Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
THEORY OF COMPUTATION
Lecture One:
Automata Theory
1Er. Deepinder KaurAutomata Theory
Theory of Computation
In theoretical computer science and mathematics,
the theory
of computation is the branch that deals ...
Automata theory
• The word “Automata“ is the plural of “automaton" which
simply means any machine.
• automata theory is th...
Abstract Machine
• An abstract machine, also called an abstract computer, is a
theoretical model of a computer hardware or...
Applications of Automata
• A variety of properties concerning the models, grammars, and
languages will be proven.
• These ...
Automaton
• An automaton is an abstract model of a digital
computer
• It has a mechanism to read input (string over a give...
Automaton
• With every automaton, a transition function is
associated which gives the next state in terms of
the current s...
Components of an automaton
• Input file : Contains strings of input symbols
• Storage unit: consists of an unlimited numbe...
Some Terms used in automaton theory
• Alphabets-Everything in mathematics is based on symbols. This
is also true for autom...
• The set of strings, including empty, over an alphabet ∑ is
denoted by ∑*.
• ∑+
= ∑* -{є}
• Languages-A set of strings wh...
• Langauge in set forms-
{w|some logical view about w}
e.g {an
bn
|n>=1}
• Kleene closure- Given an alphabet, a language i...
Finite Automaton
• One of the powerful models of computation which
are restricted model of actual computer is called
finit...
2.2 Deterministic Finite Automata
– graphic model for a DFA
13Automata Theory Er. Deepinder Kaur
Main parts of pictorial representation of Finite
machine
• Strings are fed into device by means of an input tape which is
...
Main parts of pictorial representation of Finite
machine
• After reading an input symbol, reading head moves one square to...
DFA:
Deterministic Finite Automaton
• An informal definition (formal version later):
– A diagram with a finite number of s...
Finite Automata FA
• Its goal is to act as a recognizer for specific a
language/pattern.
• Any problem can be presented in...
Deterministic Finite Automata DFA
FA = “a 5-tuple “ (Q, Σ, , q0, F)
1. Q: {q0, q1, q2, …} is set of states.
2. Σ: {a, b...
Transition function 
: Q x Σ→Q
Maps from domain of (states, letters) to range
of states.
19
(q0, a)
(q2, b)
(q1, b)
q1...
Transition function 
• : Q x Σ→Q
• Maps from domain of (states, letters) to range
of states.
20
(q0, a)
(q2, b)
(q1, b)
...
How does FA work?
1. Starts from a start state.
2. Loop
Reads a sequence of letters
1. Until input string finishes
2. If t...
Transition System
FA = “a 5-tuple “ (Q, Σ, , q0, F)
1. Q: {q0, q1, q2, …} is set of states.
2. Σ: {a, b, …} set of alph...
Transition System
Transition Diagrams Transition Tables
23Automata Theory Er. Deepinder Kaur
Transition Diagram Notations
• If any state q in Q is the starting state then
it is represented by the circle with arrow a...
Transition Diagram
Can be represented by directed labeled graph/Transition table
Vertex is a state
States= nodes
Start...
Alternative Representation: Transition
Table
26
0 1
A A B
B A C
C C C
Rows = states
Columns =
input symbols
Final states
s...
Acceptability of a string
A string is accepted by a transition system if
• There exist a path from initial state to final
...
Example1.1
• Build an FA that accepts only aab
28
S1
-
S3
a
S2
a b
+
S4
a b
S1 S2 ?
S2 S3 ?
S3 ? ?
S4 ? ?
Automata Theory ...
Example withTransition Table
29
0 1
A C B
B D A
C A D
D B C
*
Check for 110101
Automata Theory Er. Deepinder Kaur
Example withTransition Table
30
Solution:-
(A,110101)= (B,10101)
(A,0101)
(C,101)
(D,01)
(B,1)
A*Automata Theory Er....
