Singular value automata and approximate minimization

被引：5
|
作者：
Balle, Borja [1 ]
Panangaden, Prakash [2 ]
Precup, Doina [2 ]
机构：
[1] Amazon Res, Cambridge, England
[2] McGill Univ, Sch Comp Sci, Montreal, PQ, Canada
来源：
MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE | 2019年 / 29卷 / 09期
关键词：
WEIGHTED AUTOMATA;
D O I：
10.1017/S0960129519000094
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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 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 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.
引用
收藏
页码：1444 / 1478
页数：35
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