Singular value automata and approximate minimization

Singular value automata and approximate minimization

The present paper uses spectral theory of linear operators to construct approximatelyminimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finite-rank infinite Hankel matrices based on their representati...

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Veröffentlicht in:Mathematical structures in computer science 2019-10, Vol.29 (9), p.1444-1478
Hauptverfasser: Balle, Borja, Panangaden, Prakash, Precup, Doina
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Sprache:eng
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Algorithms
Canonical forms
Hankel matrices
Linear operators
Singular value decomposition
Spectral theory
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creator Balle, Borja
Panangaden, Prakash
Precup, Doina
description The present paper uses spectral theory of linear operators to construct approximatelyminimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finite-rank 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 Hankelmatrix, and (iii) an algorithmto construct approximateminimizations of given weighted automata by truncating the canonical form.We give bounds on the quality of our approximation.
doi_str_mv 10.1017/S0960129519000094
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subjects Algorithms
Canonical forms
Hankel matrices
Linear operators
Singular value decomposition
Spectral theory
title Singular value automata and approximate minimization
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