Finite state transducers for modular möbius number systems
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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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.