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International Workshop on Computational Logic in Multi-Agent Systems

CLIMA 2011: Computational Logic in Multi-Agent Systems pp 41–57Cite as

Three Steps

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6814))

Abstract

Given is a deal of ten cards over three players, such that two players each get four cards and the remaining player (the ‘eavesdropper’) two cards. We show that there does not exist a protocol of two steps for the four-card players to inform each other safely of their hands of cards, and we then present a protocol of three steps that achieves that goal. We verify the properties of that protocol by combinatorial and, mainly, logical (model checking) means. No such three-step protocol for cards was known. The method can be generalized. This will advance the characterization of card deals for which such exchanges of secrets are possible.

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Author information

Authors and Affiliations

  1. University of Sevilla, Spain

    Hans van Ditmarsch & Fernando Soler–Toscano

Authors
  1. Hans van Ditmarsch
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  2. Fernando Soler–Toscano
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Editor information

Editors and Affiliations

  1. Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia, Departamento de Informática, CENTRIA, Quinta da Torre, 2829-516, Caparica, Portugal

    João Leite

  2. Università di Bologna, Laboratorio di Informatica Avanzata, Dipartimento di Informatica, Elettronica e Sistemistica, Viale Risorgimento 2, 40136, Bologna, Italy

    Paolo Torroni

  3. Department of Information Science and Media Studies, University of Bergen, P.O. Box 7802, 5020, Bergen, Norway

    Thomas Ågotnes

  4. University of Torino, Italy

    Guido Boella

  5. Faculté des Sciences, de la Technologie et de la Communication, Université du Luxembourg, 6 Rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Leon van der Torre

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© 2011 Springer-Verlag Berlin Heidelberg

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van Ditmarsch, H., Soler–Toscano, F. (2011). Three Steps. In: Leite, J., Torroni, P., Ågotnes, T., Boella, G., van der Torre, L. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2011. Lecture Notes in Computer Science(), vol 6814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22359-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-22359-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22358-7

  • Online ISBN: 978-3-642-22359-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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