The algorithm to perform the task is Algorithm 4. Algorithm 4 : Element as Product of Strong Generators Input : a group G acting on f~ = { 1,2 ..... n }; an element g of G; a base and strong generating set for G; Schreier vectors v (i), 1 < i < k, for the stabiliser chain; Output : a symbolic product, word, expressing g in terms of the strong generators;

Write a classifier algorithm for p(Y |X,α)

Discrete Structure

Give a dynamic programming algorithm using the following optimal subproblem structureLCIS+(i; j) : is the longest closed to increasing subsequence that ends and XiXj , i.e., its last elementis Xj and its second to last element is Xi. Give a recursive formula, prove its correctness and write abottom-up implementation.

Given: Language L2 = {w ϵ {a,b}* | w contains substring aab} Construct the DFA representing the given language L2. Assume the layout of the DFA is as follows: ->A->B->C->D*. That is, the number of states are four (4) and A is the starting state and D is the accepting state. How many self-loop edge/s in the constructed DFA representing the given language L2?

Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}

3. Floyd's algorithm for the shortest Paths (algorithm 3.3) can be used to construct the matrix D, which contains the lengths of the shortest paths from any point to any other point. Given the following graph, construct the adjacency matrix W and use the recursive relation to construct D¹. Note that the entire process starting with W is W (= Dº) -> D¹ -> D² -> D³ ->.........-> D^ (= D). You only need to show the step from W to D¹. To get extra credit show the remaining steps to obtain D5 (=D). V5 3 3 5 V1 1 V4 2 9 1 4 2 V2 V3 3