Before revision:  A polynomial time algorithm that solves this (existence ) problem was only known for the case of the binary alphabet . We focus on a special class of strings---here referred to as "purely alternating"---that generalize the special structure of binary strings to larger alphabets. We show that for the case of purely alternating strings from an alphabet of size \leq 5, the existence problem can be solved in linear time .
After revision:  A polynomial time algorithm that solves this (existence ) problem was only known for the case of the binary alphabet .