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Exercise 7.3.2: Consider the following two languages: Li = {a"b2ncm n,m >0} L2 = {a" mc2m...
Construct NFA that accept L1 L2 , where Li = {a”bam+1, n > 0, m>0}; } = {a,b} L2 = {ab”, n >0}; £ = {a,b}
Part C Only Let Σ = {a,b}. For each of the following languages, find a grammar that generates it. (a) Li {a"6" : n > 0,m< n}. (b) L2 = {ang 2n: n > 2). (c) L3 {an+35" : n > 2}.
Question 3 (5 Points) Find context free grammars L = a"b",n is a multiple of three Find context-free grammars for the following languages (with n 2 0, m 2 0) ** L = {a"bm : n < m+3}. (a) (b) L= {a"bm : n = m - 1}. L = {a"bm 2m}. L {a"b" 2n < m < 3n}. (c) (d)
2. (10 points) Use the pumping lemma for context free grammars to show the following languages are not context-free. (a) (5 points) . (b) (5 points) L = {w ◦ Reverse(w) ◦ w | w ∈ {0,1}∗}. I free grammar for this language L. lemma for context free grammars to show t 1. {OʻPOT<)} L = {w • Reverse(w) w we {0,1}*). DA+hattha follaurino lano
Let L, be the language accepted by the DFA below and L2 = {0"1"Om1 mol 1|n, m, k > 0}. Create a CFG that generates L3 = L, UL2 using the techniques pre sented in textbook. 0 start -> 0 10
Prove this using the definition R7: log(n*) is O(log n) for any fixed x > 0
1. Show that the following languae is context-free: {amb” cm:n, m >0} U {CPb9qP : P, q>0}
Roots (20 points). Consider the loop-gain transfer function L(S) = TS-a)n-m where n and m are integers such that n > m and a € R. Also, consider the characteristic equation 1+ KL(S) = 0, with 0 <KER, which can be equivalently written as nam (s– an-m + K = TI (s – rj) = 0. Show that num ri=(n - m), for any 0 <KER.
The languages L1 = {anbm | m = n or m = 2n } and L2 = {a n b m | n <= m <= 2n } are context free. a. Choose one of the languages and write a CFG for it. b. Write the PDA that comes from your grammar (part a). Show the first 4 moves it would make on some string in your language (of length at least 4). Be sure to show state, input, and...
Problem 1 Create a CFG that generates each of the languages below. [10 points] [10 points] wR is a substring of r if there are strings y, z E {a, b)" such that r = ywR2. A = {w I w E {a, b)" has more as than bs} B = {w#r l w,xe(a, b)" and wR a. b. is a substring of r). Rememb er, c. [10 points] C = {amb"ck 1 m, n > 0 and k =...