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.
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References
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© 1988 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/BFb0017143
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