Abstract
De Bruijn sequences of order n represent the set A n of all words of length n over a given alphabet A in the sense that they contain occurrences of each of these words. Recently, the computational problem of representing subsets of A n by partial words, which are sequences that may have holes that match each letter of A, was considered and shown to be in \(\mathcal{NP}\). However, membership in \(\mathcal{P}\) remained open. In this paper, we show that deciding if a subset is representable can be done in polynomial time. Our approach is graph theoretical.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–1060775.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstel, J., Perrin, D.: The origins of combinatorics on words. European Journal of Combinatorics 28(3), 996–1022 (2007)
Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press, Boca Raton (2008)
Blanchet-Sadri, F., Simmons, S.: Deciding representability of sets of words of equal length. Theoretical Computer Science 475, 34–46 (2013)
Chung, F., Diaconis, P., Graham, R.: Universal cycles for combinatorial structures. Discrete Mathematics 110, 43–59 (1992)
Fredericksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Review 24, 195–221 (1982)
Fredricksen, H., Maiorana, J.: Necklaces of beads in k colors and k-ary de Bruijn sequences. Discrete Mathematics 23(3), 207–210 (1978)
Hurlbert, G., Isaak, G.: On the de Bruijn torus problem. Journal of Combinatorial Theory, Series A 64(1), 50–62 (1993)
Lind, D., Marcus, B.: Symbolic Dynamics and Codings. Cambridge University Press (1995)
van Lint, J.H., MacWilliams, F.J., Sloane, N.J.A.: On pseudo-random arrays. SIAM Journal on Applied Mathematics 36, 62–72 (1979)
Martin, M.H.: A problem in arrangements. Bulletin of the American Mathematical Society 40(12), 859–864 (1934)
Tarjan, R.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)
Tuliani, J.: De Bruijn sequences with efficient decoding algorithms. Discrete Mathematics 226(1-3), 313–336 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blanchet-Sadri, F., Munteanu, S. (2013). Deciding Representability of Sets of Words of Equal Length in Polynomial Time. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-45278-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45277-2
Online ISBN: 978-3-642-45278-9
eBook Packages: Computer ScienceComputer Science (R0)