Generating necklaces and strings with forbidden substrings

Abstract

Given a length m string f over a k-ary alphabet and a pos-itive integer n, we develop ecient algorithms to generate (a) all k-ary strings of length n that have no substring equal to f, (b) all k-ary circular strings of length n that have no substring equal to f, and (c) all k-ary necklaces of length n that have no substring equal to f, where f is an aperiodic necklace. Each of the algorithms runs in amortized time O(1) per string generated, independent of k, m, and n.