Abstract
We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects.
For numbers corresponding to Catalan objects of low structural complexity our algorithms provide super-exponential gains while their average case complexity is within constant factors of their traditional counterparts.
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Tarau, P. (2014). Computing with Catalan Families. In: Dediu, AH., MartÃn-Vide, C., Sierra-RodrÃguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_46
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DOI: https://doi.org/10.1007/978-3-319-04921-2_46
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04920-5
Online ISBN: 978-3-319-04921-2
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