Prove that each of the following languages is not regular
A) L= {a^n b^m c^k : k = 2n + 3m and n, m, k ≥ 0}
B) L = {a^n : n is a power of 5}
Prove that each of the following languages is not regular A) L= {a^n b^m c^k :...
5. Prove that the following languages are not regular: (a) L = {a"bak-k < n+1). (b) L-(angla": kメn + 1). (c) L = {anglak : n = l or l k} . (d) L = {anb : n2 1} L = {w : na (w)关nb (w)). "(f) L = {ww : w E {a, b)'). (g) L = {w"www" : w E {a,b}*}
Show that the following languages are not
regular.
Parts(b) and (c)
5. Prove that the following languages are not regular: (a) L = {amb’ak: k sn +1}. (b) L = {a” b'ak : kun +1}. (c) L = {a"b'ak: n=1 or 1 # k}.
Prove that the following are not regular languages. Just B and F
please
Prove that the following are not regular languages. {0^n1^n | n Greaterthanorequalto 1}. This language, consisting of a string of 0's followed by an equal-length string of l's, is the language L_01 we considered informally at the beginning of the section. Here, you should apply the pumping lemma in the proof. The set of strings of balanced parentheses. These are the strings of characters "(" and ")"...
Which of the following languages are regular. Prove (by providing a regular expression) or disprove. a. L1 = {ai bj ck dl | (i + j)mod 2 = (k + l)mod 2 , i, j, k, l ≥ 0} b. L2 = {ai bj ck dl | (i + j) = (k + l), i, j, k, l ≥ 0}
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e {a,b}*} {w w E {a, b}* and no two b's in w have odd number of a's in between}. (b) L2 (c) L3 a" (d) L4 vw n = 3k, for k > 0}. a, b}*}
disprove that the given lan 4. [20 Points For each of the following languages, prove or guage is regular (a) L1www e...
3" (25%) Give regular expressions for the following languages on {a, b). (a) L,-(a"b": n 4, m 3) (b) The complement of Li. (c) L- (w: w mod 3 03. Note: lw: the length of w (d) L3 w: |w mod 30 naww) appear)
3" (25%) Give regular expressions for the following languages on {a, b). (a) L,-(a"b": n 4, m 3) (b) The complement of Li. (c) L- (w: w mod 3 03. Note: lw: the length of w...
Prove that the following languages are not regular. You may use
the pumping lemma and the closure of the class of regular languages
under union, intersection, and compliment.
a){}
b){}
c) {
is not a palindrome}
*d)}
0"1"0" m,n>0
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
Consider the following languages over the binary alphabet {a, b}: L:={a^nb^m:n≥m} Answer if it is regular or not, and prove it, and explain.
1. (Non-regular languages) Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, complement, and reverse (b) L2 = { w | w ∈ {0, 1}* is not a palindrome }. A palindrome is a string that reads the same forward and backward