منابع مشابه
Text Compression using Abstract Numeration System on a Regular Language
An abstract numeration system (ANS) is a numeration system that provides a one-to-one correspondence between the natural numbers and a regular language. In this paper, we define an ANS-based compression as an extension of this correspondence. In addition, we show the following results: 1) an average compression ratio is computable from a language, 2) an ANS-based compression runs in sublinear t...
متن کاملNumeration systems on a regular language: arithmetic operations, recognizability and formal power series
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L ⊂ Σ∗. For these systems, we obtain a characterization of recognizable sets of integers in terms of rational formal series. We also show that, if the complexity of L is Θ(n) (resp. if L is the complement of a polynomial language...
متن کاملGeneralization of automatic sequences for numeration systems on a regular language
Let L be an infinite regular language on a totally ordered alphabet (Σ, <). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the output alphabet of the automaton. This process generalizes the concept of k-automatic sequence for abstract numeration systems on a regular language (instead of...
متن کاملNumeration Systems, Linear Recurrences, and Regular Sets
A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...
متن کاملAdditive Functions with Respect to Numeration Systems on Regular Languages
Additive numeration systems and the corresponding additive arithmetic functions have been studied from various points of view since the seminal papers of H. Delange [4, 5], where such functions were investigated for the usual q-adic numeration system. Later more exotic systems of numeration, such as general linear numeration systems [13, 14], especially such systems defined by linear recurring ...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2000
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s002240010014