Y. Li and J. Sawada classified a type of language called a reflectable language [Inform. Process. Lett. 109 (2009) 296-300], and gave a generic recursive algorithm GrayCode to list all strings of length n for any reflectable language in Gray code order. GrayCode runs in O(n) worst-case time per string for any application. Based on Williamson's algorithm for k-ary strings, a generic non-recursive algorithm GenericNext is proposed in this paper to list all strings of length for any reflectable language in Gray code order, but the worst-case time is 0(1) per string for all the applications mentioned in Y. Li and J. Sawada's paper.
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