English

Singular value automata and approximate minimization

Formal Languages and Automata Theory 2019-11-13 v2

Abstract

The present paper uses spectral theory of linear operators to construct approximately minimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the SVD decomposition of infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankel matrix and (iii) an algorithm to construct approximate minimizations of given weighted automata by truncating the canonical form. We give bounds on the quality of our approximation.

Keywords

Cite

@article{arxiv.1711.05994,
  title  = {Singular value automata and approximate minimization},
  author = {Borja Balle and Prakash Panangaden and Doina Precup},
  journal= {arXiv preprint arXiv:1711.05994},
  year   = {2019}
}
R2 v1 2026-06-22T22:47:55.348Z