuous Domainsp. 33
Introductionp. 33
Quasicontiuous domainsp. 34
Strictly complete regularity of the Lawson topologyp. 36
U[subscript k]-admitting dcpos need not be soberp. 41
Introductionp. 41
U[subscript k]-admitting for locally compact dcpo'sp. 42
U[subscript k]-admitting does not always imply soberp. 45
The Largest Topologically Cartesian Closed Categories of Domains as Topological Spacesp. 51
Introduction and Preliminariesp. 51
Relations between tcc and ccc categoriesp. 53
FS is the largest tcc full subcategory of CONT[subscript [perpendicular, bottom]p. 55
F-FS is the largest tcc full subcategory of CONTp. 59
On the Equivalence of Some Approaches to Computability on the Real Linep. 67
Introductionp. 68
The TTE approach to real number computationsp. 71
The domain-theoretic approach to real number computabilityp. 76
The language Real PCFp. 84
The equivalence resultsp. 91
Concluding remarksp. 98
Appendixp. 99
The continuous functionals of finite types over the realsp. 103
Introductionp. 103
The typesp. 105
The hereditarily total objectsp. 110
Density and co-densityp. 111
Limit spacesp. 117
The traditional approachp. 118
Compact Semantics on Bc-domainsp. 125
Introductionp. 125
Preliminaries and Characterizations for Semantics Continuityp. 127
The Compactness Theorem And Applicationsp. 132
Conclusionp. 136
Normal Subsets in Abstract Basesp. 137
Introductionp. 137
Prerequisitesp. 139
Normal subsets and sub-domainsp. 140
The dcpo class of abstract bases and a fixed point theoremp. 145
Semantics of Logic Programs and Representation of Smyth Powerdomainp. 151
Introductionp. 152
Domains and information systemsp. 154
Main representation theoremp. 158
Proofsp. 160
Examplesp. 166
Semantics of disjunctive logic programsp. 169
Clausal logic over sequent structuresp. 174
Conclusionp. 179
Domains of view: a foundation for specification and analysisp. 183
Introductionp. 183
Kripke modal transition systemsp. 185
Fuzzy Kripke modal transition systemsp. 195
Modal Markov chainsp. 206
Modal relationsp. 209
Related workp. 213
Semantic Theory and Proof System of Open Bisimulation for the [pi]-Calculus with Mismatchingp. 219
Introductionp. 220
Operational Semantics of the [pi superscript [not equal]-Calculusp. 222
Open Bisimulation and Its Symbolic Characterizationp. 225
Proof System for Open Bisimulationp. 232
The Weak Casep. 237
Conclusionsp. 241
Axiomatization without Prefix Combinatorp. 245
Introductionp. 245
Preliminariesp. 250
Polyadic X-Calculusp. 252
A Process Calculus without Precedencep. 256
Ground Bisimilarity for Atomic X-Calculusp. 262
Axiomatization in the Absence of Prefix, Summation and Match Combinatorsp. 264
Final Remarksp. 271
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792371434
ISBN-10: 0792371437
Series: Semantic Structures in Computation, Volume 1
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 273
Published: 31st October 2001
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.13 x 16.51  x 2.54
Weight (kg): 0.59