Lower bounds for randomized mutual exclusion

@article{Kushilevitz1993LowerBF,
  title={Lower bounds for randomized mutual exclusion},
  author={Eyal Kushilevitz and Y. Mansour and Michael O. Rabin and David Zuckerman},
  journal={SIAM J. Comput.},
  year={1993},
  volume={27},
  pages={1550-1563}
}
We establish, for the rst time, lower bounds for randomized mutual exclusion algorithms (with a read-modify-write operation). Our main result is that a constant-size shared variable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of ›(log logn) bits on the size of the shared variable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that… 
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References

SHOWING 1-10 OF 25 REFERENCES
Randomized mutual exclusion algorithms revisited
TLDR
Randomization yields simple algorithms for mutual-exclusion with bounded waiting, employing a shared variable of considerably smaller size than the lower-bound established in [1] for deterministic algorithms.
Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion
TLDR
This paper presents a general methodology to prove correctness statements of randomized distributed algorithms by a series of refinements, which terminate in a statement independent of the schedule.
Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols
TLDR
This work exhibits a probabilistic solution for this problem, which guarantees that as long as a majority of the processes continues to operate, a decision will be made (Theorem 1).
N-Process Mutual Exclusion with Bounded Waiting by 4 Log_2 N-Valued Shared Variable
  • M. Rabin
  • Computer Science
    J. Comput. Syst. Sci.
  • 1982
Better Computing on the Anonymous Ring
On processor coordination using asynchronous hardware
TLDR
It is shown that the coordination problem cannot be solved by means of a deterministic protocol even if the system consists of only two processors, and the impossibility result holds for the most powerful type of shared atomic registers and does not assume symmetric protocols.
Probabilistic computations: Toward a unified measure of complexity
  • A. Yao
  • Mathematics
    18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
  • 1977
TLDR
Two approaches to the study of expected running time of algoritruns lead naturally to two different definitions of intrinsic complexity of a problem, which are the distributional complexity and the randomized complexity, respectively.
Data Requirements for Implementation of N-Process Mutual Exclusion Using a Single Shared Variable
An analysis is made of the shared memory requirements for implementing mutual excluslon of N asynchronous parallel processes m a model where the only primitive communication mechamsm is a general
Optimal algorithms for Byzantine agreement
TLDR
For both synchronous and asynchronous networks whose lines do not guarantee private communication, the authors may use cryptography to obtain algorithms optimal both in fault tolerance and running time against computationally bounded adversaries.
...
...