MELJUN CORTES
 Automata are abstract mathematical models

of machines that perform computations on
an input by moving through a series ...
 Automaton
 An automaton is represented formally by the 5-

tuple of elements {Q,Σ,δ,q0,A}, where:
▪ Q is a finite set o...
 Automaton
 An automaton is represented formally by the 5-

tuple of elements {Q,Σ,δ,q0,A}, where:
▪ δ is the transition...
 Input word
 An automaton reads a finite string of symbols

a1,a2,...., an , where ai ∈ Σ, which is called a input
word....
 Run
 A run of the automaton on an input word w =

a1,a2,...., an ∈ Σ*, is a sequence of states q0,q1,q2,....,
qn, where...
 A finite automaton (FA) is a simple idealized

machine used to recognize patterns within
input taken from some character...
 A finite automaton consists of:





a finite set S of N states
a special start state
a set of final (or accepting) ...
 We execute our FA on an input sequence as

follows:
 Begin in the start state
 If the next input char matches the labe...
 It is a finite state machine which accepts the

word "nice". In this FSM the only accepting
state is number 7.
 For each input symbol in Σ, there is exactly

one transition of each state (possibly back to
the state itself).
 It do ...


A deterministic finite automaton (DFA)
consists of
 A finite set of states (often denoted Q)
 A finite set Σ of symbo...
 A start state often denoted q0
 A set of final or accepting states (often denoted F)

 We have q0 ∈ Q and F ⊆ Q
 So a DFA is mathematically represented as a

5-uple

 (Q, Σ, δ, q0, F )

 The transition function δ is a function in
...
 How to present a

DFA? With a
transition table
 How to present a

DFA? With a
transition table
 Inputs

0

1
 How to present a

DFA? With a
transition table
 Inputs
 States

0

q0
q1
q2

1
 How to present a

DFA? With a
transition table
 The → indicates the

start state

0

 q0
q1
q2

1
 How to present a

DFA? With a
transition table
 The → indicates the

start state
 The ∗ indicates the
final state(s)

0...
 How to present a

DFA? With a
transition table
 δ (q0,0) = q1
 δ (q0,0) = q0

0

 q0
q1
* q2

1

q1

q0
 How to present a

DFA? With a
transition table
 δ (q0,0) = q1
 δ (q0,0) = q0
 δ (q1,0) = q2
 δ (q1,0) = q1

0

1

 ...
 How to present a

0

1

 q0

q1

q0

q1

q2

q1

* q2

q2

q2

DFA? With a transition
table
 δ (q0,0) = q1
 δ (q0,0) ...
 Construct a DFA that accepts the language
 L = {010, 1}
 ( Σ = {0, 1} )
 Construct a DFA that accepts the language
 L = {010, 1}
 ( Σ = {0, 1} )
 Set of all strings over {0,1} where 1 is always

even.
 Set of all strings over {0,1} where 1 is always

even.
 Set of all strings over {0,1} where 1 is always

odd.
 Set of all strings over {0,1} where 1 is always

odd.
MELJUN CORTES Automata Theory
MELJUN CORTES Automata Theory
MELJUN CORTES Automata Theory
Upcoming SlideShare
Loading in...5
×

MELJUN CORTES Automata Theory

168

Published on

MELJUN CORTES Automata Theory

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
168
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
23
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

MELJUN CORTES Automata Theory

  1. 1. MELJUN CORTES
  2. 2.  Automata are abstract mathematical models of machines that perform computations on an input by moving through a series of states or configurations.
  3. 3.  Automaton  An automaton is represented formally by the 5- tuple of elements {Q,Σ,δ,q0,A}, where: ▪ Q is a finite set of states. ▪ Σ is a finite set of symbols.
  4. 4.  Automaton  An automaton is represented formally by the 5- tuple of elements {Q,Σ,δ,q0,A}, where: ▪ δ is the transition function. ▪ q0 is the start state, where q0∈ Q. ▪ A is a set of states of Q (i.e. A⊆Q) called accept states.
  5. 5.  Input word  An automaton reads a finite string of symbols a1,a2,...., an , where ai ∈ Σ, which is called a input word.  Accepting word  A word w ∈ Σ* is accepted by the automaton if qn ∈ A.
  6. 6.  Run  A run of the automaton on an input word w = a1,a2,...., an ∈ Σ*, is a sequence of states q0,q1,q2,...., qn, where qi ∈ Q such that q0 is the start state and qi = δ(qi-1,ai) for 0 < i ≤ n.
  7. 7.  A finite automaton (FA) is a simple idealized machine used to recognize patterns within input taken from some character set (or alphabet) C.
  8. 8.  A finite automaton consists of:     a finite set S of N states a special start state a set of final (or accepting) states a set of transitions T from one state to another, labeled with chars in C  As noted above, we can represent a FA graphically, with nodes for states, and arcs for transitions.
  9. 9.  We execute our FA on an input sequence as follows:  Begin in the start state  If the next input char matches the label on a transition from the current state to a new state, go to that new state  Continue making transitions on each input char ▪ If no move is possible, then stop ▪ If in accepting state, then accept
  10. 10.  It is a finite state machine which accepts the word "nice". In this FSM the only accepting state is number 7.
  11. 11.  For each input symbol in Σ, there is exactly one transition of each state (possibly back to the state itself).  It do not accept empty strings.
  12. 12.  A deterministic finite automaton (DFA) consists of  A finite set of states (often denoted Q)  A finite set Σ of symbols (alphabet)  A transition function that takes as argument a state and a symbol and returns a state (often denoted δ)
  13. 13.  A start state often denoted q0  A set of final or accepting states (often denoted F)  We have q0 ∈ Q and F ⊆ Q
  14. 14.  So a DFA is mathematically represented as a 5-uple  (Q, Σ, δ, q0, F )  The transition function δ is a function in  Q×Σ→Q  Q × Σ is the set of 2-tuples (q, a) with q ∈ Q and a ∈ Σ
  15. 15.  How to present a DFA? With a transition table
  16. 16.  How to present a DFA? With a transition table  Inputs 0 1
  17. 17.  How to present a DFA? With a transition table  Inputs  States 0 q0 q1 q2 1
  18. 18.  How to present a DFA? With a transition table  The → indicates the start state 0  q0 q1 q2 1
  19. 19.  How to present a DFA? With a transition table  The → indicates the start state  The ∗ indicates the final state(s) 0  q0 q1 * q2 1
  20. 20.  How to present a DFA? With a transition table  δ (q0,0) = q1  δ (q0,0) = q0 0  q0 q1 * q2 1 q1 q0
  21. 21.  How to present a DFA? With a transition table  δ (q0,0) = q1  δ (q0,0) = q0  δ (q1,0) = q2  δ (q1,0) = q1 0 1  q0 q1 q0 q1 q2 q1 * q2
  22. 22.  How to present a 0 1  q0 q1 q0 q1 q2 q1 * q2 q2 q2 DFA? With a transition table  δ (q0,0) = q1  δ (q0,0) = q0  δ (q1,0) = q2  δ (q1,0) = q1  δ (q2,0) = q2  δ (q2,0) = q2
  23. 23.  Construct a DFA that accepts the language  L = {010, 1}  ( Σ = {0, 1} )
  24. 24.  Construct a DFA that accepts the language  L = {010, 1}  ( Σ = {0, 1} )
  25. 25.  Set of all strings over {0,1} where 1 is always even.
  26. 26.  Set of all strings over {0,1} where 1 is always even.
  27. 27.  Set of all strings over {0,1} where 1 is always odd.
  28. 28.  Set of all strings over {0,1} where 1 is always odd.
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×