Vector space formulation of probabilistic finite state automata

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• 作者：Yicheng Wen¹ ; ^{ywen2000@gmail.com} ; Asok Ray ; ^axr2@psu.edu
• 关键词：Probabilistic finite state automata ; Normed vector space ; Pattern recognition
• 刊名：Journal of Computer and System Sciences
• 出版年：2012
• 期刊代码：186_00220000
• 类别：et
• 出版时间：July, 2012
• 卷：78
• 期：4
• 页码：1127-1141
• 文件大小：409 K

摘要

This paper develops a vector space model of a class of probabilistic finite state automata (PFSA) that are constructed from finite-length symbol sequences. The vector space is constructed over the real field, where the algebraic operations of vector addition and the associated scalar multiplication operations are defined on a probability measure space, and implications of these algebraic operations are interpreted. The zero element of this vector space is semantically equivalent to a PFSA, referred to as symbolic white noise. A norm is introduced on the vector space of PFSA, which provides a measure of the information content. An application example is presented in the framework of pattern recognition for identification of robot motion in a laboratory environment.