Space Lower Bounds for the Signal Detection Problem
36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019)(2020)
摘要
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. For the general case, we prove a lower bound of m ≥ n 2 . For restricted versions of the problem, where the processes are oblivious or where the signaller must write a fixed sequence of values, we prove a tight lower bound of m ≥ 2 n . We also consider a version of the problem where each reader takes at most two steps. In this case, we prove that m = n + 1 blackboard values are necessary and sufficient.
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关键词
Signal detection,ABA problem,Space complexity,Lower bounds
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