Vector space formulation of probabilistic finite state automata |
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Authors: | Yicheng Wen Asok Ray |
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Affiliation: | College of Engineering, Pennsylvania State University, University Park, PA 16802, United States |
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Abstract: | 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. |
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