论文信息 - Regular maps in generalized number systems

Regular maps in generalized number systems

This paper extends some results of Allouche and Shallit for o-regular sequences to numerat ion systems in algebraic number fields and to linear numeration systems. We also construc t au tomata tha t perform addition and multiplication by a fixed number.

R. Tichy | J. Allouche | K. Scheicher

[1] Donald Ervin Knuth,et al. The Art of Computer Programming , 1968 .

[2] Gilles Christol,et al. Ensembles Presque Periodiques k-Reconnaissables , 1979, Theor. Comput. Sci..

[3] G. Rauzy,et al. Suites algébriques, automates et substitutions , 1980 .

[4] I. Kátai,et al. Canonical number systems in imaginary quadratic fields , 1981 .

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

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

[7] Patrick Morton,et al. Paper Folding, Digit Patterns and Groups of Arithmetic Fractals , 1989 .

[8] Christiane Frougny. Confluent Linear Numeration Systems , 1992, Theor. Comput. Sci..

[9] J. Allouche. Finite automata and arithmetic. , 1993 .

[10] H. Prodinger,et al. The Sum‐of‐Digits Function for Complex Bases , 1998 .

[11] ELEMENTARY PROPERTIES OF CANONICAL NUMBER SYSTEMS IN QUADRATIC FIELDS , 1998 .