Automata Theory 31
Properties of transition function
1. (q,λ)=q
• It comes back to same state
• It requires an input symb...
Facts in designing FA
First of all we have to analyze set of strings.
Make sure that every state is check for output sta...
Language of a DFA
• Automata of all kinds define languages.
• If A is an automaton, L(A) is its language.
• For a DFA A, L...
Language
• A language is a set of strings.
For example, {0, 1}, {all English words}, {0, 0, 0, ...} are
all languages.
Aut...
Example #8:
• Let Σ = {0, 1}. Give DFAs for {}, {ε}, Σ*
, and Σ+
.
For {}:
For Σ*
: For Σ+
:
Er. Deepinder Kaur
0/1
q0
0/1...
Example: Design a FA that accepts set of strings such that every string
ends in 00, over the alphabet
{0,1} i,e ∑={0, 1}
I...
• 1 0 0
start 0
1 1
q0 q1 q2q2
Automata Theory 37Er. Deepinder Kaur
Ex 2 –
• Construct a DFA that accepts a’s and b’s and
‘aa’ must be substring
38Automata Theory Er. Deepinder Kaur
Example: String in a Language
39
Start
a
20 1
a
Minimal condition : aa
Automata Theory Er. Deepinder Kaur
Example: String in a Language
40
Start
There may be aabbaa.bbbbaa,aa,aab,aabb,….
a
20 1
a
b
Automata Theory Er. Deepinder ...
Example: String in a Language
41
Start
a
b
A CB
a
b a,b
.
Automata Theory Er. Deepinder Kaur
Ex : (0+1)*00(0+1)*
• Idea: Suppose the string x1x2 ···xn is on
the tape. Then we check x1x2, x2x3, ...,
xn-1xn in turn.
•...
• Step 2. Find all edges by the following
consideration:
Consider x1x2.
• If x1=1, then we give up x1x2 and continue to
ch...
(0+1)*00(0+1)*
0 0
0
1
1
1
Automata Theory 44Er. Deepinder Kaur
Ex 1
All words that start with “a” over the alphabet
{a,b}
a(a+b)*
Automata Theory 45
1
2b
a 3
a,b
a,b3
Er. Deepinder Kaur
Ex3
• All words that start with triple letter
(aaa+bbb)(a+b)*
Automata Theory 46Er. Deepinder Kaur
Ex3
Automata Theory 47
1-
2a 3
a,b
4
b 5
b
6+
b
a a
Er. Deepinder Kaur
Ex4
• All words with even count of letters having “a” in an
even position from the start, where the first letter is
letter...
Ex4
Automata Theory 49
-
a,b
Er. Deepinder Kaur
EX5:Construct DFA to accept (0+1)*
0
1
Automata Theory 50Er. Deepinder Kaur
Ex 6:Construct DFA to accept 00(0+1)*
0 0
0
11
1
0 1
Automata Theory 51Er. Deepinder Kaur
(0+1)*(00+01)
0 0
1
1
1
0
0
1
Automata Theory 52Er. Deepinder Kaur
Construct a FA that accepts set of strings where the number of 0s in
every string is multiple of 3 over alphabet ∑={0,1}
1...
Design FA which accepts set of strings containing exactly four
1s in every string over alphabet ∑={0,1}
1
q2q4q0 q1 q2
1 1...
Design a FA that accepts strings containing exactly one 1 over alphabet
{0,1}. Also draw the transition table for the FA g...
Transition table for previous problem
δ/∑ 0 1
q1 q1 q2
*q2 q2 q3
q3 q3 q3
Non final state that transit in
self loop for al...
Design an FA that accepts the language
L={w ϵ (0,1)*/ second symbol of w is ‘0’ and fourth input is ‘1’}
q0 q3q1 q2
0 1
1/...
Design DFA for the language
L={w ϵ (a,b)*/nb(w) mod 3 > 1}
As given in the language, this can be interpreted that number o...
Design FA over alphabet ∑= {0,1} which accepts the set of strings either
start with 01 or end with 01
q0 q1
q3
q4
q2
0 1
1...
Example #4:
• Give a DFA M such that:
L(M) = {x | x is a string of 0’s and 1’s and |x| >= 2}
Er. Deepinder Kaur
q1
q0
q2
0...
Example #5:
• Give a DFA M such that:
L(M) = {x | x is a string of (zero or more) a’s and b’s such
that x does not contain...
Example #6:
• Give a DFA M such that:
L(M) = {x | x is a string of a’s, b’s and c’s such that x
contains the substring aba...
DFA Practice
• Design a FA which accepts the only input 101
over input set {0,1}
• Strings that end in ab
• Strings that c...
Upcoming SlideShare
Loading in …5
×

