In [13,14,7], the modeling of silent tasks by means of so-called 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 r-operators, to solve new algorithmic problems. With these new results, the r-semi-groups appear to be a powerful tool to design stabilizing silent tasks. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Ducourthial, B. (2007). r-semi-groups: A generic approach for designing stabilizing silent tasks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4838 LNCS, pp. 281–295). Springer Verlag. https://doi.org/10.1007/978-3-540-76627-8_22
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