Probabilistic Power Domains, Information Systems, and Locales (1994) [3 citations — 1 self]
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author = {Reinhold Heckmann},
title = {Probabilistic Power Domains, Information Systems, and Locales},
booktitle = {Mathematical Foundations of Programming Semantics VIII, volume 802 of Lecture Notes in Computer Science},
year = {1994},
pages = {410--437},
publisher = {Springer Verlag}
}
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Abstract:
The probabilistic power domain construction of Jones and Plotkin [6, 7] is defined by a construction on dcpo's. We present alternative definitions in terms of information systems `a la Vickers [12], and in terms of locales. On continuous domains, all three definitions coincide. 1 Introduction To model probabilistic and randomized algorithms in the semantic framework of dcpo's and Scott continuous functions, Jones and Plotkin introduce in [6, 7] the probabilistic power domain construction PD . It forms a computational monad in the sense of [8] in the category of dcpo's and continuous functions and various of its subcategories of `domains'. Every probabilistic powerdomain PDX is equipped with a family of binary operations + p indexed by a real number p between 0 and 1 such that A+ p B denotes the result of choosing A with probability p and B with probability 1 \Gamma p. Other applications of PD were found in [1]. The probabilistic powerdomain of the upper power space [10] of a second ...
Citations
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| 524 | Flows in networks – Ford, Fulkerson - 1962 |
| 234 | Domains for Denotational Semantics – Scott - 1982 |
| 107 | Probabilistic Nondeterminism – Jones - 1990 |
| 94 | A probabilistic powerdomain of evaluations – Jones, Plotkin - 1989 |
| 62 | Dynamical systems, measures and fractals via domain theory – Edalat - 1995 |
| 24 | Topology via Logic, volume 5 of Cambridge Tracts – Vickers - 1989 |
| 23 | Domains and Predicate Transformers: a Topological View – Power - 1983 |
| 9 | Continuous information systems – Hoofman - 1993 |
| 9 | Information systems for continuous posets – Vickers - 1993 |
| 7 | Non-Stable Models of Linear Logic – Hoofman - 1992 |
