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hwsol2 - Theory of Algorithms Spring 2000 Homework 2...

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Unformatted text preview: Theory of Algorithms. Spring 2000. Homework 2 Solutions. Section 2.1 (1) 0001, 01001 are accepted. 0000110 is not. (2) (a) b E u a, b b ca E (c) (b) ca E b c E a (d) aQ E ca E a ‡b E j c a a a ‡ bE E w a E b ca E a, b b ca E ca E c a, b c a, b cb E a b b ca E E cb E ‡b E a b b a, b c a, b cE b c (6) L(M ) = { bn abm : n, m ≥ 0 } ∪ { bn abm awb : n, m ≥ 0, w ∈ {a, b}∗ } = the set of all strings w ∈ {a, b}∗ such that w has at least one a, and if w has more than one a, then w ends with a b. (7) (a) E a,E b E a, b E ‰ a, b (d) a y a, b E (b) a, b a,E b E (c) a,E b a, b (e) aE T b T T b b b© a E a a E b T T b babb T % a Ex E aE © b We did this in class. ‰ 1 b E‡a E ‡a Ex i a a E a b (9) (a) (b) 1 E 1 c0 E i c0 E 0 0,1 0E c E 1 0 Q j 1 1 c 1s ‡ i0 0s }1 T 1# 0 (11) 0 a ab Wa T b bE a~ a a E %E b T bab C s E b ‚ a E aE a b‰b j bs C aE b T bs b b bE CE a T a b Ca s T a ” E b E b b oa a as C j 'b T a 2 (c) (d) These two take up too much space. I’ll do them in class. ...
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hwsol2 - Theory of Algorithms Spring 2000 Homework 2...

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