Summary: Lower Bounds for Restricted-Use Objects
February 2, 2012
Concurrent objects play a key role in the design of applications for multi-core architectures,
making it imperative to precisely understand their complexity requirements. For some objects, it
is known that implementations can be significantly more efficient when their usage is restricted.
However, apart from the specific restriction of one-shot implementations, where each process
may apply only a single operation to the object, very little is known about the complexities of
objects under general restrictions.
This paper draws a more complete picture by defining a large class of objects for which
an operation applied to the object can be "perturbed" L consecutive times, and proving lower
bounds on the time and space complexity of deterministic implementations of such objects. This
class includes bounded-value max registers, limited-use approximate and exact counters, and
limited-use collect and compare-and-swap objects; L depends on the number of times the object
can be accessed or the maximum value it can support.