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# numeration system

### On the enumerating series of an abstract numeration system

... abstract numeration system ...abstract numeration systems given by Theorem 1, it is interesting to further in- vestigate the construction which, given L and a recognisable set of numbers X computes ...

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### Representing real numbers in a generalized numeration system

... The 3 2 -number system introduced by Akiyama, Frougny and Sakarovitch (2008) has a numeration language which is not context-free.. AIM : To provide a unified approach for representing re[r] ...

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### Convergence of Pascal-Like Triangles in Parry–Bertrand Numeration Systems

... of numeration systems. The numeration systems occurring in this paper essentially have two ...the numeration system comes from a particular ...

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### Abstract Numeration Systems : Recognizability, Decidability, Multidimensional S-Automatic Words, and Real Numbers

... linear numeration system U for which both rep U (N) and addition are rec- ognizable by finite automata ...characterize numeration systems U for which addition is computable by a finite ...linear ...

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### Abstract numeration systems on bounded languages and multiplication by a constant

... with z ℓ > z ℓ−1 > · · · > z 1 ≥ 0. Fraenkel [4] called this system combinatorial numeration system and referred to Lehmer [8]. Even if this seems to be a folklore result, the only proof ...

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### Automatic sequences in rational base numeration systems (and even more)

... ◦ É. Charlier, M. Le Gonidec, and M. Rigo, Representing real numbers in a generalized numeration system, J. Comput. System Sci. 77 (2011), no. 4, 743–759. ◦ A. Cobham, Uniform tag sequences, Math. ...

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### Abstract numeration systems on bounded languages and multiplication by a constant

... as considered for instance in [9]. A set X ⊆ N is said to be B ` -recognizable if rep ` (X) is a regular language over the alphabet Σ ` , i.e., accepted by a finite automaton. This one-to-one correspondence between the ...

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### Regular sequences and synchronized sequences in abstract numeration systems

... ` ] ∈ N d+1 : ∃m, [ m n ] ∈ G f ∧ ` < m}. Since for all n ∈ N d , f (n) = Card{` ∈ N : [ n ` ] ∈ X}, the result follows from Theorem 53. Remark 65. Even though both families of S-automatic sequences and (S, N)-regular ...

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### A decision problem for ultimately periodic sets in non-standard numeration systems

... or not X is ultimately periodic, i.e., whether or not X is a finite union of arithmetic progressions ? J. Honkala showed in [1] that Problem 1 turns out to be decidable for the usual integer base b ≥ 2 numeration ...

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### A decision problem for ultimately periodic sets in non-standard numeration systems

... linear numeration system such that N is U -recognizable and satisfying a relation like (1) with a k = ±1 (the main reason for this assumption is that 1 and −1 are the only two integers invertible modulo n ...

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### Structure of the minimal automaton of a numeration language and applications to state complexity

... the numeration system has a dominant root β > 1 (see the next section for the definition), we are able to provide a more specific description of the ...

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### Behavior of digital sequences through exotic numeration systems

... Tribonacci numeration system T = (T (n)) n>0 built on the language of words over {0, 1} avoiding three consecutive ones, we conjecture that a result similar to Theorem 2 should hold for the corresponding ...

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### Abstract numeration systems

... Theorem Let ℓ be a positive integer. For the abstract numeration system S = (a ∗ 1 . . . a ∗ ℓ , {a 1 < . . . < a ℓ }), multiplication by λ > 1 preserves S-recognizability if and only if one of ...

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### Structure of the minimal automaton of a numeration language

... linear numeration systems containing the Fibonacci numeration ...Fibonacci numeration system F , we show that the number of states of the trim minimal automaton accepting 0 ∗ ...

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### Automatic sequences based on Parry or Bertrand numeration systems

... Parry numeration system is not closed under taking images by uniform substitutions or periodic deletion of ...Parry numeration systems and ...positional numeration system U with regular ...

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### Abstract numeration systems : a survey.

... ABSTRACT NUMERATION SYSTEMS DEFINITION ...abstract numeration system is a triple S = ( L , Σ, <) where L is a regular language over a totally ordered alphabet (Σ, <) ...

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### Abstract numeration systems

... An abstract numeration system (ANS) is a triple S = (L, Σ, <) where L is an innite regular language over a totally ordered alphabet (Σ, <) . By enumerating the words of L w.r.t. the radix order < ...

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### Ultimate periodicity problem for linear numeration systems

... Theorem Let U be a numeration system satisfying (H1), (H2) and (H3), and such that the gcd of the coefficients of the recurrence relation of U is larger than 1. Assume there is a computable positive integer ...

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### THI safety system

... RESPONSE TIME To measure the response time, the beam is tuned to lose 4µAe in SSC1. We cut the beam by the chopper and we set the threshold to 2µAe. The beam is then sent through the cyclotron, and the safety ...

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### System engineering approach applied to Galileo system

... This section addresses the allocation of the system specifi- cation to the system segments. The requirement derivation addressed in the previous section is the result of the System Design Activity. ...

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