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Semantics of sub-probabilistic programs

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Abstract

The aim of this paper is to extend the probabilistic choice in probabilistic programs to sub-probabilistic choice, i.e., of the form (p)P ⋈(q)Q where p + q ⩽ 1. It means that program P is executed with probability p and program Q is executed with probability q. Then, starting from an initial state, the execution of a sub-probabilistic program results in a sub-probability distribution. This paper presents two equivalent semantics for a sub-probabilistic while-programming language. One of these interprets programs as sub-probabilistic distributions on state spaces via denotational semantics. The other interprets programs as bounded expectation transformers via wp-semantics. This paper proposes an axiomatic systems for total logic, and proves its soundness and completeness in a classical pattern on the structure of programs.

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Authors and Affiliations

  1. Institute of Theoretical Computing, Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Yixiang Chen

  2. Information Engineering College, Hangzhou Dianzi University, Hangzhou, 310037, China

    Hengyang Wu

Authors
  1. Yixiang Chen
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  2. Hengyang Wu
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Correspondence to Yixiang Chen.

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Chen, Y., Wu, H. Semantics of sub-probabilistic programs. Front. Comput. Sci. China 2, 29–38 (2008). https://doi.org/10.1007/s11704-008-0004-0

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  • DOI: https://doi.org/10.1007/s11704-008-0004-0

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