Probabilistic CKY Assignment

    Below we give the CKY chart for a parse of the 10-word sentence:

      The agency sees use of the codes as a way.

    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.

    Probabalistic Context Free Grammar

    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
    

    Lexicon

    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