Introduction to fa and dfa

Introduction to finite automata and dfa

Related Books

Free with a 30 day trial from Scribd

See all
  • Be the first to comment

Introduction to fa and dfa

  1. 1. THEORY OF COMPUTATION Lecture One: Automata Theory 1Er. Deepinder KaurAutomata Theory
  2. 2. Theory of Computation In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: • automata theory, • computability theory • computational complexity theory. Er. Deepinder Kaur 2Automata Theory
  3. 3. Automata theory • The word “Automata“ is the plural of “automaton" which simply means any machine. • automata theory is the study of abstract machines and problems they are able to solve. • Automata theory is closely related to formal language theory as the automata are often classified by the class of formal languages they are able to recognize. Er. Deepinder KaurAutomata Theory 3
  4. 4. Abstract Machine • An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in Automata theory. Er. Deepinder KaurAutomata Theory 4
  5. 5. Applications of Automata • A variety of properties concerning the models, grammars, and languages will be proven. • These algorithms form the basis of tools for processing languages, e.g., parsers, compilers, assemblers, etc. • Other algorithms will form the basis of tools that automatically construct language processors, e.g., yacc, lex, etc. – Note that our perspective will be similar to, yet different from a compiler class. • Additionally, some things will be proven to be non-computable, e.g., the enhanced compiler. Automata Theory 5Er. Deepinder Kaur
  6. 6. Automaton • An automaton is an abstract model of a digital computer • It has a mechanism to read input (string over a given alphabet, e.g. strings of 0’s and 1’s on Σ = {0,1}) written on an input file. • A finite automaton has a set of states • Its control moves from state to state in response to external “inputs” Automata Theory 6Er. Deepinder Kaur
  7. 7. Automaton • With every automaton, a transition function is associated which gives the next state in terms of the current state • An automaton can be represented by a graph in which the vertices give the internal states and the edges transitions • The labels on the edges show what happens (in terms of input and output) during the transitions Automata Theory 7Er. Deepinder Kaur
  8. 8. Components of an automaton • Input file : Contains strings of input symbols • Storage unit: consists of an unlimited number of cells, each capable of holding a single symbol from an alphabet • Control unit : can be in any one of a finite number of internal states and can change states in defined manner Automata Theory 8Er. Deepinder Kaur
  9. 9. Some Terms used in automaton theory • Alphabets-Everything in mathematics is based on symbols. This is also true for automata theory. Alphabets are defined as a finite set of symbols. An example of alphabet is a set of decimal numbers ∑={0,1,2,3,4,5,6,7,8,9} • Strings- A string is a finite sequence of symbols selected from some alphabet If ∑ {a,b} is an alphabet then abab is string over alphabet ∑. A string is generally denoted by w. The length of string is denoted by | w| • Empty string is string with zero occurrence of symbols . This string is represented by є Automata Theory 9Er. Deepinder Kaur
  10. 10. • The set of strings, including empty, over an alphabet ∑ is denoted by ∑*. • ∑+ = ∑* -{є} • Languages-A set of strings which are chosen from some ∑*, where ∑ is a particular alphabet, is called a language . If ∑ is an alphabet, and L subset of ∑*, then L is said to be language over alphabet ∑. For example the language of all strings consisting of n 0’s followed by n 1’s for some n>=0: {є,01,0011,000111,-------} Automata Theory 10Er. Deepinder Kaur
  11. 11. • Langauge in set forms- {w|some logical view about w} e.g {an bn |n>=1} • Kleene closure- Given an alphabet, a language in which any string of letters from ∑ is a word, even the null string, is called closure of the alphabet . It is denoted by writing a star, after the name of alphabet as a superscript ∑*. Automata Theory 11Er. Deepinder Kaur
