Complexity measure based on Lempel-Ziv algorithms (in particular on the LZ77). In fact the measure was proposed earlier, in 1976 on On the Complexity of Finite Sequences. It is defined as the number of tokens in the LZ77 algorithm.
Algorithm to compute LZ complexity measure
See also Descriptional complexity
On the non-randomness of maximum Lempel Ziv complexity sequences of finite size
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
On Lempel-Ziv Complexity of Sequences – We derive recurrences for counting the number a(n,r) of sequences of length n with Lempel-Ziv complexity r
Relations with entropy
Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity pdf
Redundancy
On point-wise redundancy rate of Bender-Wolf's variant of SWLZ algorithm
On the pointwise redundancy of the LZ78 algorithm
They give results similar to Simplicity bias/Coding theorem method, but for Finite-state sources.
Universal redundancy rates do not exist
Redundancy of the Lempel-Ziv codes
A Simple Technique for Bounding the Pointwise Redundancy of the 1978 Lempel-Ziv Algorithm