Semantics of Probabilistic Programs: A Weak Limit Approach

  • Alessandra Di Pierro
  • Herbert Wiklicky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8301)


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.


Hilbert Space Tensor Product Classical State Weak Limit Operator Semantic 
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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Alessandra Di Pierro
    • 1
  • Herbert Wiklicky
    • 2
  1. 1.Dipartimento di InformaticaUniversità di VeronaItaly
  2. 2.Department of ComputingImperial College LondonUK

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