hw04 - D j if the state accepts only decimal integers; DH j...

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SE 3306 - Mathematical Foundations of SE Homework # 4 Due on 03/25/2009 – 10:30am (1) Let Σ = { a,b,c } . Give a FSA that will describe 1. L 1 = { x Σ * | (x begins with c) (x contains two consecutive bs } . 2. L 2 = { x Σ * || x | a is odd ∧ | x | b is even } . (2) Let Σ = { 0 , 1 ,..., 9 } . Give a FSA that will describe L = { x Σ * | the number represented by x is divisible by 7 } . (3) Use the algorithm given in class to identify the connected states of the FSA given below: s0 s2 s4 s1 s3 s5 0 1 0,1 1 0 0 1 1 0 0,1 (4) Convert the regular expression ( a b ) * a ( a b ) * to a FSA. You must follow the procedure presented in class. (5) Convert the following regular grammar to a FSA G 1 = ( { I,F } , { 0 , 1 ,. } ,I, { I 0 I,I 1 I,I 0 .F,I 1 .F,F 0 F,F 1 F,F λ } ) You must follow the procedure presented in class.
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(6) Given Σ = { 0 , 1 ,..., 9 ,A,B,C,D,F } . Construct a FSA to recognize decimal integer numbers as well as hexadecimal numbers. Name the acceptance states according to the following scheme:
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Unformatted text preview: D j if the state accepts only decimal integers; DH j if the state can accept both decimal integers and hexadecimal numbers; and H j if the state can accept only hexadecimal numbers (where j is some index of the state). (7) Convert the FSA given below to a regular expression. You must follow the procedure presented in class. s2 s1 a a a b b b s0 (8) What is model theory? (9) What is Godels Completeness Theorem? How is it dierent from the soundness theorem? (10) (Extra Credit - Due on April 1) Let L be the set of strings that agree with some initial part of the pattern 0 1 10 2 10 3 10 4 10 5 ... . Thus L = { , 01 , 010 , 0100 , 01001 , 010010 , 0100100 ,... } . Using the Pumping Lemma, prove that L is not a regular language....
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hw04 - D j if the state accepts only decimal integers; DH j...

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