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Distributed computing must adapt its techniques to networks of mobile agents. Indeed, we are facing new problems like the small size of memory and the lack of computational power. In this paper, we extend the results of Angluin et al (see [4,3,2,1]) by finding self-stabilizing algorithms to count the number of agents in the network. We focus on two different models of communication, with a fixed base...
We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. We...
A non-empty word w of a, b* is a Lyndon word if and only if it is strictly smaller for the lexicographical order than any of its proper suffixes. Such a word w is either a letter or admits a standard factorization uv where v is its smallest proper suffix. For any Lyndon word v, we show that the set of Lyndon words having v as right factor of the standard factorization is rational and compute...
Various criteria have been defined to evaluate the significance of sets of words, the computation of them often being difficult. We provide explicit expressions for the waiting time in such a context. In order to assess the significance of a cluster of potential binding sites, we extend them to the co-occurrence problem. We point out that these criteria values depend on a few fundamental parameters...
We address the problem of verification by model checking of the basic population protocol (PP) model of Angluin et al. [1]. This problem has received special attention in the last two years and new tools have been proposed to deal with it. We show that the problem can be solved by using the existing model-checking tools, e.g., Spin and Prism. In order to do so, we apply the counter abstraction to...
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