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Time and Space Lower Bounds for Implementations Using k-CAS

Summary: Time and Space Lower Bounds
for Implementations Using k-CAS
(Extended Abstract)
Hagit Attiya1
and Danny Hendler2
Department of Computer Science, Technion
Department of Computer Science, University of Toronto
Abstract. This paper presents lower bounds on the time- and space-
complexity of implementations that use the k compare-and-swap (k-
CAS) synchronization primitives. We prove that the use of k-CAS prim-
itives cannot improve neither the time- nor the space-complexity of im-
plementations of widely-used concurrent objects, such as counter, stack,
queue, and collect. Surprisingly, the use of k-CAS may even increase the
space complexity required by such implementations.
We prove that the worst-case average number of steps performed by
processes for any n-process implementation of a counter, stack or queue
object is (logk+1 n), even if the implementation can use j-CAS for
j k. This bound holds even if a k-CAS operation is allowed to read the


Source: Attiya, Hagit - Department of Computer Science, Technion, Israel Institute of Technology


Collections: Computer Technologies and Information Sciences