Input a sentence zi Tn parameters qsu v and er s Definitions

Input: a sentence zi... Tn, parameters q(s|u, v) and e(r s) Definitions: Define K to be the set of possible tags. Define K-1 o*, and Kk = K for k = 1 n. Initialization: Set (0,*,*) = 1. Algorithm: . For k=1..n r(k, u,v) = max (r(k-1, w, u) × q(ulu, u) x e(zklu)) . Return maxueKn-WEKn (r(n, thu) × q(STOP|u, u)) Figure 1: The basic Viterbi Algorithm. Part #4 15 points Consider a trigram HMM, as introduced in class. We saw that the Viterbi algorithm could be used to find where the max is taken over all sequences yi ...yn+1 such that yi E K for i = 1 n, and yn +1 HMM.) In a trigram tagger we assume that p takes the form STOP. (Recall that K is the set of possible tags in the 12 1 Recall that we have assumed in this definition that yo-y-l-*, and yn+1 STOP. The Viterbi algorithm is shown in figure 1. Now consider a \"skip\" tagger, where p takes the form n+1 we have assumed in this definition that yo = y-,-y-2-*, and yn+1 = STOP n a regular trigram ote that a \"skip\" tagger replaces the term q(yy-2 y tagger with We call it a skip tagger because yi-i is now omitted from the conditioning nformation

Solution

In modular arithmetic the set of congruence classes relatively prime to the modulus number, say n, form a group under multiplication called the multiplicative group of integers modulo n. It is also called the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. (Units refers to elements with a multiplicative inverse.)