Context-Free Series on Trees

Abstract

We investigate context-free (CF) series on trees with coefficients on a semiring; they are obtained as components of the least solutions of systems of equations having polynomials on their right-hand sides. The relationship between CF series on trees and CF tree-grammars and recursive program schemes is also examined. Polypodes, a new algebraic structure, are introduced in order to study in common series on trees and words and applications are given.