An Efficient Shift Rule for the Prefer-Max De Bruijn Sequence

Abstract A shift rule for the prefer-max De Bruijn sequence is formulated, for all sequence orders, and over any finite alphabet. An efficient algorithm for this shift rule is presented, which has linear (in the sequence order) time and memory complexity.

[1]  Anthony Ralston A New Memoryless Algorithm for De Bruijn Sequences , 1981, J. Algorithms.

[2]  Harold Fredricksen Generation of the Ford Sequence of Length 2n, n Large , 1972, J. Comb. Theory, Ser. A.

[3]  de Ng Dick Bruijn,et al.  Circuits and Trees in Oriented Linear Graphs , 1951 .

[4]  Frank Ruskey,et al.  Generating Necklaces , 1992, J. Algorithms.

[5]  Frank Ruskey,et al.  Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2) , 2000, J. Algorithms.

[6]  Richard M. Wilson,et al.  A course in combinatorics , 1992 .

[7]  Tuvi Etzion An Algorithm for Constructing m-ary de Bruijn Sequences , 1986, J. Algorithms.

[8]  Joe Sawada,et al.  Constructing de Bruijn sequences with co-lexicographic order: The k-ary Grandmama sequence , 2018, Eur. J. Comb..

[9]  H. Fredricksen A Survey of Full Length Nonlinear Shift Register Cycle Algorithms , 1982 .

[10]  Harold Fredricksen,et al.  Necklaces of beads in k colors and k-ary de Bruijn sequences , 1978, Discret. Math..

[11]  R. Lyndon,et al.  Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series , 1958 .

[12]  Harold Fredricksen,et al.  Lexicographic Compositions and deBruijn Sequences , 1977, J. Comb. Theory, Ser. A.

[13]  Joe Sawada,et al.  A surprisingly simple de Bruijn sequence construction , 2016, Discret. Math..

[14]  Tero Harju,et al.  Combinatorics on Words , 2004 .

[15]  S. Chowla On a problem of arrangements , 1939 .

[16]  Jean Pierre Duval,et al.  Factorizing Words over an Ordered Alphabet , 1983, J. Algorithms.