An inner product space on irreducible and synchronizable probabilistic finite state automata

Patrick Adenis, Yicheng Wen, Asok Ray

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal languagetheoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment.

Original languageEnglish (US)
Pages (from-to)281-310
Number of pages30
JournalMathematics of Control, Signals, and Systems
Volume23
Issue number4
DOIs
StatePublished - Jan 1 2012

Fingerprint

Finite State Automata
Inner product space
Finite automata
Formulation
Algebraic Approach
Vector spaces
Probability Measure
Vector space
Eliminate
Robot
Semantics
Experimental Data
Robots
Specification
Specifications
Motion
Modeling
Model

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics

Cite this

@article{be73b476806e46fdadf771358b2af203,
title = "An inner product space on irreducible and synchronizable probabilistic finite state automata",
abstract = "Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal languagetheoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment.",
author = "Patrick Adenis and Yicheng Wen and Asok Ray",
year = "2012",
month = "1",
day = "1",
doi = "10.1007/s00498-012-0075-1",
language = "English (US)",
volume = "23",
pages = "281--310",
journal = "Mathematics of Control, Signals, and Systems",
issn = "0932-4194",
publisher = "Springer London",
number = "4",

}

An inner product space on irreducible and synchronizable probabilistic finite state automata. / Adenis, Patrick; Wen, Yicheng; Ray, Asok.

In: Mathematics of Control, Signals, and Systems, Vol. 23, No. 4, 01.01.2012, p. 281-310.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An inner product space on irreducible and synchronizable probabilistic finite state automata

AU - Adenis, Patrick

AU - Wen, Yicheng

AU - Ray, Asok

PY - 2012/1/1

Y1 - 2012/1/1

N2 - Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal languagetheoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment.

AB - Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal languagetheoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment.

UR - http://www.scopus.com/inward/record.url?scp=84885594094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885594094&partnerID=8YFLogxK

U2 - 10.1007/s00498-012-0075-1

DO - 10.1007/s00498-012-0075-1

M3 - Article

AN - SCOPUS:84885594094

VL - 23

SP - 281

EP - 310

JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

SN - 0932-4194

IS - 4

ER -