Algebraic hierarchical decomposition of finite state automata: Comparison of implementations for Krohn-Rhodes theory. The hierarchical algebraic decomposition of finite state automata (Krohn-Rhodes Theory) has been a mathematical theory without any computational implementations until the present paper, although several possible and promising practical applications, such as automated object-oriented programming in software development, formal methods for understanding in artificial intelligence, and a widely applicable integer-valued complexity measure, have been described. As a remedy for the situation, our new implementation, described here, is freely available as open-source software. We also present two different computer algebraic implementations of the Krohn-Rhodes decomposition, the V∪T and holonomy decompositions, and compare their efficiency in terms of the number of hierarchical levels in the resulting cascade decompositions.