  12. 12. Finite Automaton • One of the powerful models of computation which are restricted model of actual computer is called finite automata. These machines are very similar to CPU of a computer .They are restricted model as they lack memory. • Finite automation is called finite because number of possible states and number of letter in alphabet are both finite and automation because the change of state is totally governed by the input. Automata Theory 12Er. Deepinder Kaur
  13. 13. 2.2 Deterministic Finite Automata – graphic model for a DFA 13Automata Theory Er. Deepinder Kaur
  14. 14. Main parts of pictorial representation of Finite machine • Strings are fed into device by means of an input tape which is divided into square with each symbol in each square. • Main part of machine is a black box which serve that what symbol is written at any position on input tape by means of a movable reading head • P0,p1,p2,p3,p4 are the states in finite control system and x and y are input symbols. • At regular intervals, the automation reads one symbol from input tape and then enters in a new state that depends only on current state and the symbol just read. Automata Theory 14Er. Deepinder Kaur
  15. 15. Main parts of pictorial representation of Finite machine • After reading an input symbol, reading head moves one square to the right on input tape so that on next move, it will read the symbol in next tape square. This process is repeated again and again • Automation then indicates approval or disapproval • If it winds up in one of the final states, the input string is considered to be accepted. The language accepted by the machine is the set of strings it accepts. Automata Theory 15Er. Deepinder Kaur
  16. 16. DFA: Deterministic Finite Automaton • An informal definition (formal version later): – A diagram with a finite number of states represented by circles – An arrow points to one of the states, the unique start state – Double circles mark any number of the states as accepting states – For every state, for every symbol in Σ, there is exactly one arrow labeled with that symbol going to another state (or back to the same state) Automata Theory Er. Deepinder Kaur
  17. 17. Finite Automata FA • Its goal is to act as a recognizer for specific a language/pattern. • Any problem can be presented in form of decidable problem that can be answered by Yes/No. • Hence FA (machine with limited memory) can solve any problem. 17Automata Theory Er. Deepinder Kaur
  18. 18. Deterministic Finite Automata DFA FA = “a 5-tuple “ (Q, Σ, , q0, F) 1. Q: {q0, q1, q2, …} is set of states. 2. Σ: {a, b, …} set of alphabet. 3. (delta): represents the set of transitions that FA can take between its states.  : Q x Σ→Q Q x Σ to Q, this function:  Takes a state and input symbol as arguments.  Returns a single state.  : Q x Σ→Q 4. q0 Q is the start state. 5. F Q is the set of final/accepting states. 18 ∈ ⊂ Automata Theory Er. Deepinder Kaur
  19. 19. Transition function  : Q x Σ→Q Maps from domain of (states, letters) to range of states. 19 (q0, a) (q2, b) (q1, b) q1 q2 q3 Automata Theory Er. Deepinder Kaur
  20. 20. Transition function  • : Q x Σ→Q • Maps from domain of (states, letters) to range of states. 20 (q0, a) (q2, b) (q1, b) q1 q2 q3 Automata Theory Er. Deepinder Kaur
  21. 21. How does FA work? 1. Starts from a start state. 2. Loop Reads a sequence of letters 1. Until input string finishes 2. If the current state is a final state then Input string is accepted. 1. Else Input string is NOT accepted. • But how can FA be designed and represented? 21Automata Theory Er. Deepinder Kaur
  22. 22. Transition System FA = “a 5-tuple “ (Q, Σ, , q0, F) 1. Q: {q0, q1, q2, …} is set of states. 2. Σ: {a, b, …} set of alphabet. 3. (delta): represents the set of transitions that FA can take between its states.  : Q x Σ→Q Q x Σ to Q, this function:  Takes a state and input symbol as arguments.  Returns a single state.  : Q x Σ→Q 4. q0 Q is the start state. 5. F Q is the set of final/accepting states. 22 ∈ ⊂ Automata Theory Er. Deepinder Kaur
