Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 26.11.2019 |
| Speaker: | Pavla Veselá, FJFI, České vysoké učení technické v Praze |
| Title: | Two applications of the spectrum of numbers |
| Abstract: | The first application is restricted to the case that $\beta>1 $ and the alphabet is $ A = \{-M, \dots, M \}$, $M\geq 1$ integer. We will show that the set of infinite $(\beta, A)$-representations of 0 is recognizable by a finite Büchi automaton if and only if the spectrum $S_{A}(\beta)$ has no accumulation point. For the second application we consider the on-line algorithm for division of Trivedi and Ercegovac generalized to a complex numeration system. The numeration system $ (\beta, A) $ allows preprocessing if and only if the spectrum $S_{A}(\beta)$ has no accumulation point. |
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