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Explore the concept of Deterministic Finite Automata (DFA) and Regular Languages with detailed explanations on input processing, state transitions, acceptance, and rejection criteria. Learn key components like transition graphs, alphabets, initial configurations, and more.
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Deterministic Finite Automata And Regular Languages Costas Busch - LSU
Deterministic Finite Automaton (DFA) Input Tape String Output “Accept” or “Reject” Finite Automaton Costas Busch - LSU
Transition Graph initial state accepting state transition state Costas Busch - LSU
Alphabet For every state, there is a transition for every symbol in the alphabet Costas Busch - LSU
Initial Configuration Input Tape Input String Initial state Costas Busch - LSU
Scanning the Input head Costas Busch - LSU
Input finished accept Last state determines the outcome Costas Busch - LSU
A Rejection Case Input String Costas Busch - LSU
Input finished reject Last state determines the outcome Costas Busch - LSU
Another Rejection Case Tape is empty Input Finished (no symbol read) reject Costas Busch - LSU
This automaton accepts only one string Language Accepted: Costas Busch - LSU
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 Costas Busch - LSU
Another Example Accept state Accept state Accept state Costas Busch - LSU
Empty Tape Input Finished accept Costas Busch - LSU
Another Example trap state Accept state Costas Busch - LSU
Input String Costas Busch - LSU
Input finished accept Costas Busch - LSU
A rejection case Input String Costas Busch - LSU
Input finished reject Costas Busch - LSU
Language Accepted: Costas Busch - LSU
Another Example Alphabet: Language Accepted: Costas Busch - LSU
Formal Definition Deterministic Finite Automaton (DFA) : set of states : input alphabet : transition function : initial state : set of accepting states Costas Busch - LSU
Set of States Example Costas Busch - LSU
Input Alphabet :the input alphabet never contains empty string Example Costas Busch - LSU
Initial State Example Costas Busch - LSU
Set of Accepting States Example Costas Busch - LSU
Transition Function Describes the result of a transition from state with symbol Costas Busch - LSU
Example: Costas Busch - LSU
Transition Table for symbols states Costas Busch - LSU
Extended Transition Function Describes the resulting state after scanning string from state Costas Busch - LSU
Example: Costas Busch - LSU
Special case: for any state Costas Busch - LSU
In general: implies that there is a walk of transitions states may be repeated Costas Busch - LSU
Language Accepted by DFA Language accepted by DFA : it is denoted as and contains all the strings accepted by We also say that recognizes Costas Busch - LSU
For a DFA Language accepted by : Costas Busch - LSU
Language rejected by : Costas Busch - LSU
More DFA Examples Empty language All strings Costas Busch - LSU
Language of the empty string Costas Busch - LSU