### 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.

Original language | English (US) |
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Pages (from-to) | 1127-1141 |

Number of pages | 15 |

Journal | Journal of Computer and System Sciences |

Volume | 78 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

}

*Journal of Computer and System Sciences*, vol. 78, no. 4, pp. 1127-1141. https://doi.org/10.1016/j.jcss.2012.02.001

**Vector space formulation of probabilistic finite state automata.** / Wen, Yicheng; Ray, Asok.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Vector space formulation of probabilistic finite state automata

AU - Wen, Yicheng

AU - Ray, Asok

PY - 2012/7/1

Y1 - 2012/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84858437533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858437533&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2012.02.001

DO - 10.1016/j.jcss.2012.02.001

M3 - Article

AN - SCOPUS:84858437533

VL - 78

SP - 1127

EP - 1141

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 4

ER -