For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse wR of w as simply w written backwards: Given w = w1w2…wn with wi ∈ ∑ for 1 ≤ i ≤ n, wR = wn…w2w1. Similarly, for any language A over ∑, we define its reverse language as the language containing the reverse of all its strings: Given a language A, AR = { wR | w ∈ A}. Show that the class of regular languages is closed under reversal.

Q: Give dfa's for the languages (a)L= {ab^wb?: we {a,b}*}, WE (b)L= {ab"a™: n> 2,m23}, (c)L= {w¡abw2:…

A: Given: AS PER OUR POLICY “Since you have posted a question with multiple sub-parts, we will solve…

Q: Given: Language L = { w is in {0, 1}* | w has even number of 0’s} Sample strings L = {00,…

A: Here i am writing CFG  for this language:…

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: 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: For Σ= {a, b, c, d, e, ..., z}, consider the set L of words w such that the last symbol of w is a…

A: For Σ= {a, b, c, d, e, ..., z}, consider the set L of words w such that the last symbol of w is a…

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A:

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A:

Q: Design a deterministic finite-state automaton that accepts any strings over (1,0}, which begins, and…

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A: Given: Goal: Design minimum state DFA and report the minimum number of states.

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A: We need to find a RE for all strings which contain two consecutive 0.

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A: L1= wa^n/ w is an arbitrary string containing a's and b's, of length n L2= {w/01^*0(11+00)^*}

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A: the solution is an given below :

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A: Given a DFA to accept L, we convert it to a new NFA to accept shift(L) by the followingintuitive…

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A: Given:- h : {0, 1}* --> { a, b }*  h(e) = e h(0) = aa h(1) = b h(L) = {h(w) | w ∈ L }⊂= {a, b}*

Q: Let L be the language over the unary alphabet Σ = {1}consisting of all strings whose length is the…

A: Step1 take the string of the langauge which is greater than or equal to n Step2 : verify all…

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…

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A: Answer as given below:

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

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Q: A palindrome is a string that reads the same backward as forward, i.e., w = wR. A palindromic…

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Q: For languages A and B over E, define the language A ÷ B as follows: A÷ B = {w E E* : there exists x…

A: The solution for the above-given question is given below:

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Q: Consider the language ReachTM = { | M is a TM, w is a string, q is a state of M, and M will reach…

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Q: Let T be a TM accepting language L. Show that if there is an integer n so that no matter what the…

A: Answer: I have given answer in the handwritten format.

Q: Give a regular expression for the smallest language L over E= {0,1} such that € EL •0EL VXEL,…

A: Step 1: Σ = {0,1} ε ε L     0 ε L     1 ε L   This means Null string, 0,1 all the 3 are present in…

Q: If A is any language, let A 1/3 – 1/3 be the set of all strings in A with their middle thirds…

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Q: a) Prove that the following language is NOT a CFL using the CFL pumping lemma. L = { 0m1=0m |n >m}…

A: Solution:

Q: Q.1: In each case below, find a CFG generating the given language. a. The set of odd-length strings…

A: The Answer start from step-2.

Q: Let Σ be the alphabet {a,b}. Let L be the language describe by                     Σ∗ −…

A: Here in this question, it asks us to draw Finite automata the accepts the   Σ∗ − (ε|Σ∗b)aa(ε|bΣ∗)…

Q: Given a regular language L = { b1 b2 b3 b4 ... b2n-1 b2n } over some alphabet ∑. Give the…

A: The complete answer is given below .

Q: For cach language L over a given alphabet E, let (L, E) denote the language over E obtained from L…

A: Decidable language: A language is decidable if a Turing machine accepts and halts on every input…

Q: Consider the language L on = {0,1} with L=(w| w has an even number of 0's and ends with 1} 1. Find 3…

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: Suppose L is a language over {a,b}, and there is a fixed integer k such that for every x ∈ Σ*, xz ∈…

A:

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A: Let's discuss what things language makes decidable and recognisable.

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A: Given:

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A:

Q: Prove that the language L = {0^l 1^m 2^n | 0<=l<=m<=m } over the alphabet {0,1,2} is not…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: For any string w 6=/ E, the principal suffix of w is the string resulting by removing the first…

A: Deterministic limited automata (or DFA) are limited state machines that acknowledge or dismiss…

Q: Consider the following pushdown automata : M1: Q = {q0, q1, q2}, ∑ = {a, b, c}, Γ = {X}, q0 = q0, F…

A: We need to find the shortest string accepted by the automaton, M1.

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A:

Q: D. Čonstruct the CFG in CNF of the given language: 1. Language L = {w is in {a, b}* | w = a"b?n…

A: CFG is the short form of Context Free Grammar. It is used to generate all possible patterns of the…

Q: Let L be a language: L = {: M be TM which runs in polyno time}, and prove L is undecidable for the…

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Q: Show that the language, L = {0™1" | m # n}, is not regular, following the steps below. %3D In class,…

A: Given that, Two languages L1 and L2 and it contains {0, 1} Consider languages L1 and L2 as, L1= {a,…

Q: Present a DFA (deterministic finite automaton) that recognizes/accepts the language: L1 = { w ∈…

A: Construct FA for {w | w  {a, b}} and Na = 0 mod 3 means having 3 as a multiple of a. Construct FA…

Q: Consider the language L= {a, bc } over E= {a, b, c}. Find: (а) L° (b) L'

A: L0 = { a null string} L2 = {aa, abc, bca, bcbc}