Use Pumping Lemma to show that the following language is not regular: L ={0^n+m 1^n 0^m | m,n >= 0}
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- Hi, This part is about regular expressions (REs) and finite-state automata (FSAs). Notation: in the REs below, the Kleene star has higher precedence than sequencing; andsequencing has higher precedence than +. E.g. 10∗1 + 11∗1 = (1(0∗)1) + (1(1∗)1). Consider the regular expression r: (01 + 11)∗10 (1∗ + 0∗) 1.1) Which of the following words (ε is the empty word) belong to the language defined by r? Options: ε, 101, 001101, 111011, 111010 1.2) For each of your answers in Question 1.1, give a brief explanation. For example, you can explain how the regular expression will accept (i.e. match) the words that belong to its language, and how it will not accept those that do not belong in it. 1.3) Give, as a transition graph, an FSA (possibly with ε-transitions) recognising the same language as r.Note: You should not use transitions with composite labels, e.g. of the form q1 →42→ q2. Thanks for the help :)The sequence of values: n, c(n), c(c(n)), c(c(c(n))), c(c(c(c(n)))),... is known as the hailstone sequence starting at n. Implement c(n) as a function. Use predicates to test the parity of each input n.Please give me the proper answer with step by steo solution Qns: Consider the CFL: L = {w | w is a string of a's and b's such that for every pair of adjacent b's, there is at least one a between them}. Design the PDA that recognizes the language L (Show Step-By-Step)
- Algorithm: JP in algebra G(V, E), a directed or undirected network, as an input for algorithm 12: Results3: s=0, 4: wt 0, 5: s(1)=, 6: , 7: d = D(1,:), and 8: while s =10: s(i) = ; 11: w, p >=d; 9: i=argmins+d; (i)12: d(u) = wt Plus wt;13: π(i) = pd = d.min A(i,:); 14; 15; The aforementioned Python version of the algebraic algorithmGiven the language L = {anbn|n ≥ 0} (a) Provide a CFG for the complement of L, that is any string of 0s and 1s not in L. (b) Provide a PDA for the complement of L, that is any string of 0s and 1s not in L. please solve this question ASAP!Use the Pumping lemma to prove sets not context free: 1. Show this set is not context free: A={a^n b^m c^p | n > m >p > 0}. 2. Show this set is not context free: B={w rev(w) w | w ∈ {a,b}*}. 3. Show this set is not context free: C = {w ∈ {a,b,c,d}* | #a(w) = #b(w) and #c(w) = #d(w)}.
- Suppose L1, L2 are two regular languages over the alphabet Σ = {a, b}. Consider the following two new languages: shuffle1(L1, L2) = {a1b1 . . . anbn : a1 . . . an ∈ L1, b1 . . . bn ∈ L2, ai, bi ∈ Σ, ai = bi, i ∈ [1 . . . n]} shuffle2(L1, L2) = {a1b1 . . . anbn : a1 . . . an ∈ L1, b1 . . . bn ∈ L2, ai, bi ∈ Σ, an−(i−1) = bi, i ∈ [1 . . . n]} Notice how shuffle1, shuffle2 are similar, but not quite the same. One of them is necessarily regular and the other is not necessarily regular.Which is which? Prove your answer. If part of your proof relies on a construction, you do not need to prove its correctness.Present a coding technnique that accepts 2 numbers x,y that will result into a transformation L: R^2 -> R^2 Example: L(x,y) = (x-y,x+y) .Lecture: Analysis of Algorithm >> Matrix Chain Multiplication << Please write C code of the matrix chain multiplication (A1.A2.A3) by using dynamic programming as given below. Then calculate the algorithmic complexity. A1: 3x4 P0=3 P1=4 P2=2 P3=5A2: 4x2A3: 2x5