Language Technology, Fall 2014
Exercise 1 - FUN with morphology and entropy 
(Due Monday 10/6 11:59pm on Blackboard)
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1. Redo the pluralization transducer from the quiz:
   Besides the default +s rule, you'd also consider the following rules: 
   {-s, -x, -sh, -ch} + es (e.g. buses, boxes, bushes, matches), 
   -f + -ves (e.g. leaves), and
   -y + -ies (e.g. flies). 
   You don't need to consider any other rules or irregularities (e.g. tooth => teeth).

   (a) include a photo of your transducer on paper
   (b) include a carmel text file for your transducer, and test it with
       at least five examples.

2. Derive this central equation in Noisy-Channel model rigorously (see slide 4):

   argmax_{t..t} P(t..t|w..w) 
 ~ argmax_{t_1..t_n} P(t_1)     P(t_2|t_1) P(t_3|t_2 t_1) ... P(t_n|t_{n-1} t_{n-2}) 
                     P(w_1|t_1) P(w_2|t_2) P(w_3|t_3)     ... P(w_n|t_n).

here "~" means "approximately equal". 

In each step of your derivation, it's either an equality or an approximation, and
* in case of equality, annotate the law/rule used (e.g., Bayes rule), 
* in case of approximation, explain the reason/assumption behind it.

Also explain why this model is intuitively called "HMM".

   
3. Play the Shannon Game at least once (it's fun!), and report your entropy.

http://www.math.ucsd.edu/~crypto/java/ENTROPY/

(if it doesn't run, System Preference->Java->Security->Edit Site List,
and add http://www.math.ucsd.edu to that list.)

a) take a screen shot of your result.
b) work out the formula that was used to calculate your entropy in this game,
   and verify it with your result.
c) write a short paragraph of observations from your game and your result.