Prove that each of the following languages is context-free by constructing a pushdown au- tomaton (PDA) that recognizes that language. The notation num (c) means the number of times character e appears in string uw; the notation wk means the reverse of string w. L = {wi#w2 | w1, w2 E {a,b}* and 2 · numw1 (a) = num(a) and numwiw2(a) is odd}

Q: = A language over alphabet = {0,1,2,3,4,5,6,7) in which reverse of each string (for instance,…

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Q: For languages A and B, let the shuffle of A and B be the language {w| w = a1b1 · · · akbk, where a1…

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Q: Given: Language L2 = {w ϵ {a,b}* | w contains substring aab} Construct the DFA representing the…

A: Solution:

Q: 4. Consider the following languages. • ANFAFIN = {(N) |N is an NFA and L(N) is finite} • EREX = {(R)…

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Q: Consider the following languages. Which of them is/are irregular? I) L = {a"b" | m = n} II) L = {All…

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Q: Construct a PDA that matches all strings in the language over {x,y} such that each string has at…

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Q: L = { w ? { a, b, c, d }*| na(w), nb(w), nc(w), nd(w) ≥ 0, na(w)+nc(w)+nd(w) < nb(w) } Is L a…

A: The Pumping Lemma for Context-free Languages is a belonging that context-free languages have to…

Q: Show that the following languages are not context-free: A. The language of palindromes over {0, 1}…

A: Answer:-

Q: Build a DFA for the following language: L = { w | w is a string over a , and b starts ( aa or bb )…

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Q: Design a PDA for L = {a' bi ck /j> = i + k and ijk > 0}. Process the string aaabbbbbcc using…

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Q: Please provide the CFG (Context-Free Grammer) for all string of this language: L = {0p 1q 2r , where…

A: L = {0p 1q 2r , where p = q + r} 0p 1q 2r  : p 0's followed by q 1's followed by r 2'sp=q+r :…

Q: Let’s define languages: L1    = {wan | w is an arbitrary string containing a’s and b’s, of length…

A: L1= wa^n/ w is an arbitrary string containing a's and b's, of length n L2= {w/01^*0(11+00)^*}

Q: Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s…

A: Introduction A formal grammar called context-free grammar is used to produce every conceivable…

Q: Let Cbe the language over {a, b,c, d, e, f} accepting all strings so that: 1.There are precisely…

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Q: B generates the regular language, L= {ab" | a 2 1 and m 2 2}. Implement the above FSM as a C++…

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Q: a PDA for the following language=

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Q: The finite state machine (FSM): a b. a A B C generates the regular language, L = {a"b™ | a 2 1 and m…

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Q: Question 2 : Identify a few valid strings of the following language over {0, 1, 2}: B = {w | w is of…

A:

Q: Let Σ = {0, 1,#}. Show that the following language over Σ is not context-free: {x#y#z: x,y,z =…

A:

Q: Let E = {a, b, #} and L = {w |w can be written as t#s#t with s, t e {a, b}*}. Show that L is not…

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Q: I need help to construct a dpda for the language {w in {a,b}^*| w has an unequal amount of a and b}

A: In automata theory, DPDA is Deterministic pushdown automata is a variation of pushdown automata. The…

Q: Suppose that L, is a regular language and L, is a context-free language. Which one of the following…

A: Explanation:L1 is  regular and L2 is  context-free language.Every regular language is context-free…

Q: Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s…

A: CFG is a formal grammar which is used to generate the all possible strings in given formal…

Q: Prove that the following language is not context-free: L = {w#t|w_is a substring of t, where w,t E…

A: We can prove a language is not context free, using pumping lemma for context free language:Pumping…

Q: 4. Consider the following languages. ANFAFIN = {{N) | N is an NFA and L(N) is finite} EREX = {(R) |…

A: Below is the answer to above question. I hope this will be helpful for you

Q: Write a regular expression for each of the following languages over {a,b}: • String of a's and b's…

A: Question: String of a's and b's that begin with a and end with b. Answer: ^a(a+b)*b$ Explanation: ^…

Q: Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a's…

A: By establishing a context-free grammar (CFG), it is possible to demonstrate the context-freeness of…

Q: In certain programming languages, comments appear between delimiters such as /# and #/.  Let C be…

A: Let M be the DFA that recognizes the language C.The state diagram of M is as follows.

Q: Give regular expressions that describe the following languages containing the set of all strings…

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Q: M bê thế lãnguage over {a, f} accepting all štřings so that: 1. There are precisely two e's in the…

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Q: A palindrome is a string that reads the same backward as forward, i.e., w = wR. A palindromic…

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Q: 2. Prove that the following language is not context free using the pumping lemma for context free…

A: Solution for following question -   Pumping Lemma for CFL states that for any Context Free Language…

Q: Write down Regular Expressions for the following languages. A. Strings of alphabet {a, b, c} which…

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Q: nguage L =

A:

Q: Let L be the language defined by the following regular expression 0(0 | 1)∗1(0 | 1)∗ Write 3…

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Q: Construct an NFA that recognizes L

A: Given :-Let L = { w ∈ { a, b, c }* | w contain exactly one b or start with ac }

Q: 0 or more

A: DFA  in which each input symbol determine the state

Q: Use the Pumping Lemma to show the following language L is NOT regular. L= {w E (a, b, c}*; where w…

A: use pumping lemma to show that language L is not regular. L= {w={a,b,c}*}

Q: Let Σ be a non-empty alphabet and LCE* be a context-free language. Which of the following languages…

A: reverse_1(L): Given a language L ⊆ Σ*, reverse_1(L) = {xy : ∃x, y ∈ Σ*, x ∈ L and yR ∈…

Q: Given the parent language L={w∈{a,b,c}}*, what is the language the following regular expression…

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Q: For each of the following languages L, give a regular expression that represents L and draw or…

A: a) below is the DSA

Q: Construct regular expressions over Σ = {0,1} representing the following languages:

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Q: Let Σ = {a, b}. For each k ≥ 1, let Ck be the language consisting of all strings that contain an a…

A: NFA stands for Non-deterministic Finite Automata. It contains many paths for particular input symbol…