Abstract
The theorem of factorisation forests shows the existence of nested factorisations — a la Ramsey — for finite words. This theorem has important applications in semigroup theory, and beyond.
We provide two improvements to the standard result. First we improve on all previously known bounds for the standard theorem. Second, we extend it to every ‘complete linear ordering’. We use this variant in a simplified proof of complementation of automata over words of countable scattered domain.
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Colcombet, T. (2007). Factorisation Forests for Infinite Words. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_20
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DOI: https://doi.org/10.1007/978-3-540-74240-1_20
Publisher Name: Springer, Berlin, Heidelberg
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