Abstract
Randomized algorithms, or probabilistic algorithms, extend the notion of algorithm by introducing input of random data and random choices in the process of computation. A new mathematical theory of the semantic domains for randomized algorithms, or randomized domains, is developed, which intrinsically extends Scott’s domain theory for deterministic computation. Main results include the characterization theorems and practical axiom systems for randomized domains, and the construction of the universal reflexive randomized domainR ∞. The theory readily provides denotational semantics for a class of high level probabilistic programming languages and is also directly applicable to probabilistic logics, inductive inference, and theory of stochastic programming.
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The contents of this paper is based on the D. Sc. dissertation of the author submitted to the University of Tokyo, Dec., 1987.
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Yamada, S. Characterizations of semantic domains for randomized algorithms. Japan J. Appl. Math. 6, 111–146 (1989). https://doi.org/10.1007/BF03167919
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DOI: https://doi.org/10.1007/BF03167919