Automatic sequences are not suitable sequences for cryptographic
applications since both their subword complexity
and their expansion complexity are small, and their correlation measure
of order 2 is large. These sequences are
highly predictable despite having a large maximum order
complexity. However, recent results show that polynomial
subsequences of automatic sequences, such as the Thue-Morse sequence, are
better candidates for pseudorandom
sequences. A natural generalization of automatic sequences are morphic
sequences, given by a fixed point of a
prolongable morphism that is not necessarily uniform. In this talk,
I will present my results on lowers bounds
for the maximum order complexity of the Thue-Morse sequence and
the sum of digits function in Zeckendorf
base, which are respectively an automatic and a morphic sequence.