CS 390 Solutions to Homework 4

Textbook pp. 112 - 115:

3.1 (c) 110

3.2 (d) 010

3.3 (b) Below r₁ = r and r₂ = s.

=
For (r₁ + r₂)^* represent all strings consisting of concatenation of any number of strings of r₁ and r₂ in any order. Hence r₁(r₁ + r₂)^* represent all strings of r₁(r₁ + r₂)^*(r₁(r₁ + r₂)^*)^*.
Conversely r₁(r₁ + r₂)^*(r₁(r₁ + r₂)^*)^* represent all strings of r₁(r₁ + r₂)^*, because you don't have to use anything from (r₁(r₁ + r₂)^*)^*.

3.8 (b)

3.9 (d)
(f)

3.10 (a) Strings of 0's and 1's containing an odd number of 1's.

3.17 (d) (I) \Lambda
(II) a(a+bb*a)*
(III) a(a+bb*a)*b(b)* = a(a+b)*b
(IV) b(a + b)*