Let Σ = {a, b, c} and f : Σ∗ → Σ ∗ the function that for input w yields the string obtained by duplicating each a. E.g. f(baaca) = baaaacaa. Prove that if L is a regular language, then so is {f(w) | w ∈ L}. [Hint: Use induction on regular expressions.]

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: Exercise 6 (Ex. 17, Chapter 2 of (Martin; 2011]). Let L be the language AnBn = (a"b" | n 2 0). a.…

A: check the answer below :

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: Define a CFG that generates the language over the alphabet Σ = {α,β,θ} defined by the regular…

A: The given regular expression is : β(α + β)*αθα(α + β + θ)*β We need to find context-free grammar for…

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: Extra Credit: Given any language A, let A₁ = {x | for some y, |x| = |y| and xy = A}. Prove that the…

A: Closure Properties• Recall that we can carry out operations on one or more languages to obtain a new…

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: Please give me the proper answer with step by steo solution Qns: Consider the CFL: L = {w | w is a…

A: Introduction: In computer science, a pushdown automaton (PDA) is a type of automaton that reads an…

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: 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: Build a deterministic FA Ms for the following language Ls= L(Ms) = {x over {a, b}| if x contains…

A: Deterministic Finite Automata(DFA):DFA consists of Q - finite set of states∑ - input symbolq0 –…

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: 1. Given L₁ = {a, abc, a c) and L₂ = {ab, c ba) are the languages over = {a, b, c), determine L₁ L2…

A: Given :

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: 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: (1) {w € [a, b]*: w contains at least one instance of aaba, bbb or ababa} Testing strings: €, a, b,…

A: In this question we have to design a NFA design where a language us provided which should have at…

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: Given S = (a, b, c}. Prove this language is regular: L = {u €S*:u has at least 1 a, 1 b, and 1c)…

A:

Q: Derive the string a*(ab+10) from G:

A: Solution - In the given question, we have to find the Left most and Right most derivation for the…

Q: Let A be a language such that Ā Sm PCP and ETM Sm A. What can you say about A? Briefly xplain your…

A: Answer is described below

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: Let Z={a,b,c}. Show that (b) The set of all languages over Σ is uncountable

A: We need to prove the set of all languages over sigma is uncountable.

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: Let FH be the set of first halves of the strings in A. FH = {x | xy ∈ A} for some y, and |x| = |y|.…

A:

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: 1. (a) Consider the following NFA (over the alphabet (0, 1}). i) What is the shortest string…

A: i) In a given NFA the shortest string accepted by the NFA is "01" ii) The regular expression for L…

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 E = {0,1} and La be the language of all strings that represent binary numbers that are not…

A: In given question, we have two languages La and Lb. We have asked about their complements and…

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: Prove that the following language is non-regular, using the Pumping Lemma. L = {ambcr | m, n, r =…

A: The pumping lemma is a fundamental result in formal language theory that provides a way to prove…

Q: consider the language L = {a^f b^g|f<g} on albhabet E = {a,b}. Show that L is not reguar. %3D

A: The answer is

Q: construct an NFA that realizes the language L over the alphabet {a, b, c} that consists of all…

A: Here is the NFA about the string given:

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: 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: 1. Prove that in the alphabet Σ = {a,b}, the language A = {w/w has the form a"b" a" for some…

A: A language is defined as a set of strings of symbols that may be constrained by specific…

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