CONDITIONAL ENTROPY OF SOME AUTOMATIC SEQUENCES

Burrows and Sulston have introduced conditional block entropies H-n from information theory in order to give a quantitative measure of disorder for sequences and, if possible, a characterization of quasicrystalline sequences. We give here some properties concerning these block entropies and give an explicit formula for the sequences (H-n)(n is an element of N) corresponding to the Thue-Morse sequence, the Rudin-Shapiro sequence and the paperfolding sequence. We deduce from these computations that this measure of disorder does not enable us to distinguish between deterministic sequences even if they have different spectral properties.