Star-height of an N-rational series
We prove a new result on N-rational series in one variable. This result gives, under an appropriate hypothesis, a necessary and sufficient condition for an N-rational series to be of star-height 1. The proof uses a theorem of Handelman on integral companion matrices.
Unable to display preview. Download preview PDF.
- [BOY94]M. BOYLE. Symbolic dynamics and matrices. In R. Brualdi S. Friedland and V. Klee, editors, Combinatorial and Graph-Theoretic Problems in Linear Algebra, volume 50 of IMA Volumes in Mathematics and Its Applications. 1994.Google Scholar
- [BR88]J. BERSTEL and C. REUTENAUER. Rational series and their languages. Springer-Verlag, Berlin, 1988.Google Scholar
- [GAN59]F.R. GANTMACHER. The theory of matrices. Chelsea, New-York, 1959.Google Scholar
- [HAN92]D.E. HANDELMAN. Spectral radii of primitive integral companion matrices and log-concave polynomials. In Peter Walters, editor, Symbolic Dynamic and its Applications, volume 135 of Contempory Mathemetics, pages 231–238. 1992.Google Scholar
- [HAS89]K. HASHIGUCHI. Relative star-height, star-height and finite automata with distance functions. In J.-E. Pin, editor, Formal Properties of finite automata and applications, volume 386 of Lecture Notes In Computer Sciences, pages 74–88. Springer, 1989.Google Scholar
- [LIN84]D. LIND. The entropies of topological Markov shifts and a related class of algebraic integers. Ergod. Th. and Dynam. Syst., 4:283–300, 1984.Google Scholar
- [MIN88]H. MINC. Nonnegative matrices. Wiley Inter-Sciences, 1988.Google Scholar
- [SS78]A. SALOMAA and M. SOITTOLA. Automata theoretic aspect of formal power series. Springer-Verlag, Berlin, 1978.Google Scholar