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
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Learning Stochastic Regular Grammars by Means of a State Merging Method
ICGI '94 Proceedings of the Second International Colloquium on Grammatical Inference and Applications
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
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 time series analysis via wavelet-based partitioning
Signal Processing - Special section: Distributed source coding
Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations
SIAM Journal on Control and Optimization
Vector space formulation of probabilistic finite state automata
Journal of Computer and System Sciences
Unsupervised restoration of hidden nonstationary Markov chains using evidential priors
IEEE Transactions on Signal Processing - Part II
Location Estimation of a Random Signal Source Based on Correlated Sensor Observations
IEEE Transactions on Signal Processing
A Parametric Copula-Based Framework for Hypothesis Testing Using Heterogeneous Data
IEEE Transactions on Signal Processing
Adaptive pattern classification for symbolic dynamic systems
Signal Processing
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Probabilistic finite state automata (PFSA) have been widely used as an analysis tool for signal representation and modeling of physical systems. This paper presents a new method to address these issues by bringing in the notion of vector-space formulation of symbolic systems in the setting of PFSA. In this context, a link is established between the formal language theory and functional analysis by defining an inner product space over a class of stochastic regular languages, represented by PFSA models that are constructed from finite-length symbol sequences. The norm induced by the inner product is interpreted as a measure of the information contained in the respective PFSA. Numerical examples are presented to illustrate the computational steps in the proposed method and to demonstrate model order reduction via orthogonal projection from a general Hilbert space of PFSA onto a (closed) Markov subspace that belongs to a class of shifts of finite type. These concepts are validated by analyzing time series of ultrasonic signals, collected from an experimental apparatus, for fatigue damage detection in polycrystalline alloys.