hwsol1 - Theory of Algorithms. Spring 2000. Homework 1...

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Unformatted text preview: Theory of Algorithms. Spring 2000. Homework 1 Solutions. Section 1.2 (4) All but the third string are in L * . (5) If L = { a n b n +1 : n } then L 6 = L * . For example, L * but / L . If L = { w : n a ( w ) = n b ( w ) } then L = L * . (6) There are no languages L such that L * = L * . One way to see this is that for any language L , L * but / L * . (8) (a) S BaB B bB | (b) S AaA A aA | bA | (c) S B | BaB | BaBaB | BaBaBaB B bB | (9) L ( G ) = { ( ab ) n | n } . (10) L ( G ) = because there is no way to derive a string that doesnt contain one of the auxiliary symbols S , A , B . (11) (a) S aSb | B B bB | b (b) S aSbb | . (c) S aaaAb A aAb | (d) S aaaA A aAb | (e) S S 1 S 2 S 1 aS 1 b | B B bB | b S 2 aS 2 bb | (f) S S 1 | S 2 S 1 aS 1 b | B B bB | b S 2 aS 2 bb | (g) S S 1 S 1 S 1 S 1 aS 1 b | B B bB | b (h) S SS |...
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This note was uploaded on 07/17/2011 for the course MAD 3512 taught by Professor Staff during the Spring '07 term at University of Florida.

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hwsol1 - Theory of Algorithms. Spring 2000. Homework 1...

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