1. COSC 3340: Introduction to Theory of Computation
University of Houston
Dr. Verma
Lecture 2
Lecture 2
UofH - COSC Dr. Verma

2. 1st model -- Deterministic Finite Automaton (DFA)
Read only Head
Finite Control
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3. DFA (contd.) The DFA has: a finite set of states
1 special state - initial state
0 or more special states - final states
input alphabet
transition table containing
(state, symbol) -> next state
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4. Informally -- How does a DFA work?
An input string is placed on the tape (left-justified).
DFA begins in the start state.
Head placed on leftmost cell.
DFA goes into a loop until the entire string is read.
In each step, DFA consults a transition table and changes state based on (s, ) where
s - current state
 - symbol scanned by head
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5. How does a DFA work? (contd.)
After reading input string,
if DFA state final, input accepted
if DFA state not final, input rejected
Language of DFA -- set of all strings accepted by DFA.
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6. Pictorial representation of DFA
(q,σ) -> q'
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7. Example: Diagram of DFA L = {a2n + 1 | n >= 0}
Answer:
L = {a, aaa, aaaaa, ...}
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8. JFLAP Step-By-Step
aaa
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9. JFLAP Step-By-Step
aaa
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10. JFLAP Step-By-Step
aaa
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11. JFLAP Step-By-Step
aaa
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12. Formal definition of DFA
DFA M = (Q, , , s, F)
Where,
Q is finite set of states
 is input alphabet
s  Q is initial state
F  Q is set of final states
: Q X  -> Q
Lecture 2
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13. Formal definition of L(M)
L(M) - Language accepted by M
Define *:
*(q, ) = q
*(q, wσ) = (*(q,w),σ)
Definition: L(M) = { w in * | * (s,w) in F }.
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14. Example: L(M) = {w in {a,b}* | w contains even no. of a's}
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15. JFLAP Step-By-Step aa
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16. JFLAP Step-By-Step aa
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17. JFLAP Step-By-Step aa
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18. JFLAP Step-By-Step ab
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19. JFLAP Step-By-Step ab
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20. JFLAP Step-By-Step ab
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21. Given a language, how to define DFA?
Creative process requiring you to:
(i) Put yourself in DFA's shoes
(ii) Find finite amount of info, based on
which string accepted/rejected
(iii) From step (ii), determine number of states and then transitions.
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22. Regular Languages
Definition: A Language is regular iff there is a DFA that accepts it.
Examples: 
{} *
{w in {0,1}* | second symbol of w is a 1} Exercise
{w in {0,1}* | second last symbol of w is a 1} Exercise
{w in {0,1}* | w contains 010 as a substring} - (importance?)
Lecture 2
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