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A Knowledge-Based Analysis of Global Function Computation

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Book cover Distributed Computing (DISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4167))

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Abstract

Consider a distributed system N in which each agent has an input value and each communication link has a weight. Given a global function, that is, a function f whose value depends on the whole network, the goal is for every agent to eventually compute the value f(N). We call this problem global function computation. Various solutions for instances of this problem, such as Boolean function computation, leader election, (minimum) spanning tree construction, and network determination, have been proposed, each under particular assumptions about what processors know about the system and how this knowledge can be acquired. We give a necessary and sufficient condition for the problem to be solvable that generalizes a number of well-known results [3, 28, 29]. We then provide a knowledge-based (kb) program (like those of Fagin, Halpern, Moses, and Vardi [8,9]) that solves global function computation whenever possible. Finally, we improve the message overhead inherent in our initial kb program by giving a counterfactual belief-based program [15] that also solves the global function computation whenever possible, but where agents send messages only when they believe it is necessary to do so. The latter program is shown to be implemented by a number of well-known algorithms for solving leader election.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, NY, 14853, USA

    Joseph Y. Halpern & Sabina Petride

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  1. Joseph Y. Halpern
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  2. Sabina Petride
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Editors and Affiliations

  1. Department of Computer Science, Ben Gurion University of the Negev, Israel

    Shlomi Dolev

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© 2006 Springer-Verlag Berlin Heidelberg

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Halpern, J.Y., Petride, S. (2006). A Knowledge-Based Analysis of Global Function Computation. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_10

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  • DOI: https://doi.org/10.1007/11864219_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44624-8

  • Online ISBN: 978-3-540-44627-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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