Numeration Systems, Linear Recurrences, and Regular Sets

A numeration system based on a strictly increasing sequence of positive integers u0=1, u1u2,... expresses a non-negative integer n as a sum n=∑ j=0 i ajuj. In this case we say the string a i a i −1 ...a1 a0 is a representation for n.

[1]  Christiane Frougny,et al.  Representation of numbers in nonclassical numeration systems , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.

[2]  Donald E. Knuth,et al.  fundamental algorithms , 1969 .

[3]  A. Brauer,et al.  On a problem of Frobenius. , 1962 .

[4]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[5]  Arto Salomaa,et al.  Ambiguity and Decision Problems Concerning Number Systems , 1983, Inf. Control..

[6]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[7]  Rina S. Cohen,et al.  Star Height of Certain Families of Regular Events , 1970, J. Comput. Syst. Sci..

[8]  Derick Wood,et al.  Pm Numbers, Ambiguity, and Regularity , 1993, RAIRO Theor. Informatics Appl..

[9]  Christiane Frougny,et al.  Linear Numeration Systems of Order Two , 1988, Inf. Comput..

[10]  Christiane Frougny.  Linear numeration systems, 0-developments and finite automata t , .

[11]  Aviezri S. Fraenkel,et al.  Systems of numeration , 1983, IEEE Symposium on Computer Arithmetic.

[12]  Jean Berstel,et al.  Fibonacci Words — A Survey , 1986 .

[13]  Derick Wood,et al.  L Codes and Number Systems , 1983, Theor. Comput. Sci..

[14]  Jeffrey Shallit.  A Generalization of Automatic Sequences , 1988, Theor. Comput. Sci..

[15]  Aviezri S. Fraenkel,et al.  The Use and Usefulness of Numeration Systems , 1989, Inf. Comput..

[16]  Christiane Frougny,et al.  Fibonacci Numeration Systems and Rational Functions , 1996, MFCS.

[17]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[18]  P. Fatou.  Séries trigonométriques et séries de Taylor , 1906 .

[19]  B. Reznick.  Some Binary Partition Functions , 1990 .

[20]  Christiane Frougny.  Fibonacci representations and finite automata , 1991, IEEE Trans. Inf. Theory.

[21]  Christiane Frougny.  Systemes de numeration lineaires et automates finis , 1989 .

[22]  William H. Kautz.  Ieee Transactions on Information Theory Co~tcluding Remarks , 2022 .

[23]  Juha Honkala.  A Decision Method for The Recognizability of Sets Defined by Number Systems , 1986, RAIRO Theor. Informatics Appl..

[24]  Christiane Frougny.  Linear Numeration Systems, Theta-Developments and Finite Automata , 1989, STACS.

[25]  G. Pólya,et al.  Problems and theorems in analysis , 1983 .

[26]  Juha Honkala.  Bases and Ambiguity of Number Systems , 1984, Theor. Comput. Sci..

[27]  Antonio Restivo,et al.  Representations lf Integers and Language Theory , 1984, MFCS.

[28]  Juha Honkala.  Unique representation in number systems and L codes , 1982, Discret. Appl. Math..