Abstract
Word chains are an extension of addition chains to words and can be used as a complexity measure for languages. Let Σ ={ a , b } and ϕ be the morphism ϕ:Σ ∗ → Σ ∗ given by ϕ ( a )= ab and ϕ ( b )= ba . We study word chains for the iterates ϕ n ( a ) of the Thue-Morse word. The length of optimal word chains for ϕ n ( a ) is proved to be 2 n −1, and a conjecture on the enumeration of optimal word chains computing ϕ n ( a ) is proposed.
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