On three-element codes
We show that three-element codes have some special properties which do not hold even for four-element codes. Firstly, for each three-element code A, if u and v are words in pref(xAθ) π pref(yAθ), with x, y ∈ A, x ≠ y, then one of them is a prefix of the other, i.e., among the words which can be covered in two different ways from left to right there exists a unique maximal (possibly infinite) element. Secondly, each three-element code has a bounded delay in at least one direction.
KeywordsBinary Code Primitive Root Free Monoid Bounded Delay Common Prefix
Unable to display preview. Download preview PDF.
- Berstel, J. and Perrin, D., The Theory of Codes, (to appear).Google Scholar
- Colomb, S. and Gordon, B., Codes with bounded synchronization delay, Inform. and Control 8 (1965), 355–372.Google Scholar
- Karhumäki, J., A property of three-element codes, Proceedings of STACS84, Lecture Notes in Computer Science (Springer, 1984).Google Scholar
- Karhumäki, J., The Ehrenfeucht Conjecture: A compactness claim for finitely generated free monoids, Theoret. Comput. Sci. (to appear).Google Scholar
- Lothaire, M., Combinatorics on Words, Addison-Wesley, Reading, Mass (1983).Google Scholar
- De Luca, A., Perrin, D., Restivo, A. and Termini, S., Synchronization and simplification, Discrete Math. 27 (1979) 297–308.Google Scholar
- Salomaa, A., Jewels of Formal Language Theory, Computer Science Press, Rochville, Maryland (1981).Google Scholar
- Schützenberger, M.P., Une theorie algebraique du codage, Seminaire Dubreil-Pisot, annee 55–56, exp. n. 15 Inst. Henri Poincare, Paris (1956).Google Scholar