28+Slides--Finite+Automata+II

28+Slides--Finite+Automata+II - CS103 HO#28 Finite Automata...

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Unformatted text preview: CS103 HO#28 Finite Automata II 4/22/11 1 Note: It is important to do the reading in the Sipser text. You should try to understand it line by line. Come to office hours , write us with questions, or talk to your classmates! Suppose L = {w { a , b } * | no two consecutive characters are the same} q 1 a b b a a, b q 2 q 3 q 4 a b last character a, only b OK reject input last character b, only a OK Q = {q 1 , q 2 , q 3 , q 4 } = {a, b} q 1 is the start state F = {q 1 , q 2 , q 3 } a b q 1 q 2 q 3 q 2 q 4 q 3 q 3 q 2 q 4 q 4 q 4 q 4 Suppose L = {w | w = a m b n for m, n > 0} q 1 b a q 2 q 4 q 3 a a b b a, b Suppose L = {w | w is the string representation of a floating point number } d . d +, E d d d d d +, d E +2.0 532.67 0.3E123 1.5006E+27-0.4E-2-6E8 d stands for any decimal digit (transitions to non-accepting state for illegal inputs not shown) Let = {a, b, c, d} Let L Missing = {w | there is a symbol from not in w} Start state: all letters missing After one character, the state could be a read, b, c, d still missing b read, a, c, d still missing c read, a, b, d still missing d read, a, b, c still missing After two characters, the state could be any of the previous, or a, b read, c, d still missing a, c read, b, d still missing ... After three characters, ... Some Important Definitions Let M = (Q, , , q , F) be a finite automaton and let w = w 1 , w 2 , ..., w n be a string where each w i . Then m accepts w if there exists a sequence of states r , r 1 , ..., r n in Q such that: 1. r = q , 2. (r i , w i+1 ) = r i+1 for i = 0, 1, ..., n 1, and 3. r n F. q 1 a b b a a, b q 2 q 3 q 4 a b Q = {q 1 , q 2 , q 3 , q 4 } = {a, b} q 1 is the start state : Q Q F = {q 1 , q 2 , q 3 } a b q 1 q 2 q 3 q 2 q 4 q 3 q 3 q 2 q 4 q 4 q 4 q 4 CS103 HO#28 Finite Automata II 4/22/11 2 Some Important Definitions Let M = (Q, , , q , F) be a finite automaton and let w = w 1 , w 2 , ..., w n be a string where each w i . Then m accepts w if there exists a sequence of states r , r 1 , ..., r n in Q such that: 1. r = q , 2. (r i , w i+1 ) = r i+1 for i = 0, 1, ..., n 1, and 3. r n F. We say that M recognizes language A if A = { w | M accepts w } A language is called a regular language if some finite automaton recognizes it. More Important Definitions Let A and B be languages. We define the regular operations union, concatenation, and star as follows: Union : A B = { x | x A or x B } Concatenation : A B = { xy | x A and y B } Star : A * = { x 1 x 2 ... x k | k 0 and each x i...
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This note was uploaded on 06/01/2011 for the course EE 103 taught by Professor Plummer during the Spring '11 term at Stanford.

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28+Slides--Finite+Automata+II - CS103 HO#28 Finite Automata...

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