# numeration system

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

**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 ...

13

### Representing real numbers in a generalized numeration system

27

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

**numeration**systems. The

**numeration**systems occurring in this paper essentially have two ...the

**numeration**

**system**comes from a particular ...

22

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

**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 ...

180

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

**system**combinatorial

**numeration**

**system**and referred to Lehmer [8]. Even if this seems to be a folklore result, the only proof ...

20

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

**numeration**

**system**, J. Comput.

**System**Sci. 77 (2011), no. 4, 743–759. ◦ A. Cobham, Uniform tag sequences, Math. ...

41

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

19

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

38

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

**numeration**...

2

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

**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 ...

13

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

**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 ...

13

### Behavior of digital sequences through exotic numeration systems

**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 ...

36

### Abstract numeration systems

**numeration**

**system**S = (a ∗ 1 . . . a ∗ ℓ , {a 1 < . . . < a ℓ }), multiplication by λ > 1 preserves S-recognizability if and only if one of ...

39

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

**numeration**systems containing the Fibonacci

**numeration**...Fibonacci

**numeration**

**system**F , we show that the number of states of the trim minimal automaton accepting 0 ∗ ...

9

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

**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 ...

15

### Abstract numeration systems : a survey.

**NUMERATION**SYSTEMS DEFINITION ...abstract

**numeration**

**system**is a triple S = ( L , Σ, <) where L is a regular language over a totally ordered alphabet (Σ, <) ...

72

### Abstract numeration systems

**numeration**

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

54

### Ultimate periodicity problem for linear numeration systems

**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 ...

51

### THI safety system

4

### System engineering approach applied to Galileo system

**system**specifi- cation to the

**system**segments. The requirement derivation addressed in the previous section is the result of the

**System**Design Activity. ...

9