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Fast Arithmetical Algorithms in Möbius Number Systems
Aug. 2012 (vol. 61 no. 8)
pp. 1097-1109
Petr Kůrka, Charles University in Prague, Prague
We analyze the time complexity of exact real arithmetical algorithms in Möbius number systems. Using the methods of Ergodic theory, we associate to any Möbius number system its transaction quotient {\bf T}\ge 1 and show that the norm of the state matrix after n transactions is of the order {\bf T}^n. We argue that the Bimodular Möbius number system introduced in Kůrka has transaction quotient less than 1.2, so that it computes the arithmetical operations faster than any standard positional system.

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Index Terms:
Expansion subshifts, exact real arithmetical algorithms, emissions, absorptions, transactions.
Citation:
Petr Kůrka, "Fast Arithmetical Algorithms in Möbius Number Systems," IEEE Transactions on Computers, vol. 61, no. 8, pp. 1097-1109, Aug. 2012, doi:10.1109/TC.2012.87
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