1. A language model can be used to predict the next word in a sequence of words. For
example, given the sequence of words "the cat is", a language model can predict the
next word to be "sitting" or "sleeping". Language models are used in many
applications such as speech recognition and natural language processing e.g. in
chatGPT. Using a practical example, describe how a language model can be designed
using NFA or DFA. What are the limitations of designing a language through the
NFA/DFA approach?
2. Write short notes on the DFA minimization. Show how a vending machine state
diagram can be minimized. What is the significance of the minimization? Include all
the necessary diagrams [ if any]