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Fall 2004COMP 3351 Finite Automata
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Fall 2004COMP 3352 Finite Automaton Input String Output String Finite Automaton
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Fall 2004COMP 3353 Finite Accepter Input “Accept” or “Reject” String Finite Automaton Output
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Fall 2004COMP 3354 Transition Graph initial state final state “accept” state transition abba - Finite Accepter
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Fall 2004COMP 3355 Initial Configuration Input String
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Fall 2004COMP 3356 Reading the Input
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Fall 2004COMP 3357
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Fall 2004COMP 3358
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Fall 2004COMP 3359
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Fall 2004COMP 33510 Output: “accept” Input finished
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Fall 2004COMP 33511 Rejection
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Fall 2004COMP 33512
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Fall 2004COMP 33513
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Fall 2004COMP 33514
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Fall 2004COMP 33515 Output: “reject” Input finished
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Fall 2004COMP 33516 Another Rejection
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Fall 2004COMP 33517 Output: “reject”
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Fall 2004COMP 33518 Another Example
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Fall 2004COMP 33519
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Fall 2004COMP 33520
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Fall 2004COMP 33521
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Fall 2004COMP 33522 Output: “accept” Input finished
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Fall 2004COMP 33523 Rejection
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Fall 2004COMP 33524
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Fall 2004COMP 33525
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Fall 2004COMP 33526
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Fall 2004COMP 33527 Output: “reject” Input finished
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Fall 2004COMP 33528 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 )
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Fall 2004COMP 33529 Input Alphabet
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Fall 2004COMP 33530 Set of States
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Fall 2004COMP 33531 Initial State
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Fall 2004COMP 33532 Set of Final States
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Fall 2004COMP 33533 Transition Function
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Fall 2004COMP 33534
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Fall 2004COMP 33535
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Fall 2004COMP 33536
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Fall 2004COMP 33537 Transition Function
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Fall 2004COMP 33538 Extended Transition Function
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Fall 2004COMP 33539
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Fall 2004COMP 33540
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Fall 2004COMP 33541
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Fall 2004COMP 33542 Observation: There is a walk from to with label
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Fall 2004COMP 33543 Example: There is a walk from to with label
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Fall 2004COMP 33544 Recursive Definition
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Fall 2004COMP 33545
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Fall 2004COMP 33546 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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Fall 2004COMP 33547 Example accept
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Fall 2004COMP 33548 Another Example accept
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Fall 2004COMP 33549 Formally For a DFA Language accepted by :
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Fall 2004COMP 33550 Observation Language rejected by :
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Fall 2004COMP 33551 More Examples accept trap state
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Fall 2004COMP 33552 = { all strings with prefix } accept
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Fall 2004COMP 33553 = { all strings without substring }
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Fall 2004COMP 33554 Regular Languages A language is regular if there is a DFA such that All regular languages form a language family
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Fall 2004COMP 33555 { all strings with prefix } { all strings with suffix } { all strings without substring } Examples of regular languages: There exist automata that accept these Languages (see previous slides).
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Fall 2004COMP 33556 Another Example The language is regular:
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Fall 2004COMP 33557 There exist languages which are not Regular: There is no DFA that accepts such a language (we will prove this later!) Example:
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