TU Graz, March 2012

Automata, languages and numeration systems

• Finite automata and rational languages of finite words

• Finite automata and infinite words

• Integer base numeration systems

• Real base numeration systems

• Pisot numbers, Parry numbers and Perron numbers

• Numeration systems defined by a basis

Bibliography

[1] V. Berthé and M. Rigo, Preliminaries, Chapter 1 in Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds), Cambridge University Press, 2010. Download.

[2] Ch. Frougny, Numeration systems, Chapter 7 in M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 2002.

[3] Ch. Frougny and J. Sakarovitch, Number representation and finite automata, Chapter 2 in Combinatorics, Automata and Number Theory, V. Berthé, M. Rigo (Eds), Cambridge University Press, 2010.

[4] Ch. Frougny and B. Solomyak, Finite beta-expansions, Ergodic Theory & Dynamical Systems 12 (1992) 713--723. Download.

[5] D. Perrin and J.-E. Pin, Infinite words, Pure and Applied Mathematics Vol 141, Elsevier, 2004. Chapter 1 available here.

[6] J.-E. Pin, Mathematical Foundations of Automata Theory, preprint, 2012. Download.

[7] J. Sakarovitch, Elements of Automata Theory, Cambridge University Press, 2009.