Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
On the learnability and usage of acyclic probabilistic finite automata
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Learning Stochastic Regular Grammars by Means of a State Merging Method
ICGI '94 Proceedings of the Second International Colloquium on Grammatical Inference and Applications
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Symbolic dynamic analysis of complex systems for anomaly detection
Signal Processing
Blind construction of optimal nonlinear recursive predictors for discrete sequences
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Probabilistic Finite-State Machines-Part I
IEEE Transactions on Pattern Analysis and Machine Intelligence
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations
SIAM Journal on Control and Optimization
A Parametric Copula-Based Framework for Hypothesis Testing Using Heterogeneous Data
IEEE Transactions on Signal Processing
| Hi-index | 0.00 |
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.