Stochastic Equationality

摘要

We introduce systems of equations of stochastic tree series and we consider two types of solutions, the [IO] and the OI, according to the substitutions we use to solve them. We show the existence of least [IO]- and OI-solutions whose non-zero components are proved to be stochastic tree series. A Kleene characterization holds for stochastically OI-equational tree series, i.e., components of least OI-solutions. Furthermore, we consider stochastic algebras and we state a Mezei-Wright type result relating least solutions of systems in arbitrary stochastic algebras and the term algebra.