Singular value automata and approximate minimization
Borja Balle, Prakash Panangaden, Doina Precup
TL;DR
This paper introduces spectral methods for constructing approximately minimal weighted automata, including a new SVD algorithm for infinite Hankel matrices, a canonical form, and an approximation technique with quality bounds.
Contribution
It presents novel algorithms for SVD decomposition, canonical form derivation, and approximate minimization of weighted automata using spectral theory.
Findings
New SVD algorithm for infinite Hankel matrices
Canonical form for weighted automata from SVD
Approximate minimization with proven quality bounds
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.
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