Finite Automata Fall 2004 COMP 335 1 Finite
- Slides: 57
Finite Automata Fall 2004 COMP 335 1
Finite Automaton Input String Output Finite Automaton Fall 2004 COMP 335 String 2
Finite Accepter Input String Output Finite Automaton Fall 2004 COMP 335 “Accept” or “Reject” 3
Transition Graph abba - Finite Accepter initial state Fall 2004 transition COMP 335 final state “accept” 4
Initial Configuration Input String Fall 2004 COMP 335 5
Reading the Input Fall 2004 COMP 335 6
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Input finished Output: “accept” Fall 2004 COMP 335 10
Rejection Fall 2004 COMP 335 11
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Input finished Output: “reject” Fall 2004 COMP 335 15
Another Rejection Fall 2004 COMP 335 16
Output: Fall 2004 “reject” COMP 335 17
Another Example Fall 2004 COMP 335 18
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Input finished Output: “accept” Fall 2004 COMP 335 22
Rejection Fall 2004 COMP 335 23
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Input finished Output: “reject” Fall 2004 COMP 335 27
Formalities Deterministic Finite Accepter (DFA) : (A finite) set of states : (A finite) set of input alphabet : transition function : initial state (an element of Q) : set of final states (a subset of Q) Fall 2004 COMP 335 28
Input Alphabet Fall 2004 COMP 335 29
Set of States Fall 2004 COMP 335 30
Initial State Fall 2004 COMP 335 31
Set of Final States Fall 2004 COMP 335 32
Transition Function Fall 2004 COMP 335 33
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Transition Function Fall 2004 COMP 335 37
Extended Transition Function Fall 2004 COMP 335 38
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Observation: There is a walk from with label Fall 2004 COMP 335 to 42
Example: There is a walk from with label Fall 2004 COMP 335 to 43
Recursive Definition Fall 2004 COMP 335 44
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Languages Accepted by DFAs Take DFA Definition: The language contains all input strings accepted by = { strings that drive Fall 2004 COMP 335 to a final state} 46
Example accept Fall 2004 COMP 335 47
Another Example accept Fall 2004 accept COMP 335 accept 48
Formally For a DFA Language accepted by Fall 2004 : COMP 335 49
Observation Language rejected by Fall 2004 : COMP 335 50
More Examples accept Fall 2004 COMP 335 trap state 51
= { all strings with prefix } accept Fall 2004 COMP 335 52
= { all strings without substring } Fall 2004 COMP 335 53
Regular Languages A language is regular if there is a DFA such that All regular languages form a language family Fall 2004 COMP 335 54
Examples of regular languages: { all strings with prefix } { all strings with suffix } { all strings without substring } There exist automata that accept these Languages (see previous slides). Fall 2004 COMP 335 55
Another Example The language is regular: Fall 2004 COMP 335 56
There exist languages which are not Regular: Example: There is no DFA that accepts such a language (we will prove this later!) Fall 2004 COMP 335 57
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- String matching with finite automata
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- An informal picture of finite automata
- Automata diagram
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- Finite automata with epsilon transitions
- Limitations of finite automata
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- Diagram fsa
- Finite automata
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- Finite subordinate clauses
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- Finite verb
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