Publication 2012 Issue No. 8 - Aug. Abstract - Fast Arithmetical Algorithms in Möbius Number Systems
Fast Arithmetical Algorithms in Möbius Number Systems
Aug. 2012 (vol. 61 no. 8)
pp. 1097-1109
 ASCII Text x Petr Kůrka, "Fast Arithmetical Algorithms in Möbius Number Systems," IEEE Transactions on Computers, vol. 61, no. 8, pp. 1097-1109, Aug., 2012.
 BibTex x @article{ 10.1109/TC.2012.87,author = {Petr Kůrka},title = {Fast Arithmetical Algorithms in Möbius Number Systems},journal ={IEEE Transactions on Computers},volume = {61},number = {8},issn = {0018-9340},year = {2012},pages = {1097-1109},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2012.87},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Fast Arithmetical Algorithms in Möbius Number SystemsIS - 8SN - 0018-9340SP1097EP1109EPD - 1097-1109A1 - Petr Kůrka, PY - 2012KW - Expansion subshiftsKW - exact real arithmetical algorithmsKW - emissionsKW - absorptionsKW - transactions.VL - 61JA - IEEE Transactions on ComputersER -
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