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Unformatted text preview: l an Eulerian cycle in a graph is a path that traverses each edge of the
graph exactly once, and begins and ends at the same vertex. Then an Eulerian
cycle in an order N − 1 de Bruijn graph is an order N de Bruijn sequence. An
example illustrates this correspondence. To build this example, we describe the
prefer 1 algorithm for generating binary order N de Bruijn sequences. By an
N -string we mean a string of length N .
1. Begin with an empty list L of N -strings visited so far, and with the N string 00 . . . 0, called the current N -string.
2. Add the current N -string to L.
3. Append 1 to the left of, and remove the right-most entry of, the current
string, if this gives a string not already in L, then loop to step 2.
4. If the operation of step 3 gives an N -string already in L, append 0 to the
right of, and remove the right-most entry of, the current string. If this
gives a string not already in L, then loop to step 2. 66 CHAPTER 2. ITERATED FUNCTION SYSTEMS
5. If neither steps 3 or 4 gives rise to...
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