Abstract
We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This is simply a known upper bound on the cover time of a random walk. This allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space logn with input commutativity, where n is the number of nodes in the network. We also give a logn-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.
This work has in part been supported by the EU (European Social Fund - ESF) and Greek national funds through (i) the Operational Programme “Education and Lifelong Learning” (EdLL), under the title “Foundations of Dynamic Distributed Computing Systems” (FOCUS), and (ii) the National Strategic Reference Framework (NSRF) (Regional Operational Programme - Western Greece) under the title “Advanced Systems and Services over Wireless and Mobile Networks” (number 312179).
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Michail, O., Chatzigiannakis, I., Spirakis, P.G. (2012). Terminating Population Protocols via Some Minimal Global Knowledge Assumptions. In: Richa, A.W., Scheideler, C. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2012. Lecture Notes in Computer Science, vol 7596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33536-5_8
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DOI: https://doi.org/10.1007/978-3-642-33536-5_8
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