L = {w = {a,b}*||w| = 0 (mod 2) A the two middle letters are differnet}

Q: Construct Pushdown Automata (PDA) for the language {a2nbn‒2} for n=2,3,4,…  defined over ∑={a,b}.

A: The language given

Q: a) Define the string set S as follows: Basis step: abc ∈ S Recursive step: If x ∈ S, then axa ∈ S…

A: Define the string set S as follows:Basis step: abc ∈ SRecursive step: If x ∈ S, then axa ∈ S and bxb…

Q: Use induction to prove that the number of elements in any SList of depth p is 2P.

A: We have to prove that the number of elements in any SList of depth p is . Notice that the…

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A: Which of the following is the general expression for second-order forward finite differences?

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A: 2. Intersection of two sigma algebra is sigma algebra.

Q: Quéstion 2 Let L be the language L={ a3 mch | (3n+n)>m} over the alphabet E-{a,b,c}. Prove that L is…

A: This question is about application pumping lema

Q: Let S be the set of bit strings of length four or more. For example, 100111 € S, 00111100 e S, or…

A:

Q: B = {anbmcn | m, n ≥ 0}

A: To prove that the language B = {a^nb^mc^n | m, n > 0} is not regular. To do this, we use the…

Q: Use the pumping lemma to show that the language {www | w E e {a,b}*} is not regular.

A: Consider the provided question, We need to show that the language www|w∈a,b* is not regular by using…

Q: Let A be a set of m elements, where m is a nonnegative integer. Suppose you will prove by induction…

A: PRINCIPLE OF MATHEMATICAL INDUCTION: It is principle which is used to prove a statement or theorem.…

Q: Need help with number 5 please

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Q: Prove that the following is not an LR(0) grammar: E → E + T | T T →  T * F | F F → ( E ) | id

A: Given, E→E+T|TT→T*F|FF→E|id

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A: Introduction: Proof by contradiction is a method of mathematical proof in which a statement or…

Q: Prove or disprove that for every regular language, there exist an infinite number of unique NFAS…

A: The complete solutions are given below

Q: a) For example, B is a collection of sets with operations of intersection, union, and complement.…

A:

Q: Explain how generating functions can be used to find thenumber of ways in which postage of r cents…

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Q: Part 1: Proof that (a + b) · (à · b) = 0. (a + b). (a. b) = = = = = = (a. b)(a + b) ((ā· b). a) +…

A:

Q: 3). Let L= {0*1* | n>=0}. Using pumping lemma, what can be said about this language?

A: To apply the pumping lemma to the language , we can demonstrate that this language is not regular.…

Q: Prove that the set {a, b, c}* of all strings (of finite length) on {a, b, c} is count- able.

A:

Q: S is a set of strings over the alphabet (a, b) and is defined recursively as follows: Basis: AE…

A: According to the given data, find the correct option:

Q: On the set A={a,b,c,d} the table gives the folowing operation: (picture) Is (M,o) semigroup?

A:

Q: 3. Prove that if fog is injective, then g is injective.

A: Injective Function:          A function f : X →Y is said to be injective ( or one-to-one) if, for…

Q: Need help with number 6 please

A: Step 1Question Explanation: The question defines a set S of strings over the set {a, b} using a…

Q: (b) Let E be the universal set and let G = p(E),the power set of E.Define the following operations…

A: Given that →X+Y=X∪Y→XY=X∩Y→X¯=XC (i) Let us consider G=P(∑ )  X,Y∈G  here,  Now…

Q: Question 1. Basis case: Let be a recursively defined language over the alphabet E = {0,1} as…

A: We are given that ɛ∈L. Also, we are given that for ɛ∈L, the recursive steps: 0s0∈L1s1∈L holds. (a).…

Q: Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y…

A:

Q: Help me with my computational theory homework

A: Step 1: To show that the language C={ambncm+n∣m,n≥0}  is not regular using the Pumping Lemma, we…

Q: Construct Finite Automata equivalent to the Regular expression. L = ab + (aa + bb)(a+b)*

A:

Q: 1. Consider the following operations on Z a) m*n = m2 + n? b) m*n (m+n)/2 Prove or disprove: 1. a)…

A: Let us prove or disprove the properties 1- 4 in the next steps.

Q: Exercise 5-6 Prove that the following sentences are theorems. please help with 1,5,7,9 (1) A ⊃ (A ∨…

A: " Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Lemma 2.3.7. Let T be a collection of sets with the property that the intersec- tion of any two…

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Q: Use mathematical induction to prove that for every integer n ≥ 2, if a set S has n elements, then…

A: First, Let n=2 Consider a set S which has two elements S=a,b Subsets of S are ϕ,a,b,a,b Now, Subset…

Q: Let {An : n E N} be the indexed collection of sets defined by 1 2, 2+ 2n An Prove that: nMeN An = Ø

A:

Q: 3. Let Σ₁ be the language over the alphabet {a}, Σ₂ be the language over the alphabet (a, b) and N…

A: According to our guidelines i can solve only one question.

Q: 998! 2. for the following recursive functions, find f(1), f(2), f(3), and f(4) f(0)=2 f(k)…

A:

Q: a) Consider the x set {0.5, 1.0, 2.0, 5.0} and the corresponding y set {1.128, 1.543, 3.763,…

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Q: Let A1, A2, ... , An be any n sets, n 2 1. Show that (U-1 Ar) = U=1 Ar %3D

A:

Q: 1) What is the following recursive set S? • 3 ∈ S • x,y ∈ S → (x + y) ∈ S

A: (Solving the first question as per our guidelines) Question: What is the following recursive set S?…