# Discrete Mathematics & Theoretical Computer Science

## Volume 7 n° 1 (2005), pp. 51-70

author: | Grard Duchamp and Hatem Hadj Kacem and Eric Laugerotte |
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title: | Algebraic elimination of ε-transitions |

keywords: | Automata with multiplicities, epsilon-transitions, behaviour, star of matrices |

abstract: | We here describe a method of removing the ε-transitions of a weighted automaton. The
existence of a solution for this removal depends on the existence of
the star of a single matrix which, in turn, is based on the
computation of the stars of scalars in the ground semiring. We discuss
two aspects of the star problem (by infinite sums and by equations)
and give an algorithm to suppress the
ε-transitions and preserve the behaviour. Running
complexities are computed.
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reference: | Grard Duchamp and Hatem Hadj Kacem and Eric Laugerotte (2005),
Algebraic elimination of ε-transitions,
Discrete Mathematics and Theoretical Computer Science 7, pp. 51-70 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Wed May 4 23:12:41 CEST 2005 by falk