1. Deterministic
Finite Automata
And Regular Languages
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2. Deterministic Finite Automaton (DFA)
Input Tape
String
Output
“Accept” or
“Reject”
Finite
Automaton
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3. Transition Graph initial state accepting state transition state
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4. For every state, there is a transition
Alphabet
For every state, there is a transition
for every symbol in the alphabet
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5. Initial Configuration
head
Input Tape
Input String
Initial state
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6. Scanning the Input
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7. Prof. Busch - LSU

8. Prof. Busch - LSU

9. Last state determines the outcome
Input finished
accept
Last state determines the outcome
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10. A Rejection Case
Input String
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11. Prof. Busch - LSU

12. Prof. Busch - LSU

13. Last state determines the outcome
Input finished
reject
Last state determines the outcome
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14. Another Rejection Case
Tape is empty
Input Finished (no symbol read)
reject
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15. This automaton accepts only one string
Language Accepted:
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16. all the input string is scanned and the last state is accepting
To accept a string:
all the input string is scanned
and the last state is accepting
To reject a string:
all the input string is scanned
and the last state is non-accepting
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17. Another Example Accept state Accept state Accept state
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18. Another Example
Alphabet:
Language Accepted:
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19. Formal Definition Deterministic Finite Automaton (DFA) : set of states
: input alphabet
: transition function
: initial state
: set of accepting states
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20. Example:
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21. Prof. Busch - LSU

22. Transition Table for
symbols
states
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23. implies that there is a walk of transitions
In general:
implies that there is a walk of transitions
states may be repeated
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24. Language Accepted by DFA
it is denoted as and contains
all the strings accepted by
We also say that recognizes
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25. = { all strings with prefix }
accept
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26. = { all binary strings containing substring }
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27. = { all binary strings without substring }
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28. Prof. Busch - LSU

29. Regular Languages Definition: A language is regular if there is
a DFA that accepts it ( )
The languages accepted by all DFAs
form the family of regular languages
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30. Example regular languages:
{ all strings in {a,b}* with prefix }
{ all binary strings without substring }
There exist DFAs that accept these
languages (see previous slides).
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31. There exist languages which are not Regular:
There are no DFAs that accept these languages
(we will prove this in a later class)
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