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2006

Operator Algebras and the Operational Semantics of Probabilistic Languages

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Operator Algebras and the Operational Semantics of Probabilistic Languages
We investigate the construction of linear operators representing the semantics of probabilistic programming languages expressed via probabilistic transition systems. Finite transition relations, corresponding to finite automata, can easily be represented by finite dimensional matrices; for the infinite case we need to consider an appropriate generalisation of matrix algebras. We argue that C-algebras, or more precisely Approximately Finite (or AF) algebras, provide a sufficiently rich mathematical structure for modelling probabilistic processes. We show how to construct for a given probabilistic language a unique AF algebra A and how to represent the operational semantics of processes within this framework: finite computations correspond directly to operators in A, while infinite processes are represented by elements in the so-called strong closure of this algebra.
Alessandra Di Pierro, Herbert Wiklicky
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2006
Where ENTCS
Authors Alessandra Di Pierro, Herbert Wiklicky
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