The Probability of a String I: Using Inside Probabilities
We use the Inside Algorithm, a dynamic programming algorithm based on the inside probabilities: P(w1m|G) = P(N1 ==>* w1m|G) = . P(w1m|N1m1, G)=?1(1,m)
Base Case: ?j(k,k) = P(wk|Nkkj, G)=P(Nj --> wk|G)
Induction: ?j(p,q) = ?r,s?d=pq-1 P(Nj --> NrNs) ?r(p,d) ?s(d+1,q)