The length of elements in free solvable groups
Carl Droms, Jacques Lewin, Herman Servatius · Proceedings of the American Mathematical Society · 1993
We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a given word. Our main result is that the length of the element represented by a word in a free solvable group can be determined in polynomial time.