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oai:drops-oai.dagstuhl.de:10265 2024-03-06T10:45:40Z ddc:004 open_access

Space Lower Bounds for the Signal Detection Problem Ellen, Faith Gelashvili, Rati Woelfel, Philipp Zhu, Leqi Signal detection ABA problem space complexity lower bound 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Faith Ellen and Rati Gelashvili and Philipp Woelfel and Leqi Zhu 2019 Is Part Of LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2019.26 urn:nbn:de:0030-drops-102654 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.26 eng https://creativecommons.org/licenses/by/3.0/legalcode