# Week 4

I presented extra
materials (derivative of regular expressions, following a simplified version of
Brzozowski's paper; ask me
if you want a copy of this paper)
with the notion of abstract states and proofs that some languages are not regular

### Reading

Chapters 3.2, 3.3, 3.4, 4.1, 4.2

### Slides for the course

See here and an updated version
here

### Recommended exercises

Exercises 3.2.4 and 3.2.5 with the method of abstract states (compute directly a DFA)

Exercises 3.4.1, 3.4.2, 3.4.3

Exercises 4.1.1 c, e with the method of abstract states

Exercises 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.15, 4.2.17

Apply the method of the slides to test if abab is in the language
defined by a(ba)*? (ab)*? a(ba)*b?

Compute the derivatives 0\E, 1\Ewhere E = F01F and F = (0+1)* and
0\E, 1\E, 00\E, 01\E, 10\E, 11\E where E = (01+10)*, E = (101)*

Prove that the derivative a\E* is equal to (a\E)E* and that a\(EF)
is (a\E)F is epsilon is not in E and (a\E)F + a\F if epsilon is in E