1. Finite Automata
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2. Finite Automaton Input String Output Finite String Automaton
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3. Finite Accepter Input String Output “Accept” or Finite “Reject”
Automaton
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4. Transition Graph Abba -Finite Accepter initial state final state
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5. Initial Configuration
Input String
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6. Reading the Input
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10. Input finished
Output: “accept”
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11. Rejection
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15. Input finished
Output:
“reject”
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16. Another Rejection
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17. Output:
“reject”
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18. Another Example
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22. Input finished
Output: “accept”
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23. Rejection
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27. Input finished
Output: “reject”
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28. Formalities Deterministic Finite Accepter (DFA) : set of states
: input alphabet
: transition function
: initial state
: set of final states
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29. Input Alphabet
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30. Set of States
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31. Initial State
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32. Set of Final States
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33. Transition Function
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37. Transition Function
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38. Extended Transition Function
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42. Observation: There is a walk from to with label
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43. Example: There is a walk from to with label
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44. Recursive Definition
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45. Costas Busch - RPI

46. Languages Accepted by DFAs
Take DFA
Definition:
The language contains
all input strings accepted by
= { strings that drive to a final state}
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47. Example
accept
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48. Another Example
accept
accept
accept
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49. Formally
For a DFA
Language accepted by :
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50. Observation
Language rejected by :
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51. More Examples
trap state
accept
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52. = { all strings with prefix }
accept
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53. = { all strings without
substring }
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54. Regular Languages A language is regular if there is a DFA such that
All regular languages form a language family
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55. Examples of regular languages:
{ all strings with prefix }
{ all strings with prefix }
{ all strings without substring }
There exist automata that accept these
Languages (see previous slides).
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56. Another Example
The language
is regular:
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57. There exist languages which are not Regular:
Example:
There is no DFA that accepts such a language
(we will prove this later in the class)
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