Cycle structure in automata and the holonomy decomposition
Attila Egri-Nagy, Chrystopher L. Nehaniv · 2005
The algebraic hierarchical decomposition of finite state automata can be applied wherever a finite system should be ‘understood ’ using a hier-archical coordinate system. Here we use the holonomy decomposition for characterizing finite automata using derived hierarchical structure. This leads to a characterization according to the existence of different cycles within an automaton. The investigation shows that the problem of deter-mining holonomy groups can be reduced to the examination of the cycle structure of certain derived automata. The results presented here lead to the improvements of the decomposition algorithms bringing closer the possibility of the application of the cascaded decomposition for real-world problems. 1