### Abstract

This paper, which is the first of two parts, brings in the notions of vector addition and the associated scalar multiplication operations on probabilistic finite state automata (PFSA). A class of PFSA is shown to constitute a vector space over the real field ℝ, where the zero element is semantically equivalent to a subclass of PFSA, referred to as symbolic white noise. A norm is introduced on the vector space of PFSA and it quantifies the non-probabilistic behavior of a PFSA. The second part constructs a family of inner products on this vector space and presents numerical examples and applications.

Original language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 5133-5138 |

Number of pages | 6 |

State | Published - 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
---|---|

Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 5133-5138). [5990763]

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*Proceedings of the 2011 American Control Conference, ACC 2011.*, 5990763, pp. 5133-5138, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

**Modeling of symbolic systems : Part I - Vector space representation of probabilistic finite state automata.** / Wen, Yicheng; Ray, Asok; Chattopadhyay, Ishanu; Phoha, Shashi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Modeling of symbolic systems

T2 - Part I - Vector space representation of probabilistic finite state automata

AU - Wen, Yicheng

AU - Ray, Asok

AU - Chattopadhyay, Ishanu

AU - Phoha, Shashi

PY - 2011

Y1 - 2011

N2 - This paper, which is the first of two parts, brings in the notions of vector addition and the associated scalar multiplication operations on probabilistic finite state automata (PFSA). A class of PFSA is shown to constitute a vector space over the real field ℝ, where the zero element is semantically equivalent to a subclass of PFSA, referred to as symbolic white noise. A norm is introduced on the vector space of PFSA and it quantifies the non-probabilistic behavior of a PFSA. The second part constructs a family of inner products on this vector space and presents numerical examples and applications.

AB - This paper, which is the first of two parts, brings in the notions of vector addition and the associated scalar multiplication operations on probabilistic finite state automata (PFSA). A class of PFSA is shown to constitute a vector space over the real field ℝ, where the zero element is semantically equivalent to a subclass of PFSA, referred to as symbolic white noise. A norm is introduced on the vector space of PFSA and it quantifies the non-probabilistic behavior of a PFSA. The second part constructs a family of inner products on this vector space and presents numerical examples and applications.

UR - http://www.scopus.com/inward/record.url?scp=80053143393&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053143393&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781457700804

SP - 5133

EP - 5138

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -