(a) Consider the alphabet Σ = {a, b, c}. Give a recursive definition for the set...

Question

Question

(a) Consider the alphabet Σ = {a, b, c}. Give a recursive definition for the set of strings over Σ that contain exactly one c.

(b) Give a recursive definition for the set S = {x | x ∈ Z≥0 and b x 4 c is even}

engineering Computer-Science

Answer 1

Answer #1

(a) Language is S

Recursive definition

c belongs to S
aS, bS, Sa and Sb belongs to S

Explanation

At the end c must come at any place

(b) Language is S

0, 1, 2, 3 belongs to S
4 + S belongs to S

Explanation

0 1 2 3 -> floor(x / 4) = 0 even <-- Base case

4 5 6 7 -> floor(x / 4) = 1 odd

8 9 10 11 -> floor(x / 4) = 2 even <-- Add 4 each time

and so on

Answer 2

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