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