Compiler Construction: Conversion of Non Deterministic Finite Automata to Deterministic Finite Automata : from NFA to DFA

1. 1
Ms. Bushra Abdullah Al-Anesi
Compiler Construction
Alfred V. Aho, , "Compilers", Addison Wesley Publishing Company; 2 edition (2007).

2. Lexical Analysis
Chapter 3
1/23/2019
2

3. CPCS 302 ch3
Conversion of NFA to DFA
❑ Subset construction algorithm
▪ Input: An NFA N
▪ Output: A DFA D accepting the same language as N
▪ Algorithm: construct a transition table Dtran corresponding to D
3

4. CPCS 302 ch3
Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
1. Compute ε - closure (0), which are all states reachable from 0 on
ε -transitions (including 0 itself)
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5. CPCS 302 ch3
Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
1. Compute ε - closure (0), which are all states reachable from 0 on
ε -transitions (including 0 itself)
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6. CPCS 302 ch3
Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
1. Compute ε - closure (0), which are all states reachable from 0 on
ε -transitions (including 0 itself)
o ε - closure(0) = { 0, 1, 2, 4, 7}
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7. CPCS 302 ch3
Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
1. Compute ε - closure (0), which are all states reachable from 0 on
ε -transitions (including 0 itself)
o ε - closure(0) = { 0, 1, 2, 4, 7}
• Add to Dtrans table
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NFA State a b
{0,1, 2, 4, 7}

8. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}

9. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}

10. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}
{3, 8}

11. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}
ε -closure ({3, 8}) ={3, 8}

12. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}
ε -closure ({3, 8}) ={3, 8}

13. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
NFA State a b
{0,1, 2, 4, 7}
ε -closure ({3, 8}) ={3, 8} {3, 6, 1, 2, 4, 7, 8}

14. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
o Add set to Dtrans table:
• for symbol a
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7}
ε -closure ({3, 8}) ={3, 8} {3, 6, 1, 2, 4, 7, 8}

15. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
2. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, a)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, a) =
o Add set to Dtrans table:
• for symbol a
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7}
ε -closure ({3, 8}) ={3, 8} {3, 6, 1, 2, 4, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

16. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

17. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

18. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
{5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

19. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
ε -closure ({5}) ={5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

20. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
ε -closure ({5}) ={5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

21. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
ε -closure ({5}) ={5} {5, 6, 1, 2, 4, 7}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}

22. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
3. Compute for each input symbol x move({0, 1, 2, 4, 7}, x), which is
the states reachable on x-transitions (possibly preceded with ε -transitions)
followed by ε – closures (move ({0, 1, 2, 4, 7}, b)) avoiding repetitions
o move ({0, 1, 2, 4, 7}, b) =
o Add set to Dtrans table
• for symbol
• As new state if not already there
ε -closure ({5}) ={5} {5, 6, 1, 2, 4, 7}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

23. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

24. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

25. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

26. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

27. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

28. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8} { 3, 6, 1, 2, 4, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

29. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
4. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, a))
o move ({1, 2, 3, 4, 6, 7, 8}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8} { 3, 6, 1, 2, 4, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

30. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

31. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

32. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{5, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

33. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 9}) ={5, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

34. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 9}) ={5, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

35. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 9}) ={5, 9} {5, 6, 7, 1, 2, 4, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}

36. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
5. Compute ε – closures (move ({1, 2, 3, 4, 6, 7, 8}, b))
o move ({1, 2, 3, 4, 6, 7, 8}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 9}) ={5, 9} {5, 6, 7, 1, 2, 4, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8}
{ 1, 2, 4, 5, 6, 7}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}

37. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}

38. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}

39. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}

40. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) =
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}

41. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) =
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}

42. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) = { 3, 6, 1, 2, 4, 7, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}

43. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) = { 3, 6, 1, 2, 4, 7, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

44. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
6. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, a))
o move ({ 1, 2, 4, 5, 6, 7}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) = { 3, 6, 1, 2, 4, 7, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}
{3, 8}
ε - closure for symbol
a need not be
computed ➔ all have
same set of states
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

45. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

46. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

47. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{5 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

48. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5 }) ={5 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

49. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5 }) ={5 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

50. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5 }) = { 5, 6, 7, 1, 2, 4 }{5 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}

51. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
7. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7}, b))
o move ({ 1, 2, 4, 5, 6, 7}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5 }) = { 5, 6, 7, 1, 2, 4 }{5 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9}

52. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

53. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

54. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

55. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{3, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

56. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

57. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

58. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
8. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, a))
o move ({ 1, 2, 4, 5, 6, 7, 9}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) = {3, 6, 1,2, 4, 7, 8}{3, 8 }
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

59. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

60. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

61. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{5, 10}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

62. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 10}) ={5, 10}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

63. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 10}) ={5, 10}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

64. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 10}) = { 5, 6, 7, 1, 2, 4, 10 }{5, 10}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}

65. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
9. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 9}, b))
o move ({ 1, 2, 4, 5, 6, 7, 9}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5, 10}) = { 5, 6, 7, 1, 2, 4, 10 }{5, 10}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10}

66. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

67. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

68. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

69. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

70. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) ={3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

71. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
10. Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, a))
o move ({ 1, 2, 4, 5, 6, 7, 10}, a) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({3, 8}) = {3, 6, 1, 2, 4, 7, 8 }{3, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

72. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

73. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

74. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
{5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

75. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5}) ={5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

76. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5}) ={5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

77. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5}) = { 5, 6, 7, 1, 2, 4 }{5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}

78. Conversion of NFA to DFA
❑ Compute a sequence of ε – closures and moves:
11.Compute ε – closures (move ({ 1, 2, 4, 5, 6, 7, 10}, b))
o move ({ 1, 2, 4, 5, 6, 7, 10}, b) =
o Add set to Dtrans table:
• for symbol
• As new state if not already there
ε -closure ({5}) = { 5, 6, 7, 1, 2, 4 }{5}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8}
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}

79. Conversion of NFA to DFA
❑ Construct the DFA transition graph using the Dtrans table:
❑ For each NFA state in the table, create a new DFA state symbol:
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}

80. Conversion of NFA to DFA
❑ Construct the DFA transition graph using the Dtrans table:
❑ For each NFA state in the table, create a new DFA state symbol:
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
DFA State NFA State a b
A {0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
B {1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 9} =
D
C { 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
D {1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 10} =
E
E {1, 2, 4, 5, 6, 7,
10}
{1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C

81. Conversion of NFA to DFA
❑ Construct the DFA transition graph using the Dtrans table:
❑ For each NFA state in the table, create a new DFA state symbol:
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
DFA State NFA State a b
A {0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
B {1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 9} =
D
C { 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
D {1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 10} =
E
E {1, 2, 4, 5, 6, 7,
10}
{1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
❑ Construct the
graph based on
table data:
*DFA state with NFA
final state is a DFA final
state ➔ E

82. Conversion of NFA to DFA
❑ Construct the DFA transition graph using the Dtrans table:
❑ For each NFA state in the table, create a new DFA state symbol:
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
DFA State NFA State a b
A {0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
B {1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 9} =
D
C { 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
D {1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 10} =
E
E {1, 2, 4, 5, 6, 7,
10}
{1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
E
A
a B
C
b
a
D
b
a
b
a
b
a
b
Start
❑ Construct the
graph based on
table data:
*DFA state with NFA
final state is a DFA final
state ➔ E
DFA

83. Conversion of NFA to DFA
❑ Construct the DFA transition graph using the Dtrans table:
❑ For each NFA state in the table, create a new DFA state symbol:
NFA State a b
{0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 9}
{ 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} {1, 2, 4, 5, 6, 7, 10}
{1, 2, 4, 5, 6, 7, 10} {1, 2, 3, 4, 6, 7, 8} { 1, 2, 4, 5, 6, 7}
DFA State NFA State a b
A {0,1, 2, 4, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
B {1, 2, 3, 4, 6, 7, 8} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 9} =
D
C { 1, 2, 4, 5, 6, 7} {1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
D {1, 2, 4, 5, 6, 7, 9} {1, 2, 3, 4, 6, 7, 8} =
B
{1, 2, 4, 5, 6, 7, 10} =
E
E {1, 2, 4, 5, 6, 7,
10}
{1, 2, 3, 4, 6, 7, 8} =
B
{ 1, 2, 4, 5, 6, 7} = C
E
A
a B
C
b
a
D
b
a
b
a
b
a
b
Start
❑ Construct the
graph based on
table data:
*DFA state with NFA
final state is a DFA final
state ➔ E
DFA NFA

84. CPCS 302 ch3
Conversion of NFA to DFA
❑ Subset construction algorithm
▪ Input: An NFA N
▪ Output: A DFA D accepting the same language as N
▪ Algorithm: construct a transition table Dtran corresponding to D
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