Abstract
We show that for every homomorphism from A + to a finite semigroup S there exists a factorization forest of height at most 3 ∣ S ∣ − 1. Furthermore, we show that for every non-trivial group, this bound is tight. For aperiodic semigroups, we give an improved upper bound of 2 ∣ S ∣ and we show that for every n ≥ 2 there exists an aperiodic semigroup S with n elements which reaches this bound.
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Kufleitner, M. (2008). The Height of Factorization Forests. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_36
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DOI: https://doi.org/10.1007/978-3-540-85238-4_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85237-7
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