An Approach to Construct Final Random System with Output

Abstract

The paper is devoted to extending the coalgebraic technique of analysing Discrete Systems to the class of Random Systems with Output. To achieve this goal, the authors propose a randomization procedure, which uses the endofunctor of finite distributions as a tool for constructing the Random System based on a Deterministic System. Given the particular importance of final coalgebras for the analysis of systems using coalgebraic techniques, a system that claims this role and a family of morphisms, which in this case is a family of anamorphisms, are constructed. All formal constructions are illustrated by examples for the convenience of readers who do not fully master the language of category theory and coalgebraic techniques. Establishing the fact that the constructed artefacts describe the final Random System with Output and the corresponding family of anamorphisms remains an open problem.