Modeling of symbolic systems: Part I - Vector space representation of probabilistic finite state automata
Yicheng Wen, Asok Kumar Ray, Ishanu Chattopadhyay, Shashi Phoha · 2011
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.