They show that Hopcroft's algorithm has a worst case behavior for the automata recognizing Fibonacci words.
We prove that the same holds for all standard Sturmian words having an ultimately periodic directive sequence (the directive sequence for Fibonacci words is (1, 1, .
2007), Castiglione, Restivo and Sciortino replace the de Bruijn words by Fibonacci words.
The case of Fibonacci words corresponds the directive sequence (1, 1, .
n-1] for n [greater than or equal to] 1, and the standard words generated by d are the Fibonacci words 1, 0, 01, 010, 01001, .
On top of the neat patterns, I have a strange reverence for the concept of Fibonacci words, and thought it was worth noting some more words from Dave's loops, including four more fours:
Counting Dave's, this brings the total to a cool fifty-two Fibonacci words (Why cool?