  23. 23. Transition System Transition Diagrams Transition Tables 23Automata Theory Er. Deepinder Kaur
  24. 24. Transition Diagram Notations • If any state q in Q is the starting state then it is represented by the circle with arrow as • Nodes corresponding to accepting states are marked by a double circle q Automata Theory 24Er. Deepinder Kaur
  25. 25. Transition Diagram Can be represented by directed labeled graph/Transition table Vertex is a state States= nodes Starting/Initial state denoted by circle and arrow/- Final state(s) denoted by two concentric circles/+ Other states with circle Transition function  =directed arrows connecting states. 25 S1 S2 b a a,b Automata Theory Er. Deepinder Kaur
  26. 26. Alternative Representation: Transition Table 26 0 1 A A B B A C C C C Rows = states Columns = input symbols Final states starred * *Arrow for start state Automata Theory Er. Deepinder Kaur
  27. 27. Acceptability of a string A string is accepted by a transition system if • There exist a path from initial state to final state • Path traversed is equal to w 27Automata Theory Er. Deepinder Kaur
  28. 28. Example1.1 • Build an FA that accepts only aab 28 S1 - S3 a S2 a b + S4 a b S1 S2 ? S2 S3 ? S3 ? ? S4 ? ? Automata Theory Er. Deepinder Kaur
  29. 29. Example withTransition Table 29 0 1 A C B B D A C A D D B C * Check for 110101 Automata Theory Er. Deepinder Kaur
  30. 30. Example withTransition Table 30 Solution:- (A,110101)= (B,10101) (A,0101) (C,101) (D,01) (B,1) A*Automata Theory Er. Deepinder Kaur
  31. 31. Automata Theory 31 Properties of transition function 1. (q,λ)=q • It comes back to same state • It requires an input symbol to change the state of a system. 2. (q,aw)=((q,a),w) (q,w,a)=((q,w),a) Er. Deepinder Kaur
  32. 32. Facts in designing FA First of all we have to analyze set of strings. Make sure that every state is check for output state and for every input symbol from given set. No state must have two different outputs for single input symbol There must be one initial and atleast one final state in FA 32Automata Theory Er. Deepinder Kaur
  33. 33. Language of a DFA • Automata of all kinds define languages. • If A is an automaton, L(A) is its language. • For a DFA A, L(A) is the set of strings labeling paths from the start state to a final state. • Formally: L(A) = the set of strings w such that δ(q0, w) is in F. 33Automata Theory Er. Deepinder Kaur
  34. 34. Language • A language is a set of strings. For example, {0, 1}, {all English words}, {0, 0, 0, ...} are all languages. Automata Theory 34Er. Deepinder Kaur
  35. 35. Example #8: • Let Σ = {0, 1}. Give DFAs for {}, {ε}, Σ* , and Σ+ . For {}: For Σ* : For Σ+ : Er. Deepinder Kaur 0/1 q0 0/1 q0 0/1 q0 q1 0/1 Automata Theory 35
  36. 36. Example: Design a FA that accepts set of strings such that every string ends in 00, over the alphabet {0,1} i,e ∑={0, 1} Inorder to design any FA, first try to fulfill the minimum condition. Start 0 0 0 Being DFA, we must check every input symbol for output state from every state. So we have to decide output state at symbol 1 from q0,q1 and q2. Then it will be complete FA q0 q1 q2 Automata Theory 36Er. Deepinder Kaur
  37. 37. • 1 0 0 start 0 1 1 q0 q1 q2q2 Automata Theory 37Er. Deepinder Kaur
  38. 38. Ex 2 – • Construct a DFA that accepts a’s and b’s and ‘aa’ must be substring 38Automata Theory Er. Deepinder Kaur
  39. 39. Example: String in a Language 39 Start a 20 1 a Minimal condition : aa Automata Theory Er. Deepinder Kaur
  40. 40. Example: String in a Language 40 Start There may be aabbaa.bbbbaa,aa,aab,aabb,…. a 20 1 a b Automata Theory Er. Deepinder Kaur
  41. 41. Example: String in a Language 41 Start a b A CB a b a,b . Automata Theory Er. Deepinder Kaur
  42. 42. Ex : (0+1)*00(0+1)* • Idea: Suppose the string x1x2 ···xn is on the tape. Then we check x1x2, x2x3, ..., xn-1xn in turn. • Step 1. Build a checker 0 0 Automata Theory 42Er. Deepinder Kaur
