Semi - Probabilistic Automata

Observing the environment and recoganizing patterns for the purpose of decision making are fundamental to any scientific enquiry. Pattern recognition is a scientific discipline so much so that it enables perception in machines and also it has applications in diverse technology areas. Among the scientific community, statistical pattern recognition has received considerable attention in recent years. The statistical pattern recognition challenges are mostly approached by Hidden Markov Models (HMMs). A Hidden Markov Model (HMM) is a probabilistic mathematical discrete structure with the state emission probabilities apart from consisting the components of a probabilistic finite state automaton (PFA). Over the years, researches have been carried out to study the relations between HMM and PFA. Probabilistic finite state automata are mathematical models constructed to generate distributions over a set of strings. The computation of the probability of generating a string as a total, and a string with given prefix or suffix have important applications in the field of parsing. In this attempt, the Semi Probabilistic Finite State Automata (Semi-PA), the most general class of Probabilistic Automata is discussed in detail. AMS Classification: 68Q10 and 68Q45.