Given a CFG G and a variable A, consider the problem of testing whether A is usable. We say A is usable if it appears in some derivation of some string w ∈ G. Formulate this problem as a language and show that it is decidable.

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 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: Using Pumping Lemma, Prove whether the given language is Regular or not. {w|w € Even Palindrome}

A: Given language regular or not defined by pumping lemma

Q: L+Ø, and L2022 L2023 and Lº + L - your answer. hat for every non-empty language L over an alphabet…

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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: 1. Is the following language A regular or non-regular? A = {1" 0m 1" | 0 ≤ m, n ≤ 3 and m=n+2} 2. If…

A: The above language A has following conditions. 0≤m,n≤3   and   m=n+2 So one possibility is , n=0 and…

Q: Each case below defines a language over {a, b}. In each case, decide whether the language can be…

A: The answer to the Following Question:-

Q: Let Γ be a set of sentences of L1 (the language of propositional logic) and let φ be a sentence of…

A: Let Γ be a set of sentences of L1 and φ a sentence of L1. The argument with all sentences in Γ as…

Q: Prove that the language L over {a,b,c}",given by L= {wcv: |w\a = [vl6} is recursive. You must…

A: The language Lover (a,b,c} *, given by L = {wev: [wla = [vlo} is recursive. A Turing machine that…

Q: Discrete mathematics applied to computer science: homework question. Let f : A → A be a function in…

A: Here is your solution :

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

A: Introduction:

Q: Show that the language L {w e {a,b}*: n(w) n(w) + 2} is not linear. %3D

A: Answer is given below:-

Q: Build a PM that accepts the language of all words that have an a as the middle letter: (These words…

A: 1)The Language that accepts all the words that have an a as the middle letter is: waw' where w and…

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: Give a regular expression for the Language over the alphabet Σ = {a, b} containing the count of b’s…

A: As we need even( multiple of 2 ) number of b's always. so. every string will look like this   ___( b…

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: Draw and formalize a DFA for the language over Σ = {a,b,c} with strings containing an odd number of…

A:

Q: ose that L is a language on a

A: Say a group of languages is closed under an operation if the outcome of applying the operation to…

Q: Please Prove whether it is True or False. There are finitely many finite languages.

A: A regular language is composed of finite number of equivalence classes in which the string can be…

Q: Q.4: let E= {a, b} and the language L = {b a"b a" |nE{1,2,3,... }}. Check whether the language is…

A: The Answer is in Below Steps

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: Give a decision procedure for each of the following problems; argue that your procedure is correct:…

A: Below i have analysed both the question and provided answer with reason:

Q: Could you lend a hand with this issue? I'm struggling with it, and it would be immensely helpful if…

A: Explained in the answer only

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

A:

Q: DFA for the language over Σ = {a,b,c} with strings containing an odd number of as, of bs, and of c

A: DFA of the given language

Q: If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular

A: Explanation : Regular languages are languages that can be recognized by a finite automata. This…

Q: Show that the family of context-sensitive language is closed under reversal.

A: Consider that the Language L is a CFL. This means that there is a grammar G={N,?,P,S} that satisfies…

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: 1. Is the following language A regular or non-regular? A = {1" 0 1" |0 ≤m, n ≤ 3 and m = n + 2} 2.…

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Q: Question 2 1. Let L by a language over E. For each of the following statements about L, determine…

A: According to our guidelines we solve only first one: ================================== about…

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: Let L be a language. It is clear from the definition that LL". Under what circumstances are they…

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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

Q: D = {xcy | x, y = {a,b}* }

A: Conjecture: The language D = {xcy | x, y ∈ {a, b}*} is a regular language.

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: 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: 2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A =…

A: Since A is Turing recognized, there will be existence of enumerator E. Mi be the ith output of E, Mi…

Q: 1. Is the following language B regular or non-regular? B = {0% 0 | a,b ≥ 0 and a =b} 2. If your…

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