Given a regular language A, define L2 = { xz | there exists y Σ*, xyz...

Given a regular language A, define L2 = { xz | there exists y Σ*, xyz A, |x|=|z|, |y| = 2 }. Decide with a formal proof if L2 is (a) regular; or (b) not regular but context-free; or (c) not context-free.

Expert Solution

venereology answered 2 years ago

Determine if the language ?={?^?∶?=?^3????????≥0}over Σ={?}is regular.

Q5. [10] The left quotient of a regular language L1 with respect to L2 is defined...

Q5. [10] The left quotient of a regular language L1 with respect to L2 is defined as: L2/L1 = { y | x L2 , xy L1 } Show that the family of regular languages is closed under the left quotient with a regular language. Hint: Do NOT construct a DFA that accepts L2/L1 but use the definition of L2/L1 and the closure properties of regular language.

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y...

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y = 10 × x | x and y are binary integers with no leading 0s, and y is two times x}. (The alphabet for this languages is {0, 1, ×, =}.) For example, 1010 = 10 × 101 is in L2, but 1010 = 10 × 1 is not. (b)Let Σ2 = {[ 0 0 ] , [ 0 1 ] , [ 1...

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L...

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L = { aib2i : i > 0} 2) Prove the language M is not regular, over the alphabet Σ = {a, b}. M = { wwR : w is an element of Σ* i.e. w is any string, and wR means the string w written in reverse}. In other words, language M is even-length palindromes.

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The vector field given by E (x,y,z) = (yz – 2x) x + xz y + xy z may represent an electrostatic field? Why? If so, finding the potential F a from which E may be obtained.

Define a Turing machine TM3 that decides language L3 = { w | w ∈ Σ*,...

Define a Turing machine TM3 that decides language L3 = { w | w ∈ Σ*, #a(w) = #b(w) } over the alphabet Σ = {a, b}. IMPLEMENT USING JFLAP NO PAPER SOLUTION

Let L ⊆ Σ ∗ and define S(L), the suffix-language of L, as S(L) = {w...

Let L ⊆ Σ ∗ and define S(L), the suffix-language of L, as S(L) = {w ∈ Σ ∗ | x = yw for some x ∈ L, y ∈ Σ ∗ } Show that if L is regular, then S(L) is also regular.

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The electrical voltage in a certain region of space is given by the function V(x,y,z)=80+xz−sin⁡(yz). If the directional derivative of V at (1,1,π) in the direction 〈a,−1,π〉 is π, what is the value of a? Group of answer choices π22 −π22 π2 −π2 None of the above.

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and...

Consider the scalar functions f(x,y,z)g(x,y,z)=x^2+y^2+z^2, g(x,y,z)=xy+xz+yz, and=h(x,y,z)=√xyz Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are conservative?

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