Complexity, Depth, and Sophistication

T wo measures of the "meaningful" complexity of an infini te string are shown to be equivalent up to a constant (under app ropriate translati on) . "Sophis t ica tion", defined by Koppel and Atlan [3], is the size of t he projectible par t of the st ring's minimal description and forma lizes t he amount of pla nni ng which wen t into t he constru ct ion of the str ing. "Dept h". defi ned by Bennett til, is the amou nt of t ime required for the str ing to be generated from its min ima l descr iptio n and form alizes its "evolvedness. "