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Interval Probability for Sessions Types

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Logic, Language, Information, and Computation (WoLLIC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13468))

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Abstract

We propose a typing system based on multiparty session types and probabilistic interactions. We define a probabilistic process calculus using nondeterministic external choices and probabilistic internal choices. Interval probability (a generalization of traditional probability using pairs of lower and upper probabilities) are used for global and local types. We introduce a decidable proof system involving interval probability to represent and quantify the uncertain behaviour of concurrent processes. This proof system ensures type preservation and safety, even when the use of probabilities allows a process to be considered well-typed for several types. Additionally, processes remain well-typed after removing their probabilities.

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Notes

  1. 1.

    This new probabilistic approach satisfies the standard axioms for determining the probability of an event [21]. The probability of an event is a real number in the interval [0, 1], and the sum of the probabilities of the elementary events is 1; these axioms are presented by A.Kolmogorov in [13].

  2. 2.

    B. Russell called this book “undoubtedly the most important work on probability that has appeared for a very long time”.

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Authors and Affiliations

  1. Romanian Academy, Institute of Computer Science, Iaşi, Romania

    Bogdan Aman & Gabriel Ciobanu

  2. Alexandru Ioan Cuza University, Iaşi, Romania

    Bogdan Aman & Gabriel Ciobanu

Authors
  1. Bogdan Aman
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  2. Gabriel Ciobanu
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Correspondence to Bogdan Aman .

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Editors and Affiliations

  1. Technische Universität Wien, Vienna, Austria

    Agata Ciabattoni

  2. University College London, London, UK

    Elaine Pimentel

  3. Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Ruy J. G. B. de Queiroz

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Aman, B., Ciobanu, G. (2022). Interval Probability for Sessions Types. In: Ciabattoni, A., Pimentel, E., de Queiroz, R.J.G.B. (eds) Logic, Language, Information, and Computation. WoLLIC 2022. Lecture Notes in Computer Science, vol 13468. Springer, Cham. https://doi.org/10.1007/978-3-031-15298-6_8

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  • DOI: https://doi.org/10.1007/978-3-031-15298-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15297-9

  • Online ISBN: 978-3-031-15298-6

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