Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
On the improbability of reaching Byzantine agreements
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Randomized mutual exclusion algorithms revisited
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Data Requirements for Implementation of N-Process Mutual Exclusion Using a Single Shared Variable
Journal of the ACM (JACM)
Termination of Probabilistic Concurrent Program
ACM Transactions on Programming Languages and Systems (TOPLAS)
Solution of a problem in concurrent programming control
Communications of the ACM
Randomized mutual exclusion algorithms revisited
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Lower bounds for randomized mutual exclusion
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Proving time bounds for randomized distributed algorithms
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Verification of randomized distributed algorithms
Lectures on formal methods and performance analysis
Coin Lemmas with Random Variables
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Compositional Verification of Randomized Distributed Algorithms
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
The challenge of probabilistic event B
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
Using probabilistic kleene algebra for protocol verification
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
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The correctness of most randomized distributed algorithms is expressed by a statement of the form “some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled“. In this paper, we present a general methodology to prove correctness statements of such randomized algorithms. Specifically, we show how to prove such statements by a series of refinements, which terminate in a statement independent of the schedule. To demonstrate the subtlety of the issue involved in this type of analysis, we focus on Rabin's randomized distributed algorithm for mutual exclusion [6].Surprisingly, it turns out that the algorithm does not maintain one of the requirements of the problem under a certain schedule. In particular, we give a schedule under which a set of processes can suffer lockout for arbitrary long periods.