please show your work, thanks.

Problem 3 -Finite State Transducers (50 points) a) Consider the following pairs of noun lemmas with their plural forms: chair/chairs, prodigy/prodigies, prosthesis/prostheses. Design a morphotactic FST that takes a lexical description like "chair +Plural" and converts into an intermediate form suitable for orthographic processing. Show the state-by-state transition along with the correct input and output when the FST is presented with the inputs "chair +Plural" and "prosthesis +Plural". (10 points) b) Note that for some verbs ending in y, the y is replaced by a-ie when forming the plural. Design an orthographic FST that implements this replacement. Also show the state by state transition along with the correct input and output when the FST is presented with the output from (a) as the input. ( 10 points) c) Invert the FSTs in (a) and (b). (10 points) d) Write an FST to implement the Soundex algorithm. You may create a separate FST for each of the four steps, if you so wish. (20 points) The Soundex algorithm is a method commonly used in libraries and older Census records for representing people's names. It has the advantage that versions of the names that are slightly misspelled or otherwise modified (common, for example, in hand-written census records) will still have the same representation as correctly spelled names. (e.g., Jurafsky, Jarofsky, Jarovsky, and Jarovski all map to .3612 ). - Keep the first letter of the name, and drop all occurrences of non-initial a,e,h,i,o,u, w,y - Replace the remaining letters with the following numbers: b, f, p, v 1;c,g,j,k,q, s,x,z2;d,t3;14;m,n5;r6 - Replace any sequences of identical numbers, only if they derive from two or more letters that were adjacent in the original name, with a single number (i.e., 6666 ). - Convert to the form Letter Digit Digit Digit by dropping digits past the third (if necessary) or padding with trailing zeros (if necessary)