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Non-deterministic, Probabilistic, and Quantum Effects Through the Lens of Event Structures

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Programming Languages and Systems (APLAS 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15194))

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Abstract

In this paper, we consider event structures and their probabilistic and quantum extensions as originally defined by Winskel. If these structures have already been part of sophisticated computational models, they have rarely been directly studied as an immediate model of execution traces of programs. This paper offers such an analysis. We propose a simple imperative operational framework and show how to derive soundness and adequacy results with event structures considered as a semantics. We show how event structures naturally handle non-deterministic, probabilistic and quantum effects.

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Notes

  1. 1.

    for any two events \(e_1, e_2 \in E\), \(e_1 \le e_2\) is read: \(e_2\) depends on \(e_1\).

  2. 2.

    \(e \# e^{\prime } \le e^{\prime \prime }\) is to be understood as \((e \# e^{\prime })\) and \((e^{\prime } \le e^{\prime \prime })\).

  3. 3.

    i.e. a configuration x is maximal iff \(\not \exists y \in \mathcal {C}(\textrm{E})\) such that \(x \subset y\).

  4. 4.

    sk is the label for the command skip.

  5. 5.

    The proper definition of the disjoint union is \(A \uplus B = \{(0,a) | a \in A\} \cup \{ (1,b) | b \in B \}\). For \(R,S \in A \times B\), the disjoint union extends to a relation as \((i,e) R \uplus S (i^{\prime },e^{\prime })\) whenever \(i=0=i'\) and \(e R e^{\prime }\) or \(i=1=i'\) and \(e S e^{\prime }\). For the sake of keeping the notations readable, we will keep the 0s and 1s implicit.

  6. 6.

    \({C}_1\, ||\, {C}_2\) being disjoint means that \({C}_1\) and \({C}_2\) do not share any qubit.

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Acknowledgements

This work has been partially funded by the French National Research Agency (ANR) by the project RECIPROG ANR-21-CE48-0019, PPS ANR-19-CE48-0014, TaQC ANR-22-CE47-0012 and within the framework of “Plan France 2030”, under the research projects EPIQ ANR-22-PETQ-0007, OQULUS ANR-23-PETQ-0013, HQI-Acquisition ANR-22-PNCQ-0001 and HQI-R&D ANR-22-PNCQ-0002. This work is partially financed by National Funds through the Portuguese funding agency, FCT— Fundação para a Ciência e a Tecnologia, within project UIDB/50014/2020. DOI 10.54499/UIDB/50014/2020|https://doi.org/10.54499/uidb/50014/2020.

Disclosure of Interests. The authors have no competing interests to declare.

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Authors and Affiliations

  1. University of Minho and INESC-TEC, Braga, Portugal

    Vítor Fernandes

  2. Université Paris-Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay, Inria, Laboratoire Méthodes Formelles, 91190, Gif-sur-Yvette, France

    Marc de Visme & Benoît Valiron

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  1. Vítor Fernandes
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  2. Marc de Visme
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  3. Benoît Valiron
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Correspondence to Vítor Fernandes .

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Editors and Affiliations

  1. Tohoku University, Sendai, Miyagi, Japan

    Oleg Kiselyov

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Fernandes, V., Visme, M.d., Valiron, B. (2025). Non-deterministic, Probabilistic, and Quantum Effects Through the Lens of Event Structures. In: Kiselyov, O. (eds) Programming Languages and Systems. APLAS 2024. Lecture Notes in Computer Science, vol 15194. Springer, Singapore. https://doi.org/10.1007/978-981-97-8943-6_10

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  • DOI: https://doi.org/10.1007/978-981-97-8943-6_10

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