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 [5], formal methods for understanding in artificial intelligence [6], a widely applicable integer-valued complexity measure [8,7], have been described. As a remedy for the situation, our new implementation, described here, is freely available [2] as open-source software. We also present two different computer algebraic implementations of the Krohn-Rhodes decomposition, the V [T and holonomy decompositions [4,3], and compare their efficiency in terms of the number of hierarchical levels in the resulting cascade decompositions.