theory of
finite automata, along with that of their associated formal languages or
transformation semigroups (Lallement, ch. 4).  This more general study
requires the use of &quot;semi-direct products&quot; (Rotman, 1984) and their
ultimate extension into &quot;cascade products&quot; or &quot;wreath products&quot;,
together with with the corresponding notions of decomposition,
divisibility, or factorization (Barr &amp; Wells, 1990, ch. 11).
That theory appears to have long ago reached a baroque stage
of dev