TY - JOUR
T1 - An inner product space on irreducible and synchronizable probabilistic finite state automata
AU - Adenis, Patrick
AU - Wen, Yicheng
AU - Ray, Asok
N1 - Funding Information:
This work has been supported in part by the US Office of Naval Research under Grant No. N00014-09-1-0688, and by the US Army Research Laboratory and the US Army Research Office under Grant No. W911NF-07-1-0376. Any opinions, findings and conclusions or recommendations in this publication are those of the authors and do not reflect the views of the sponsoring agencies.
PY - 2012/2
Y1 - 2012/2
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
SN - 0932-4194
VL - 23
SP - 281
EP - 310
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
IS - 4
ER -