For a simple probabilistic language we present a semantics based on linear operators on infinite dimensional Hilbert spaces.We show the equivalence of this semantics with a standard operational one and we discuss its relationship with the well-known denotational semantics introduced by Kozen. For probabilistic programs, it is typical to use Banach spaces and their norm topology to model the properties to be analysed (observables). We discuss the advantages in considering instead Hilbert spaces as denotational domains, and we present a weak limit construction of the semantics of probabilistic programs which is based on the inner product structure of this space, i.e. the duality between states and observables. © Springer International Publishing 2013.
CITATION STYLE
Di Pierro, A., & Wiklicky, H. (2013). Semantics of probabilistic programs: A weak limit approach. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8301 LNCS, pp. 241–256). https://doi.org/10.1007/978-3-319-03542-0_18
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