Summary: Time and Space Lower Bounds for Restricted-Use Objects
James Aspnes1, Hagit Attiya2, Keren Censor-Hillel3, Danny Hendler4
Department of Computer Science, Yale University
Department of Computer Science, Technion
Computer Science and Artificial Intelligence Laboratory, MIT
Department of Computer Science, Ben-Gurion university of the Negev
Abstract. Concurrent objects play a key role in the design of applications for multi-core architectures
and it is imperative to precisely understand their complexity requirements. For a large class of objects,
there is good understanding of their complexity in one-shot situations (i.e., when each process applies a
single operation) or in long-lived situations (i.e., when an unbounded number of operations are applied).
However, very little is known about the complexity of intermediate situations, in which an object is
used in a restricted manner, which is neither one-shot nor long-lived; for example, when there is a
bound on the total number of operations or on the set of values supplied to the object.
This paper proves lower bounds on the time and space complexity of linearizable deterministic imple-
mentations of a large class of objects, including bounded-value max registers, limited-use approximate
and exact counters, and limited-use compare-and-swap objects. For implementations from historyless