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Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...
Cover automata for finite languages have been much studied a few years ago.
It turns out that a simple mathematical structure, namely
similarity relations over a finite set of words, is underlying these
studies. In the present work, we investigate in detail for themselves
the properties of these relations beyond the scope of finite languages.
New results with straightforward proofs
are obtained in this generalized framework,
and previous results concerning cover
automata are obtained as immediate...
In this paper, we propose a method which enables to construct almost optimal broadcast schemes on an -dimensional hypercube in the circuit switched, -port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured...
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