On two combinatorial problems arising from automata theory - Archive ouverte HAL
Conference Papers Year : 1983

On two combinatorial problems arising from automata theory

Abstract

We present some partial results on the following conjectures arising from automata theory. The first conjecture is the triangle conjecture due to Perrin and Schützenberger. Let A = {a, b} be a two-letter alphabet, d a positive integer and let B_d = {a^iba^j | 0 <= i+j <= d}. If X \subset B_d is a code, then |X| <= d+1. The second conjecture is due to Cerný and the author. Let A be an automaton with n states. If there exists a word of rank <= k in A, there exists such a word with length <= (n-k)^2.
Fichier principal
Vignette du fichier
TwoCombinatorial.pdf (152.43 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-00143937 , version 1 (28-04-2007)

Identifiers

  • HAL Id : hal-00143937 , version 1

Cite

Jean-Eric Pin. On two combinatorial problems arising from automata theory. Combinatorial mathematics (Marseille-Luminy, 1981), 1983, Marseille-Luminy, pp.535-548. ⟨hal-00143937⟩
120 View
771 Download

Share

More