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On Mobile Agent Verifiable Problems

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LATIN 2016: Theoretical Informatics (LATIN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9644))

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Abstract

We consider decision problems that are solved in a distributed fashion by synchronous mobile agents operating in an unknown, anonymous network. Each agent has a unique identifier and an input string and they have to decide collectively a property which may involve their input strings, the graph on which they are operating, and their particular starting positions. Building on recent work by Fraigniaud and Pelc [LATIN 2012, LNCS 7256, pp. 362–374], we introduce several natural new computability classes allowing for a finer classification of problems below \(\mathsf {co\text {-}MAV}\) or \(\mathsf {MAV}\), the latter being the class of problems that are verifiable when the agents are provided with an appropriate certificate. We provide inclusion and separation results among all these classes. We also determine their closure properties with respect to set-theoretic operations. Our main technical tool, which is of independent interest, is a new meta-protocol that enables the execution of a possibly infinite number of mobile agent protocols essentially in parallel, similarly to the well-known dovetailing technique from classical computability theory.

This work was partially funded by the ANR projects DISPLEXITY (ANR-11-BS02-014) and MACARON (ANR-13-JS02-002). This study has been carried out in the frame of the “Investments for the future” Programme IdEx Bordeaux – CPU (ANR-10-IDEX-03-02).

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Notes

  1. 1.

    Note that this closure property is syntactically different from the one used in [13] due to notational differences, but the two are equivalent.

  2. 2.

    It is easy to check that if \(\varPi \) is a decision problem, then \(\overline{\varPi }\) also satisfies the closure property of Definition 1. Therefore, \(\overline{\varPi }\) is also a decision problem.

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Authors and Affiliations

  1. CNRS and University of Bordeaux, LaBRI, UMR 5800, F-33400, Talence, France

    Evangelos Bampas & David Ilcinkas

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  1. Evangelos Bampas
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  2. David Ilcinkas
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Correspondence to Evangelos Bampas .

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Editors and Affiliations

  1. Carleton University, Ottawa, ON, Ontario, Canada

    Evangelos Kranakis

  2. University Chile, Santiago, Chile

    Gonzalo Navarro

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Bampas, E., Ilcinkas, D. (2016). On Mobile Agent Verifiable Problems. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_10

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  • DOI: https://doi.org/10.1007/978-3-662-49529-2_10

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