Problem 32. Let Z = {., 0, 1, ., 9} be the alphabet consisting of a. decimal point and the base-ten digits. Call a string : E 2* left-valid if it has...

Problem 32. Let Σ = {., 0, 1, ..., 9} be the alphabet consisting of a decimal point and the base-ten digits. Call a string x ∈ Σ∗ left-valid if it has the following properties.

• (i)x!=λ

• (ii) x does not contain a decimal point 

• (iii) If x != 0, then x does not start with 0. 

Call a string z ∈ Σ∗ valid if it is either left-valid or of the form 

z = x.y 

where x is left-valid and y ∈ Σ+ does not contain a decimal point. Let 

V = {z ∈ Σ*| z is valid} 

Design an NFA N such that L(N ) = V . Explain clearly why your design works.