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Zhi Xu

Zhi Xu

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    De Bruijn Sequences Revisited
    Lila Kari
    International Journal of Foundations of Computer Science, vol. 23 (2012), pp. 1307-1322
    Preview abstract A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to different settings: the multi-shift de Bruijn sequence and the pseudo de Bruijn sequence. An m-shift de Bruijn sequence of order n is a word such that every word of length n appears exactly once in w as a factor that starts at a position im + 1 for some integer i ≥ 0. A pseudo de Bruijn sequence of order n with respect to an antimorphic involution θ is a word such that for every word u of length n the total number of appearances of u and θ(u) as a factor is one. We show that the number of m-shift de Bruijn sequences of order n is an!a(m-n)(an-1) for 1 ≤ n ≤ m and is (am!)an-m for 1 ≤ m ≤ n, where a is the size of the alphabet. We provide two algorithms for generating a multi-shift de Bruijn sequence. The multi-shift de Bruijn sequence is important for solving the Frobenius problem in a free monoid. We show that the existence of pseudo de Bruijn sequences depends on the given alphabet and antimorphic involution, and obtain formulas for the number of such sequences in some particular settings. View details
    Pseudopower Avoidance
    Ehsan Chiniforooshan
    Lila Kari
    Fundamenta Informaticae, vol. 114 (2012), pp. 55-72
    Triangular and Hexagonal Tile Self-assembly Systems
    Lila Kari
    Shinnosuke Seki
    WTCS 2012, Computation, Physics and Beyond - International Workshop on Theoretical Computer Science, Springer, Berlin Heidelberg, pp. 357-375
    The Computational Complexity of Universality Problems for Prefixes, Suffixes, Factors, and Subwords of Regular Languages
    Narad Rampersad
    Jeffrey Shallit
    Fundamenta Informaticae, vol. 116 (2012), pp. 223-236
    Decision problems for convex languages
    Janusz Brzozowski
    Jeffrey Shallit
    Information and Computation, vol. 209 (2011), pp. 353-367
    De Bruijn Sequences Revisited
    Lila Kari
    AFL 2011, 13th International Conference Automata and Formal Languages, pp. 241-254
    Pseudo-power Avoidance
    Ehsan Chiniforooshan
    Lila Kari
    DLT 2010, 14th International Conference Developments in Language Theory, Springer, Berlin Heidelberg, pp. 432-433
    A Minimal Periods Algorithm with Applications
    CPM 2010, 21st Annual Symposium Combinatorial Pattern Matching, Springer, Berlin Heidelberg, pp. 51-62
    Triangular Tile Self-assembly Systems
    Lila Kari
    Shinnosuke Seki
    DNA 16, 16th International Conference DNA Computing and Molecular Programming, Springer, Berlin Heidelberg (2010), pp. 89-99
    Decision Problems for Convex Languages
    Janusz Brzozowski
    Jeffrey Shallit
    LATA 2009, Third International Conference Language and Automata Theory and Applications, Springer, Berlin Heidelberg, pp. 247-258
    The Frobenius Problem in a Free Monoid
    Jui-Yi Kao
    Jeffrey Shallit
    STACS 2008, 25th Annual Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, pp. 421-432