The document outlines concepts related to finite state automata (FSA), detailing the differences between non-deterministic finite automata (NFA) and deterministic finite automata (DFA). It explains their definitions, operational mechanisms, and includes examples along with the transition states and functions for both types of automata. The document also discusses the minimization process for DFA and provides illustrative states and transitions.

1. Akhil Kaushik
Asstt. Prof., CE Deptt.,
TIT Bhiwani
NFA & DFA

2. Regular Expression
• letter = [a –z] or [A –Z]
• digit = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 or [0-9]
• sign = [ + | -]
• Decimal = (sign)?(digit)+
• Identifier = (letter)(letter | digit)*
• Float = (sign)? (digit) +.+ (digit)*

3. Finite State Automata (FSA)

4. Finite State Automata (FSA)
• There are two main kinds of FSA:-
– Non-Deterministic Finite Automata (NFA): at a
particular state, a unique path may not be determined for
each input alphabet.
– Deterministic Finite Automata (DFA): at a particular
state, a unique path determined for each input alphabet.

5. Finite State Automata (FSA)
• For every non-deterministic automata, there is an
equivalent deterministic automata.
• The below NFA is equivalent to the regular
expression/ab*ca?/.

6. NFA
• In a NFA, for each state there can be zero, one,
two, or more transitions corresponding to a
particular symbol.
• For a particular input symbol, the machine can move
to any combination of the states in the machine.
Hence, it is called NFA.
• Only NFA state automaton can have an ε transition.
• The procedure is like: RE → NFA → DFA → Tables

7. NFA
An NFA can be represented by a 5-tuple (Q, Σ, δ, q0,
F) where:−
• Q is a finite set of states.
• Σ is a finite set of symbols called the alphabets.
• δ is the transition function where δ: Q × Σ → 2Q
• q0 is the initial state & F is the final state
(Here the power set of Q (2Q) has been taken because in
case of NFA, from a state, transition can occur to any
combination of Q states)

8. NFA – State Digrams
• Represented by digraphs called state diagram:
used to graphically represent finite state machines
to give an abstract description of the behavior of a
system.

9. NFA Examples

10. NFA Examples
00 (0 + 1)*

11. DFA
• In DFA, for each input symbol, one can determine
the state to which the machine will move. Hence, it
is called Deterministic Automaton.
• As it has a finite number of states, the machine is
called Deterministic Finite Machine.
• Q is a finite set of states.
• Σ is a finite set of symbols called the alphabet.
• δ is the transition function where δ: Q × Σ → Q

12. NFA vs DFA
• In NFA each pair of state
and input symbol can
have many possible next
states.
• NFA can use empty string
transition.
• NFA is easier to construct.
• NFA requires less space.
• In DFA the next possible
state is distinctly set.
• DFA cannot use empty
string transition.
• It is more difficult to
construct DFA.
• DFA requires more space.

13. NFA to DFA

14. NFA to DFA

15. NFA to DFA

16. NFA to DFA

17. NFA to DFA

18. NFA to DFA

19. NFA to DFA

20. Transition Table of DFA

21. DFA Minimization
• Make a partition of final & non-final states:
• T = { {E}, {A, B, C, D} }
• T = { {E}, {A, B, C}, {D} }
• T = { {E}, {A, C}, {B}, {D} } or
• T = { {E}, {A1}, {B}, {D} }

22. Akhil Kaushik
akhilkaushik05@gmail.com
9416910303
CONTACT ME AT:
Akhil Kaushik
akhilkaushik05@gmail.com
9416910303
THANK YOU !!!