hw03 - (6 ClassiFy the Following grammars according to...

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SE 3306 - Mathematical Foundations of SE Homework # 3 Due on 03/09/2009 – 10:30am (1) Let Σ = { a, b, c } . Give a regular expression 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) What are the diferent ways to represent a regular language? (3) Give examples oF sets that demonstrate the Following inequalities: 1. ( R 1 .R 2 ) * n = ( R * 1 .R * 2 ) * 2. ( R 1 .R 2 ) * n = ( R * 1 R * 2 ) * (4) Let Σ = { a, b, c } . Give right-grammars that will generate: 1. L 1 = { x Σ * | x has an even number oF as } 2. L 1 = { x Σ * | x do contain two consecutive bs } (5) Convert the regular expression ( a b ) * a ( a b ) * to a right-regular grammar. You must Follow the procedure presented in class.
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Unformatted text preview: (6) ClassiFy the Following grammars according to Chomsky’s hierarchy. 1. G 1 = ( { A, B, S } , { a, b, c } , S, { S → aSBc, S → λ, SB → bS, cB → Bc } ) 2. G 2 = ( { A, B, S } , { a, b, c } , S, { S → aSBc, S → λ, ASB → bS, cB → Bc } ) 3. G 3 = ( { A, B, S } , { a, b, c } , S, { S → aSBc, S → λ, S → bS, B → Bc } ) 4. G 4 = ( { A, B, S } , { a, b, c } , S, { S → aS, S → λ, S → bB, B → abB } ) (7) What is model theory? (8) What is Godel’s Completeness Theorem? How is it diferent From the soundness the-orem?...
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This note was uploaded on 12/12/2009 for the course SE 3306 taught by Professor Nhut during the Spring '09 term at University of Texas at Dallas, Richardson.

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