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: Develop a Turing machine for the language L={w∈{0,1}∗ ||w|isoddandwcontainsatleastone1}. This…

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Q: Consider a set of symbols = {abc}. (1) Find all strings in E* shorter than 3. (2) Let L = {1, b,…

A: set of symbols = {a,b,c}

Q: P is a predicate, f, g are functions, a is a constant, and x, y, we have ➡), f(y, x), × ), and f(a,…

A: Given that P is a predicate, f, g are functions, a is a constant, and x, y, u, v, w are variables,…

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: 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: Let Σ = {0, 1}. Define the language L7 = { ⟨A⟩ | A is a DFA, L(A) contains at least one string of…

A: In conclusion, the language 𝐿7L7​ is decidable. We've presented an algorithm that, given a DFA 𝐴A,…

Q: Prove that there is no language L such that L* = a*b* (use proof by contradiction).

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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: B = { x = {a,b,c}* | x is a palindrom.}

A: Proof: Suppose for the sake of contradiction that the language is regular and let M be its…

Q: Here is a description of a Turing machine. The input alphabet is (a, b). The state set is: {90, 9a,…

A: A Turing machine is a numerical model of calculation portraying a theoretical machine that controls…

Q: ii. Consider a language L over the alphabet Σ = {0, 1} with the following properties: L#0 • LE* • L…

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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: (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: 2. Give a CFG that generates the language L = {b'db° |i > 0} U{dd}. Also, demonstrate that your CFG…

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

A: Here is your solution :

Q: consistent with, this model? A. A message can be conceptualized as an event drawn from a sample…

A: SUMMARY   The Shannon-Weaver model is one of the earliest and most influential communication models.…

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: the first b. 3.The last symbol of the string is d. 4.Each a is immediately fo

A: Let L be the language over {a, b,c,d} accepting all strings so that: 1.All c’s occur before 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: Give a decision procedure (algorithm) to answer the question: Given a FA M accepting a language L…

A: Given :- Give a decision procedure (algorithm) to answer the question: Given a FA M accepting a…

Q: Random Trivia Give a brief, concise answer for each of the following questions. If it asks for a…

A: a). For what languages (L) is L* finite?Theorem: L* is finite if and only if L = {ε}.Proof:1.…

Q: Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s…

A: CFG is a formal grammar which is used to generate the all possible strings in given formal…

Q: 2.6 Give context-free grammars generating the following languages. gs over the alphabet (a,b) with…

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

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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: Formalize the following sentence in english: 3X. elephant(X)|

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Q: abb and bab. Note that the substrings ca

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Q: The correct statements are: To encode the union operation into a language recognition problem, we…

A: The heart of theoretical computer science is the interaction of formal languages, decision problems,…