  We relate the computational complexity of finite strings to universal
representations of their underlying symmetries. First, Boolean functions are
classified using the universal covering topologies of the circuits which
enumerate them. A binary string is classified as a fixed point of its
automorphism group; the irreducible representation of this group is the
string's universal covering group. Such a measure may be used to test the
quasi-randomness of binary sequences with regard to first-order set membership.
Next, strings over general alphabets are considered. The complexity of a
general string is given by a universal representation which recursively factors
the codeword number associated with a string. This is the complexity of the
representation recursively decoding a Godel number having the value of the
string; the result is a tree of prime numbers which forms a universal
representation of the string's group symmetries.
