Consider the language L = {a'b'c* | i # j,j # k, i # k}; it is not a context- free language. Show that it nevertheless satisfies the conditions of the context-free pumping lemma, that i s, show that there exists an m so that for all strings w in L of length at least m, we can write w = uvxyz with |vxy < m, vy > 1, such that Vi > 0 : uv'ry'z E L.

Q: Prove that the following language A is decidable (e.g., give a TM that decides A). A = {⟨M⟩ | M is…

A: We will prove that language A = {⟨M⟩ | M is an NFA and L(M) = B}, where B is a regular language, is…

Q: Let L = {w#w | w ∈ {a, b}*} be a language. Use the pumping lemma for regular languages to prove that…

A: L = {w#w| w∈ {a, b}*} string generated by this languageare aaab#aaab, babb#babb proof: If possible…

Q: language L = {a i b j c k | i 6= j, j 6= k, i 6= k}; it is not a context- free language. Show that…

A: Given : L = {a i b j c k | i == j, j== k, i == k};

Q: Closure under prefix operator. Prefix operator is defined as: prefix(w E E*) = {w1 .. wk| 0< k <…

A: Closure Under Prefix Operator. Prefix Operator Is Defined As: Prefix(W E **) = {W1 ... Wkl 03 K &lt;…

Q: Let Σ={a, b}. Let L be the language of all strings that contain two b's in their middle third. In…

A:

Q: A language L over an alphabet Σ is co-finite, if Σ∗ \L is empty or finite. Let COFNFA = {〈N 〉|N is a…

A: given A language L over an alphabet Σ is co-finite, if Σ∗ \L is empty or finite. LetCOFNFA = {〈N 〉|N…

Q: Let L be a regular language. Show that the following language L' is regular too. L' = {y : 3x € £*…

A: | x | = | y | = | z | xyz € L  L is regular then L' is regular.

Q: Consider the language of all strings which contain two consecutive 0 that ? = {11, 111, 110, 011,…

A: We need to find a RE for all strings which contain two consecutive 0.

Q: e394 Pumping Lemma for Regular Languages Here are three incorrect statements of the Pumping Lemma…

A: Below is the complete solution with explanation in detail for the given questions regarding Pumping…

Q: Give a regular expression for the smallest language L over Σ = {0, 1} such that •€¢ L 0 EL ● ● 1 EL

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider the language of all strings which contain two consecutive 0 that ? = {11, 111, 110, 011,…

A: Hellostudent  I am giving this solution as per my best of knowledge  Please  do upvote for me

Q: Given a language L over the alphabet Σ, define f(L) = {vo : v € L,o € Σ, and v=uo for some u € [*}

A: Note : A language is said to be regular iff it is accepted by a Finite Automata. Given a language L…

Q: the language F which contains all natural numbers which are not prime. The numbers in F are called…

A: According to the question, we have to  i. Prove that F is in NP by writing (in pseudo-code) the…

Q: Give a description representation of a Turing Machine Mg for language B = {w over {0, 1, #)* | w…

A: Answer: 1. Turing machine consists of a set Q of states. 2. At any stage of computation, the TM…

Q: Use the pumping lemma to prove that the language L over {a,b,c}", given by L = {wcv: |wa = |vl6} is…

A: First lets see Pumping lemma for regular languages: If a language L is regular, then there exist an…

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

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: Let L = (ab,aa, baa; and consider the strings w=ba^5baa,x=abaabaaabaa,y=a^4ba^4, z=ba^5ba^4b. Which…

A: First I consider  w = ba^5baa  means w = baaaaabaa  As I break down the above string " baa aa ab aa"…

Q: If A is any language, let A 1/3 – 1/3 be the set of all strings in A with their middle thirds…

A: the answer is given below:-

Q: Let L be any regular language over {a, b, c). Show how the Pumping Lemma can be used to demonstrate…

A:

Q: Let Z = { 0 0 ! , 0 1 ! , 1 0 ! , 1 1 ! }. Decide whether each of the following languages over Σ is…

A: Proof of Contradiction is a form of proof that establishes the truth or validity of a proposition,…

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: Give a DFA M that accepts the language L2 = {w | w ∈ {a, b} ∗ and w 6∈ {b ia j |i, j > 0 }}..

A:

Q: Use the pumping lemma to prove that the following language is not context-free. Show all cases on…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: Let B be the language defined as follows: B = {www we {a, b}*} Suppose B is a regular language. Let…

A: FALSE STATEMENTS ARE GIVEN BELOW

Q: A language L is called slithy if it contains at least two strings and has the following property:…

A: The answer to the question is given below:

Q: Let E = {a, b, c}. Use the Pumping Lemma to show that the language L defined below is not regular:…

A: The pumping lemma to show that the language L is not regular

Q: Let L = {(D) | D is a DFA over the binary alphabet, which accepts at least one string that has 100…

A:

Q: What does the Pumping lemma for regular languages say?

A: Explanation:   Pumping lemma is used to prove a given language is non-regular. It doesn't prove that…

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r€ RB, let L(r) be the…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: Consider the language L = { 3x such that x = L(M₁) L(M₂)}. Show that L is not decidable.

A: To prove that the language L is not decidable, we need to show that there is no Turing machine that…

Q: Let Σ = {a, b, c} and f : Σ∗ → Σ ∗ the function that for input w yields the string obtained by…

A: According to the question, we have to prove that if L is a regular language, then so is {f(w) | w ∈…

Q: Assume that we want to use the Pumping Lemma to prove the language L is not a regular language. Here…

A: The objective of the question is to use the Pumping Lemma to prove that a given language L is not a…