Fast Arithmetical Algorithms in Mobius Number Systems
We analyze the time complexity of exact real arithmetical algorithms in Mobius number systems. Using the methods of Ergodic theory, we associate to any Mobius number system its transaction quotient T >= 1 and show that the norm of the state matrix after n transactions is of the order T-n. We argue that the Bimodular Mobius number system introduced in Kurka [10] has transaction quotient less than 1.2, so that it computes the arithmetical operations faster than any standard positional system.
exact real arithmetical algorithms transactions expansion subshifts emissions absorptions