Bilinear Functions and Trees over the (max, +) Semiring

Authors:
Sabrina Mantaci;Vincent D. Blondel;Jean Mairesse
Affiliations:
-;-;-
Venue:
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Year:
2000

Citing 5
Cited 0

Graphs and algorithms

Graphs and algorithms
Semirings, automata, languages

Semirings, automata, languages
Rational series and their languages

Rational series and their languages
Effective constructors the formal series of trees (French)

Theoretical Computer Science
Automata on infinite objects

Handbook of theoretical computer science (vol. B)

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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.