Characterization of associative operations with prefix circuits of constant depth and linear size
SIAM Journal on Computing
Topics in distributed algorithms
Topics in distributed algorithms
Uniform self-stabilizing ring orientation
Information and Computation
Self-stabilization
Self-stabilization with r-operators
Distributed Computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Exploitation of Ljapunov Theory for Verifying Self-Stabilizing Algorithms
DISC '00 Proceedings of the 14th International Conference on Distributed Computing
The Triumph and Tribulation of System Stabilization
WDAG '95 Proceedings of the 9th International Workshop on Distributed Algorithms
Self-stabilization with path algebra
Theoretical Computer Science
IEEE/ACM Transactions on Networking (TON)
Self-stabilization of dynamic systems assuming only read/write atomicity
Distributed Computing - Special issue: Self-stabilization
Convergence of iteration systems
Distributed Computing - Special issue: Self-stabilization
Towards automatic convergence verification of self-stabilizing algorithms
SSS'05 Proceedings of the 7th international conference on Self-Stabilizing Systems
Best-effort group service in dynamic networks
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Conflict-free replicated data types
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Self-stabilizing distributed data fusion
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
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In [13,14,7], the modeling of silent tasks by means of socalled r-operators has been studied, and interesting relations have been shown between algebraic properties of a given operator and stabilizing properties of the related distributed algorithms. Modeling algorithms with algebraic operators allows to determine generic results for a wide set of distributed algorithms. Moreover, by simply checking some local algebraic properties, some global properties can be deduced. Stabilizing properties of shortest path calculus, depth-first-search tree construction, best reliable transmitters, best capacity paths, ordered ancestors list... have hence been established by simply reusing generic proofs, either in the read-write shared register models [13,14] or in the unreliable message passing models [7]. However, while this approach is promising, it may be penalized by the difficulty in designing new r-operators. In this paper, we present the fundation of the r-operators by introducing a generalization of the idempotent semi-groups, called r-semi-group. We establish the requirements on the operators to be used in distributed computation and we show that the r-semi-groups fulfill them. We investigate the connections between semi-groups and r-semi-groups, in order to ease the design of r-operators. We then show how to build new roperators, to solve new algorithmic problems. With these new results, the r-semi-groups appear to be a powerful tool to design stabilizing silent tasks.