Abstract of Paper

Bilinear Functions and Trees over the $(\max,+)$ Semiring
by Sabrina Mantaci, Vincent D. Blondel, and Jean Mairesse

Abstract:

We consider the iterates of bilinear functions over the $(\max,+)$ semiring.
Equivalently, our object of study can be viewed as recognizable tree series
over the $(\max,+)$ semiring.  In this semiring, a fundamental result
associates the asymptotic behaviour of the iterates of a linear function
with the maximal average weight of circuits in a graph naturally associated
with the function. Here we provide an analog of this result for the iterates
of bilinear functions.