  43. 43. • Step 2. Find all edges by the following consideration: Consider x1x2. • If x1=1, then we give up x1x2 and continue to check x2x3. So, we have δ(q0, 1) = q0. • If x1x2 = 01, then we also give up x1x2 and continue to check x2x3. So, δ(q1, 1) = δ(q0, 1) =q0. • If x1x2 = 00, then x1x2··· xn is accepted for any x3···xn. So, δ(q2,0)=δ(q2,1)=q2. Automata Theory 43Er. Deepinder Kaur
  44. 44. (0+1)*00(0+1)* 0 0 0 1 1 1 Automata Theory 44Er. Deepinder Kaur
  45. 45. Ex 1 All words that start with “a” over the alphabet {a,b} a(a+b)* Automata Theory 45 1 2b a 3 a,b a,b3 Er. Deepinder Kaur
  46. 46. Ex3 • All words that start with triple letter (aaa+bbb)(a+b)* Automata Theory 46Er. Deepinder Kaur
  47. 47. Ex3 Automata Theory 47 1- 2a 3 a,b 4 b 5 b 6+ b a a Er. Deepinder Kaur
  48. 48. Ex4 • All words with even count of letters having “a” in an even position from the start, where the first letter is letter number one. (a+b)a((a+b)a)* Automata Theory 48Er. Deepinder Kaur
  49. 49. Ex4 Automata Theory 49 - a,b Er. Deepinder Kaur
  50. 50. EX5:Construct DFA to accept (0+1)* 0 1 Automata Theory 50Er. Deepinder Kaur
  51. 51. Ex 6:Construct DFA to accept 00(0+1)* 0 0 0 11 1 0 1 Automata Theory 51Er. Deepinder Kaur
  52. 52. (0+1)*(00+01) 0 0 1 1 1 0 0 1 Automata Theory 52Er. Deepinder Kaur
  53. 53. Construct a FA that accepts set of strings where the number of 0s in every string is multiple of 3 over alphabet ∑={0,1} 1 1 1 start 0 0 0 As 0 existence of 0 is also multiple of 3, we have to consider starting state as the final state. q1 q2q0 Automata Theory 53Er. Deepinder Kaur
  54. 54. Design FA which accepts set of strings containing exactly four 1s in every string over alphabet ∑={0,1} 1 q2q4q0 q1 q2 1 1 q3 1 0 0 0 0 0 q5 0/1 star t 1 q5 is called the trap state or dead state. Dead states are those states which transit to themselves for all input symbols. Automata Theory 54Er. Deepinder Kaur
  55. 55. Design a FA that accepts strings containing exactly one 1 over alphabet {0,1}. Also draw the transition table for the FA generated q2q2q1 1 0 0 q3 0/1 1 start q3 is the dead state Automata Theory 55Er. Deepinder Kaur
  56. 56. Transition table for previous problem δ/∑ 0 1 q1 q1 q2 *q2 q2 q3 q3 q3 q3 Non final state that transit in self loop for all inputs Automata Theory 56Er. Deepinder Kaur
  57. 57. Design an FA that accepts the language L={w ϵ (0,1)*/ second symbol of w is ‘0’ and fourth input is ‘1’} q0 q3q1 q2 0 1 1/0 1 1/0 0 1/0 q5 0/1 start q4 Automata Theory 57Er. Deepinder Kaur
  58. 58. Design DFA for the language L={w ϵ (a,b)*/nb(w) mod 3 > 1} As given in the language, this can be interpreted that number of b mod 3 has to be greater than 1 and there is no restriction on number of a’s. Thus it will accept string with 2 bs,5 bs, 8bs and so on. q0 q1 q2 b b a a a b star t Q={q0,q1,q2} F={q2} Automata Theory 58Er. Deepinder Kaur
  59. 59. Design FA over alphabet ∑= {0,1} which accepts the set of strings either start with 01 or end with 01 q0 q1 q3 q4 q2 0 1 1/0 q5 1 0 1 0 1 0 0 1 start Automata Theory 59Er. Deepinder Kaur
  60. 60. Example #4: • Give a DFA M such that: L(M) = {x | x is a string of 0’s and 1’s and |x| >= 2} Er. Deepinder Kaur q1 q0 q2 0/1 0/1 0/1 Automata Theory 60
  61. 61. Example #5: • Give a DFA M such that: L(M) = {x | x is a string of (zero or more) a’s and b’s such that x does not contain the substring aa} Er. Deepinder Kaur q2q0 a a/b a q1 b b Automata Theory 61
  62. 62. Example #6: • Give a DFA M such that: L(M) = {x | x is a string of a’s, b’s and c’s such that x contains the substring aba} Er. Deepinder Kaur q2q0 a a/b b q1 b a b q3 a Automata Theory 62
  63. 63. DFA Practice • Design a FA which accepts the only input 101 over input set {0,1} • Strings that end in ab • Strings that contain aba • String start with 0 and ends with 1 over {0,1} • Strings made up of letters in word ‘CHARIOT’ and recognize those strings that contain the word ‘CAT’ as a substringEr. Deepinder Kaur 63Automata Theory

