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by Max Semiring, Sabrina Mantaci, Jean Mairesse
http://www.liafa.jussieu.fr/~mairesse/Article/bilin.ps.gz
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Abstract:
Abstract. We consider the iterates of bilinear functions over the semiring (max; +). Equivalently, our object of study can be viewed as recognizable tree series over the semiring (max; +). In this semiring, a fundamental result associates the asymptotic behaviour of the iterates of a linear function with the maximal average weight of the circuits in a graph naturally associated with the function. Here we provide an analog for the `iterates ' of bilinear functions. We also give a triple recognizing the formal power series of the worst case behaviour. Remark. Due to space limitations, the proofs have been omitted. A full version can be obtained from the authors on request. 1
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