Arithmetic Meyer sets and finite automata
نویسندگان
چکیده
منابع مشابه
Arithmetic Meyer sets and finite automata
Non-standard number representation has proved to be useful in the speed-up of some algorithms, and in the modelization of solids called quasicrystals. Using tools from automata theory we study the set Zβ of β-integers, that is, the set of real numbers which have a zero fractional part when expanded in a real base β, for a given β > 1. In particular, when β is a Pisot number — like the golden me...
متن کاملAutomata for Arithmetic Meyer Sets
The set Zβ of β-integers is a Meyer set when β is a Pisot number, and thus there exists a finite set F such that Zβ −Zβ ⊂ Zβ +F . We give finite automata describing the expansions of the elements of Zβ and of Zβ − Zβ . We present a construction of such a finite set F , and a method to minimize the size of F . We obtain in this way a finite transducer that performs the decomposition of the eleme...
متن کاملDiophantine Equations, Presburger Arithmetic and Finite Automata
We show that the use of nite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity.
متن کاملUnary finite automata vs. arithmetic progressions
We point out a subtle error in the proof of Chrobak's theorem that every unary NFA can be represented as a union of arithmetic progressions that is at most quadratically large. We propose a correction for this and show how Martinez's polynomial time algorithm, which realizes Chrobak's theorem, can be made correct accordingly. We also show that Martinez's algorithm cannot be improved to have log...
متن کاملDeforming Meyer sets
A linear deformation of a Meyer set M in R is the image of M under a group homomorphism of the group [M ] generated by M into R. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In the case that the deformation is a Meyer set and the deformation is injective, the deformation is pure point diffractive if the orginal set M is pure point diffractive. AMS Cl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information and Computation
سال: 2005
ISSN: 0890-5401
DOI: 10.1016/j.ic.2005.05.002