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: a. L= {x€{a, b, c }* | na(x) < n»(x) and na(x) < nc(x) }, where n(x) is the number of occurrences of…

A:

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: Provide deterministic finite automata accepting the following languages over the alphabet Σ = {a,…

A: Deterministic Finite Automata (DFAs) are formal models of computation used in theoretical computer…

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={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

A: Given: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not…

Q: For any string w=w1w2…wn, the reverse of w, written wR, is the string w in reverse order, wn…w2w1.…

A: Answer is given below-

Q: Please use the pumping lemma to prove, thank you every much. Points Consider the following language,…

A: Pumping Lemma states that if the infinite language has to be accepted by finite automata, then there…

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: Consider the following languages over Σ = {0,1} L6 is the language of the NFA given by the…

A: The NFA (Non-Deterministic Finite Automaton) that you have provided defines the language L6. We need…

Q: Problem 1 Given an alphabet Σ, a string constructed from the alphabet is a concatenation of symbols…

A: This question is from regular expression:

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: Consider the language L = AEqB = {x ∈ {a, b}∗ | na(x) = nb(x)}. a. Show that if na(x) − nb(x) =…

A: Answer: I have given answered in the handwritten format in brief explanation

Q: Give a regular expression for the language L over Σ = {0, 1} such that

A: ANSWER: Regular Expression: A regular expression is a grouping of characters that characterize an…

Q: If A is any language, let ?− 1 2 be the set of all first halves of strings in A so that ?− 1 2 = (x…

A: Any language that can be demonstrated in the form of regular expressions is said to be a language of…

Q: Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata…

A: Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata…

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: 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: Consider the language L over the alphabet (y,z) that consists of all words that contain the…

A: the solution is an given below :

Q: (4) {w € [0, 1]* : w does not have 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001,…

A: In this question we have to design a Nondeterministic Finite automata where a language consist of…

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: Example: L = {w over E = = {a, b} | |w| 2 and |w| 2 and |w| < 5 and |w| is even }. %3D

A: ∑ = {a, b}   a.   L1 = ∑0∪∑1∪∑2 This language contains string of length 0, strings of length 1 and…

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: Consider the language L = {a'b'c* | i # j,j # k, i # k}; it is not a context- free language. Show…

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

Q: True or False Statements and provide proof with your answer. a. Suppose L is the empty language,…

A: As per our company guidelines we are supposed to answer ?️only first 3️⃣ sub-parts. Kindly repost…

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: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

A: Let L be the language L={ 0n1m | n≠(m-7) } over the alphabet Σ={0,1}. Prove that L is not regular…

Q: Consider the languages L and L: L = {ww | w ∈ {a,b}∗}, all even-length strings of as and bs whose…

A: Answer as given below:

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: Consider the alphabet is Σ = {a,b,c}. For each of the following languages, specify if the language…

A: We are given three different languages and asked whether they are regular languages or not.Regular…

Q: This problem concerns languages over the alphabet Σ = {1}. For any two integers q,r ≥0, define the…

A: To show that Lr,q is regular for every q and r, we can use the following steps:Construct a regular…

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: Suppose L1, L2 are two regular languages over the alphabet Σ = {a, b}. Consider the following two…

A: Shuffle1(L1, L2) and shuffle2(L1, L2) are two new languages defined based on the shuffle operation…

Q: Q. Let A = {wtw* | w.t are strings over the alphabet {0,1,2} and |w|=|4|}. Prove that A is not a…

A:

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: Please use the pumping lemma to prove, thank you every much. Points Consider the following…

A:

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.…

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.