Consider the following pairs noun lemmas with: night/nights, city/cities. Design a morphotactic FST that takes a lexical description such as city +Plural and converts it into an intermediate form suitable for orthographic processing. Problem 1. Show the state by state transition along with the correct input and output when the FST is presented with the input and output when presented with the input city +Plural and month +Plural. Problem 2. Note that for some nouns ending in -y, the -y is replaced by an -ies when forming the plural. Design an orthographic FST that implements this replacement. Invert the FSTs in problem 1 and 2, and show the state by state parse of the surface form cities and events