Question 1. Basis case: Let be a recursively defined language over the alphabet E = {0,1} as follows. E E L, where ɛ denotes the empty string. Recursive step: if s € L then: Os0 E L f(n) = 1s1 E L a) Show the steps to construct the string 010010 starting from the base case and repeatedly applying the recursive step. b) List all non-empty strings of length four or less symbols (hint: there are six strings).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let be a recursively defined language over the alphabet Σ = {0,1} as follows. Basis case: ε ∈ L, where ε denotes the empty string. Recursive step: if s ∈ L

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Let be a recursively defined language over the alphabet E = {0,1} as follows.
Question 1.
Basis case:
E EL , where ɛ denotes the empty string.
Recursive step:
if s E L then:
JOs0
f (n) =
| 1s1 eL
E L
E L
a) Show the steps to construct the string 010010 starting from the base case and repeatedly
applying the recursive step.
b) List all non-empty strings of length four or less symbols (hint: there are six strings).
c) Use structural induction to show that the length of every string in L is even. That is, let
x be a string and let P(x) denote that la| is even. Show that Vx E L, P(x)
Transcribed Image Text:Let be a recursively defined language over the alphabet E = {0,1} as follows. Question 1. Basis case: E EL , where ɛ denotes the empty string. Recursive step: if s E L then: JOs0 f (n) = | 1s1 eL E L E L a) Show the steps to construct the string 010010 starting from the base case and repeatedly applying the recursive step. b) List all non-empty strings of length four or less symbols (hint: there are six strings). c) Use structural induction to show that the length of every string in L is even. That is, let x be a string and let P(x) denote that la| is even. Show that Vx E L, P(x)
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