An algebraic approach to modeling probabilistic discrete event systems

The author defines probabilistic languages and probabilistic automata over a finite set of events. Operators under which the set of probabilistic languages (p-languages) is closed, thus forming an algebra of p-languages, are also defined. It is shown that the operators are continuous in it. Hence, recursive equations may be defined in this algebra using fixpoints of continuous functions. Thus, p-languages form a suitable theoretical foundation for specifying and analyzing probabilistic systems