    Be the first to comment

  • sajidullah15

    Apr. 9, 2017
  • TahminaShopna

    Apr. 27, 2017
  • ajmalnaqvi1

    May. 5, 2017
  • surajtongbra

    Jun. 30, 2017
  • rahul1997prince

    Jul. 13, 2017
  • KhawarTareen

    Sep. 25, 2017
  • saurabhgupta779

    Oct. 26, 2017
  • JansariKajal

    Nov. 10, 2017
  • AshleyPawar

    Dec. 25, 2017
  • RiyaSemnan

    Jan. 23, 2018
  • shahfahad88

    Jan. 26, 2018
  • Bhth

    Feb. 2, 2018
  • khaderbashashaik1

    Feb. 19, 2018
  • hendramarcos3

    Apr. 10, 2018
  • ShivaniDhole1

    Aug. 17, 2018
  • ShivaniDhole1

    Aug. 17, 2018
  • WaqarAhmed226

    Oct. 1, 2018
  • LogeshwariLogeshwari

    Feb. 13, 2019
  • musahassan5

    Mar. 13, 2019
  • NurnabiBabul

    Oct. 10, 2020

Introduction to finite automata and dfa

Views

Total views

18,294

On Slideshare

0

From embeds

0

Number of embeds

6

Actions

Downloads

753

Shares

0

Comments

0

Likes

37

×