Abstract
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.
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Bozapalidis, S., Rahonis, G. (2013). Stochastic Equationality. In: Muntean, T., Poulakis, D., Rolland, R. (eds) Algebraic Informatics. CAI 2013. Lecture Notes in Computer Science, vol 8080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40663-8_17
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DOI: https://doi.org/10.1007/978-3-642-40663-8_17
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