Push Down Automata (PDA) | TOC (Theory of Computation) | NPDA | DPDAAshish Duggal
Push Down Automata (PDA) is part of TOC (Theory of Computation)
From this presentation you will get all the information related to PDA also it will help you to easily understand this topic. There is also one example.
This PPT is very helpful for Computer science and Computer Engineer
(B.C.A., M.C.A., B.TECH. , M.TECH.)
Push Down Automata (PDA) | TOC (Theory of Computation) | NPDA | DPDAAshish Duggal
Push Down Automata (PDA) is part of TOC (Theory of Computation)
From this presentation you will get all the information related to PDA also it will help you to easily understand this topic. There is also one example.
This PPT is very helpful for Computer science and Computer Engineer
(B.C.A., M.C.A., B.TECH. , M.TECH.)
A grammar is said to be regular, if the production is in the form -
A → αB,
A -> a,
A → ε,
for A, B ∈ N, a ∈ Σ, and ε the empty string
A regular grammar is a 4 tuple -
G = (V, Σ, P, S)
V - It is non-empty, finite set of non-terminal symbols,
Σ - finite set of terminal symbols, (Σ ∈ V),
P - a finite set of productions or rules,
S - start symbol, S ∈ (V - Σ)
This Lecture Note discusses the followings:
- What is NFA
- DFA vs NFA
- How does NFA compute
- Designing different NFA machines
- Regular operations on NFAs
- Conversion from NFA to DFA
A grammar is said to be regular, if the production is in the form -
A → αB,
A -> a,
A → ε,
for A, B ∈ N, a ∈ Σ, and ε the empty string
A regular grammar is a 4 tuple -
G = (V, Σ, P, S)
V - It is non-empty, finite set of non-terminal symbols,
Σ - finite set of terminal symbols, (Σ ∈ V),
P - a finite set of productions or rules,
S - start symbol, S ∈ (V - Σ)
This Lecture Note discusses the followings:
- What is NFA
- DFA vs NFA
- How does NFA compute
- Designing different NFA machines
- Regular operations on NFAs
- Conversion from NFA to DFA
Finite Automata: Deterministic And Non-deterministic Finite Automaton (DFA)Mohammad Ilyas Malik
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2. Non-deterministic Automaton.
• In NDFA, for a particular input symbol, the machine can move to any
combination of the states in the machine. Hence, it is called Non-
deterministic Automaton.
• Formal Definition of an NDFA
• An NDFA can be represented by a 5-tuple (Q, ∑, δ, q0, F) where −
• Q is a finite set of states.
• ∑ is a finite set of symbols called the alphabets.
• δ is the transition function where δ: Q × ∑ → 2Q
• (Here the power set of Q (2Q) has been taken because in case of NDFA,
from a state, transition can occur to any combination of Q states)
3. Deterministic Finite Automaton (DFA)
• Deterministic Finite Automaton (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
or Deterministic Finite Automaton
•Q is a finite set of states.
•∑ is a finite set of symbols called the alphabet.
•δ is the transition function where δ: Q × ∑ → Q
4. Properties
NFA
• “NFA” stands for “Nondeterministic
Finite Automata.”
• 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
DFA
• DFA” stands for “Deterministic Finite
Automata”
• 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
5. Conversion of NFA TO DFA
• Every DFA is an NFA But not vice versa
DFA δ = Q x ∑ -> Q NFA δ = Q x ∑ -> 2Q
• But there is an equivalent DFA For every NFA
NFA ˜ DFA=
6. Important point
• In DFA we combine two state into single state.
• In DFA there is only one transition to only one state
7. EXAMPLE NO1 ON CONVERSION
• L = {set of all strings over (0,1) that start with ‘0’}
∑ = {0,1)
NFA:
A B
O,1
State 0 1
->A B ɸ
B B B
11. Example 3
• L = {Set of all string over(0,1) that end with ‘01’}
• NFA
A C
O,1
State 0 1
->A {A,B} A
B ɸ C
ɸ ɸ
B
O 1
C
12. NFA converted into DFA
A
AB
State 0 1
->A AB A
AB AB AC
AB A
0
1 0
1
AB
0 1
AC
13. Example 4 NFA
• M= [ {A,B,C},(a,b), δ,A,{C}]
• NFA AND DFA is represented by 5 tuple
State a b
->A {A,B} C
B A B
ɸ {A,B}
AB
AB
a
A
b
a
a
b
bb
C
14. NFA converted into DFA
A
BC
State 0 1
->A AB C
AB AB BC
A AB
D AB
D D D
a
b a
a
AB
b b
C
D
a
a,b
b
BC
C
15. Assignment for home
• Assignment : try to find out what type of string this NFA and
Equivalent DFA accepted
16. Transition Graph
• Properties:
• Can have more than one initial state
• Empty transaction is allowed
• We allow the machine to real move than one character at a time
• If ∑ = {a,b} Draw TG for all string containing bbb or aaa
• (a+b)* (aaa+bbb) (a+b)*
• TG reduced the complexity of NFA and DFA
18. MINIMIZATION OF DFA
• Minimization of DFA is required to obtain the minimal version of any
DFA which consists of the minimum number of states possible
• DFA 5 state 4 state
00000 0000
These two are equivalent Two state ‘A’ and ‘B’ are said to be equivalent
δ(A,X) -> F δ(A,X) -> F
and and
δ (B,X) ->F δ (B,X) -> F
19. MINIMIZATION OF DFA
• If |X| = 0, then A and B are said to be 0 equivalent
• If |X| = 1, then A and B are said to be 1 equivalent
• If |X| = 2, then A and B are said to be 2 equivalent
.
.
.
if|X| = n then A and B are said to be n equivalent
We need these properties to combined two state and make one state
to get minimal version DFA
21. Example Part1
• 0 equivalence {A,B,C,D} {E}
• 1 equivalence {A,B,C) {D} {E}
• 2 equivalence {A,C} {B} {D} {E}
• 3 equivalence {A,C} {B} {D} {E}
When you find two row gives consecutive result than it time to stop the
process
Result both are
same