Google found http://www.integers-ejcnt.org/a2nta2004/a2nta2004.pdf a large review paper by V.Berthe & A.Siegel 2005. Lots of my ideas were already known and already investigated way better. It occurs to me, which was not in this review paper, but is relevant to JA speaking about the "greedy method" for finding the representation of a given real or complex number X in some funny numeration system in which there are forbidden substring rules... or anyhow "allowed sequence rules" corresponding to some finite automaton for generating the allowed digit sequences. There is actually a good algorithm, better than greedy and quite general, based on "one dimensional dynamic programming" for finding good (optimal?) such representations. Essentially, for each k-digit-long "sliding window," you keep track in a table, of the best possible approximation to X which contains each possible pattern within that window, and all-0s to the right of it. The table is indexed both by the pattern, and by the automaton-state after it prints out the last digit in that pattern. The window can then be slid over 1 hop and the new table computed from the old table. Continuing on, we have an algorithm for finding the representation of X in that funny number system. Perhaps if k is made wide enough compared to the automaton state count, this algorithm will actually find the optimal representation of X. That ought to be provable under assumptions about the radix. In any case, this clearly is far more powerful than the "greedy algorithm."