1. Finite Automata
Fall 2018

2. ∑ = {x,y}
L1= set of all strings of size 2 over an alphabet ∑
L2= set of all strings of size 3 over an alphabet ∑
L3= set of all strings start with y.

3. L1 =?
L2= ?
L3 = ?
S= ab

4. FA
FA With output
FA without output
Moore
Mealy
DFA
NDFA
€-NFA

5. DFA Example
DFA Definition/ Mathematical Model
Acceptance of stings
Construction of a DFA
Practice
NDFA Definition
NDFA Construction
Power of DFA and NDFA
Minimization of DFA

6. DFA Example
a,b A B a b C
a,b

7. DFA Definition/ Mathematical Model:

8. Find smallest string from the language.
Construction of a DFA
Find smallest string from the language.
Construct the DFA for the smallest string.
Upgrade the DFA by considering all other strings.
L1= set of all stings end with ‘a’
L2= {w | |W|>=2}

9. Practice
L3= set of all strings starts with a
L4=set of all strings contains a
L5=set of all strings start with ab
L6= set of all strings ends with ab
L7=set of all strings contains ab
L8=set of all strings start with ab
L9={w | |W|<=2}
L10={w | |W|=2}

10. NDFA Definition

11. NDFA Construction L1= set of all stings end with ‘a’
L2= {w | |W|>=2}

12. Practice: L3= set of all strings starts with a
L4=set of all strings contains a
L5=set of all strings start with ab
L6= set of all strings ends with ab
L7=set of all strings contains ab
L8=set of all strings start with ab
L9={w | |W|<=2}
L10={w | |W|=2}

13. Power of DFA and NDFA
DFA ≡ NFA
NFA ≡ DFA

14. NDFA to DFA Conversion

15. Practice

18. Practice