Abstract
In his paper [6], Schützenberger proved that two finite subsets of words are maximal prefix if their product is maximal prefix, provided this product is finite and unambiguous. The finiteness condition is necessary; however, the authors in [1] wonder whether the unambiguity hypothesis is also necessary. We answer positively by giving an example of a finite maximal prefix and ambiguous product of which the two factors are not maximal prefix. We also give a generalized version of the Schützenberger theorem where the finiteness condition is weakened.
Preview
Unable to display preview. Download preview PDF.
References
J. BERSTEL and D. PERRIN, "Theory of codes", Academic Press, Orlando, 1985.
V. BRUYERE, Maximal prefix products, Semigroup Forum 36 (1987), 147–157.
V. BRUYERE, Answer to a question about maximal prefix sets of words, submitted to Theor. Comp. Science.
N.J. FINE and H.S. WILF, Uniqueness theorems for periodic functions, Proc. Amer. Math. Soc. 16 (1965), 109–114.
M. LOTHAIRE, "Combinatorics on words", Reading, Massachusetts, Addison-Wesley, 1983.
M.P. SCHUTZENBERGER, Sur certains sous-monoïdes libres, Bull. Soc. Math. France 93 (1965), 209–223.
M.P. SCHUTZENBERGER, On a question concerning certain free submonoids, J. Combinatorial Theory 1 (1966), 437–442.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bruyere, V. (1988). On maximal prefix sets of words. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017143
Download citation
DOI: https://doi.org/10.1007/BFb0017143
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50110-7
Online ISBN: 978-3-540-45926-2
eBook Packages: Springer Book Archive