Consider the following languages over the alphabet Σ = {a, b}: 1. L1 = {xwx : x, w ∈ Σ∗} 2. L2 = {xwx : x, w ∈ Σ∗, |w| = 1} 3. L3 = {xwx : x, w ∈ Σ∗, |x| = 1} For each language, decide whether it is regular or not regular. Prove each of your claims. If you construct a FA or a regular expression, you do not need to prove the correctness of your construction.

Q: 8. Let Σ; be alphabets for i = 1, 2, 3, and L; C Σ;, i = 1, 2, 3 be three languages. Prove that (a)…

A:

Q: Use the Pumping Lemma for CFLS to prove that each of the following lan- guages is not context-free.…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  String s…

Q: (3) {w € [0, 1]*: w has 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001, 0010,…

A: We are given a language {w ∈ {0,1}*: w has 001 as a substring}.And we are asked to test given…

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: Let L be the language L={ 0K12m | k+l<m} over the alphabet E={0,1,2}. Prove that L is not regular…

A: Proved that given language is not regular

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: For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse…

A: Given: w = w1w2…wn with wi ∈ ∑ for 1 ≤ i ≤ n, Reverse of w is denoted by wR . wR = wn…w2w1 Let A be…

Q: Question 3. Consider the language L = {w€ {0, 1}* | the strings 01 and 10 occur the same number of…

A: Given language is, L={w ∈{0,1}* | the strings 01 and 10 occur same number of times in w} Pumping…

Q: Let A1, A2, and A3 be languages defined over an alphabet Σ. Define Majority(A1, A2, A3) = {w | w is…

A: Let A1, A2, and A3 be languages defined over an alphabet Σ.Define Majority(A1, A2, A3) = {w | w is…

Q: Prove or disprove whether the language P = {w^i | i ∈ N, w ∈ {a, b} ∗} is regular .

A: DFA

Q: Create a complex CFG that produces L. s L = {0¹ 14⁰ | i≥ 0}. Prove the ambiguity and construct a PDA…

A: Below i have provided handwritten solution of the problem. See below steps.

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: Please provide handwritten answer only Let L be the language L={ On1m | n#(m-7) } over the alphabet…

A: Introduction:

Q: Given the definition of language L below, do each of the following: (1) state whether or not L ∈ REG…

A: Let's examine the features and structure of the language L to determine whether it is a regular…

Q: For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse…

A: GIVEN: Let w be a string such that w=w1w2….wn. The reverse of w is wR. Where wR = wn……w3w2w1.   TO…

Q: Given the language L(r) defined over the alphabet Σ = {a,b}, where r = (0011)*, define a PDA that…

A: Given :  Given the language L(r) defined over the alphabet Σ = {a,b}, where r = (0011)*

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: Suppose I is a non empty regular language, over Σ, such that every w E L satisfies [w] = k, for some…

A: Given that, non-empty regular language L over the alphabet Σ such that every string w in L satisfies…

Q: For each of the following languages L, state whether L is regular, context-free but not regular, or…

A: When PDA(push-down automata )is possible then it is context free ,if PDA is not possible then it is…

Q: Suppose the language, L, over an alphabet Σ0 is regular, and f : Σ0 → Σ1, is a function from the…

A: The complete solution is below:

Q: Computer Science 5. Consider a language L over the binary alphabet. For any two binary strings x,…

A: Proof:- Let L be a language that means nothing more than Σ.  S⊆ Σ an infinite set there in any…

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: Create a membership testing algorithm. f = 1, 2,..... n, a group G operating on it, a permutation of…

A: function is_in_group(p : permutation; i : 1..k+l ) : boolean; (* return true if the permutation p is…

Q: Consider the language L = {a^b³ct | r, s, t € N and t ≤r× s} Problem 3 Use the pumping lemma to…

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

Q: For each of the following languages L, state whether L is regular, context-free but not regular, or…

A: Answer: Given some expression to prove which one regular and which one is context free but regular…

Q: i)Suppose h -1 is the inverse homomorphism from the alphabet E = {a, b}, and A = {0, 1}. Let L = (00…

A: Please upvote Please. I am providing you the correct answer please upvote please. I need it badly.…

Q: Question 2. Consider the language L = {a" | n is a prime number}. Is this language regular or…

A: To check L = { an | n is not a prime number } is regular or non-regular.

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: I need help with question 2 please.

A: Proof:1. Assume that C = {w | 1's equal to number of 2's, 3's, 4's}2. Assume that w is a word in C3.…

Q: 5. Consider a language L over the binary alphabet. For any two binary strings x, y we say x, y are…

A: Explanation for Question  In this Question we have to prove that a certain relation, idL, defined on…

Q: Solve whether that the following languages on Σ = {a, b, c} are not context-free. (a) L = {anb j : n…

A: a)

Q: No need to apply pumping lemma in this Queshon Demonstrate or that ; prove L= {w e {a,b,c,d}*…

A:

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: Let E be an alphabet and A C E*. (a) If c E £ and AC E*, we define APPEND.(A) as {wc ɛ E* | w E A}.…

A: Below is the answer to above question. I hope this will meet your requirement

Q: 8. Let Σ; be alphabets for i = 1, 2, 3, and L, Σ, i = 1, 2, 3 be three languages. Prove that (a) L₁…

A:

Q: Pick and answer one of the two questions below: a. Prove that the language L = {w1*lw e {0, 1}+ and…

A: It is defined as a context-free language, there is a pumping length p such that any string w ∈ L of…

Q: Consider the following languages over the alphabet (a, b): 1. The language of all non-empty words…

A: See below steps for deterministic finite automata.

Q: Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈…

A: The Answer is in step2

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…

Structured English

Structured English uses a simple English language to make structured programming easier for non-professionals. The program is divided into various parts that are known as logical statements. These statements are written in a simple English language.