Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Ellen, Faith; Gelashvili, Rati; Woelfel, Philipp; Zhu, Leqi https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-102654
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Space Lower Bounds for the Signal Detection Problem

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Abstract

Many shared memory algorithms have to deal with the problem of determining whether the value of a shared object has changed in between two successive accesses of that object by a process when the responses from both are the same. Motivated by this problem, we define the signal detection problem, which can be studied on a purely combinatorial level. Consider a system with n+1 processes consisting of n readers and one signaller. The processes communicate through a shared blackboard that can store a value from a domain of size m. Processes are scheduled by an adversary. When scheduled, a process reads the blackboard, modifies its contents arbitrarily, and, provided it is a reader, returns a Boolean value. A reader must return true if the signaller has taken a step since the reader's preceding step; otherwise it must return false.
Intuitively, in a system with n processes, signal detection should require at least n bits of shared information, i.e., m >= 2^n. But a proof of this conjecture remains elusive. We prove a lower bound of m >= n^2, as well as a tight lower bound of m >= 2^n for two restricted versions of the problem, where the processes are oblivious or where the signaller always resets the blackboard to the same fixed value. We also consider a one-shot version of the problem, where each reader takes at most two steps. In this case, we prove that it is necessary and sufficient that the blackboard can store m=n+1 values.

BibTeX - Entry

@InProceedings{ellen_et_al:LIPIcs:2019:10265,
  author =	{Faith Ellen and Rati Gelashvili and Philipp Woelfel and Leqi Zhu},
  title =	{{Space Lower Bounds for the Signal Detection Problem}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{26:1--26:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10265},
  doi =		{10.4230/LIPIcs.STACS.2019.26},
  annote =	{Keywords: Signal detection, ABA problem, space complexity, lower bound}
}

Keywords: Signal detection, ABA problem, space complexity, lower bound
Seminar: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue date: 2019
Date of publication: 12.03.2019


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