Below we give the CKY chart for a parse of the 10word sentence:
The assignment is to assign probabilities to each of the edges used in the 5 parses the example sentence has using the probabilities in the Probabilistic CF grammar below. You do not have to assign probabilities to edges not used in any of the 5 parses. You will find it helpful to use the solution to the last assignment as a guide to make sure you are considering all possible ways of building each edge.
What you need to hand in is a version of the chart below that has the Viterbi values associated with each edge in the chart used in one of the 5 parses. and your calculations. For example, a four word sentence chart might look like the chart below, using the grammar below:
1 the 
2 agency 
3 sees 
4 codes 

0  dt, .5  np, .0025  s, .0001  
1   n, .01 nbar, .01  
2    vbz, 1.0 
vp, .004 
2    n, .01 nbar, .01 
We first give the grammar the parser uses (in Chomsky Normal Form), as well as the lexicon.
pp > p np, 1.0 vpg > vbg np, 1.0 X2 > X1 pp, 1.0 vp > vbz np, .4 vp > X1 pp, .5 vp > X2 pp, .1 ap > rb a, 1.0 s > np vp, 1.0 np > dt nbar, .5 np > X3 np, .1 np > ap nbar, .05 np > nbar pp, .2 np > n n, .05 np > vbg np, .05 X3 > np cc, 1.0 X1 > vbz np, 1.0 nbar > ap nbar, .1 nbar > nbar pp, .3 nbar > n n, .5 nbar > vbg np, ..05
a: dt, .5 and: cc, 1.0 use: n,.01; np,01; nbar.01 codes: n,.01; np,01; nbar,.01 sees: vbz,1.0 of: p,.5 agency: n,.01; np,.01; nbar,.01 rapidly: rb,1.0 handling: vbg,.5 labor: n,.01; np,.01, nbar as: p,.5 costs: n,.01; np,.01 nbar,.01 controlling: vbg,.5 way: n,.01; np,.01; nbar,.01 growing: a,.5 ap,.5 the: dt,.5 widespread: a,5, ap,5
k
1 the 
2 agency 
3 sees 
4 use 
5 of 
6 the  7 codes 
8 as 
9 a 
10 way 

0  dt  np  s  s  s  
1  np nbar n  s  s  s  
2  vbz  vp X1  vp X2 X1  vp X2 X1  
3  np nbar n  np nbar  np nbar  
4  p  pp  pp  
5  dt  np  np  
6  np nbar n  np nbar  
7  p  pp  
8  dt  np  
9  np nbar n 