  The Rogers semilattice of effective programming systems (epses) is the
collection of all effective numberings of the partial computable functions
ordered such that \theta\ is less than or equal to \psi\ whenever
\theta-programs can be algorithmically translated into \psi-programs. Herein,
it is shown that an eps \psi\ is minimal in this ordering if and only if, for
each translation function t into \psi, there exists a computably enumerable
equivalence relation (ceer) R such that (i) R is a subrelation of \psi's
program equivalence relation, and (ii) R equates each \psi-program to some
program in the range of t. It is also shown that there exists a minimal eps for
which no single such R does the work for all such t. In fact, there exists a
minimal eps \psi\ such that, for each ceer R, either R contradicts \psi's
program equivalence relation, or there exists a translation function t into
\psi\ such that the range of t fails to intersect infinitely many of R's
equivalence classes.
