CSCI (Math) 361
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Due Date | To Turn In: | To Do On Own: | Solutions: |
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9/15 |
Write a program that has the following behavior: Given a string of a's
and/or b's, output "accept" if the string ends with the sequence "a, 1 or
more b's, aaa or aba, 0 or more b's"; output "reject" otherwise. You must process the string in the forward direction. You may not use any of the pattern matching capabilities of any language. |
none | Explanation, Program. |
9/17 | 1.2.3, 1.3.4, 1.3.5, 1.3.9 | 1.3.1 (for the composition of R and R), 1.3.2a for S only, 1.3.7 | Solutions |
9/20 | 1.4.2 a and b, 1.5.1, 1.5.6, Prove that the set of all real numbers is uncountable. | 1.4.1, 1.5.3, 1.5.7, 1.5.8 | Solutions |
9/22 | 1.6.2, 1.7.2 c, 1.7.3 | 1.6.1 c, d, e, 1.6.5 | Solutions |
9/24 | 1.7.4 b, 1.7.6, 1.8.2 a-d, 1.8.3 a, b | 1.7.4 a, 1.7.5 b, c, 1.8.5 | Solutions |
9/27 | 2.1.2 d (give reg expr), 2.1.3 c, 2.1.4 a(i), 2.1.4 b(i,ii,iii,v) | 2.1.1, 2.1.2 a-c, 2.1.3 b and d, 2.1.4 a(ii) | Solutions |
9/29 | 2.2.2, 2.2.3 c and d, Given M, an NFA, prove that (q,xy)|-*(p,y) iff (q,x)|-*(p,e). [Follow proof done in class.] | 2.2.1, 2.2.3 a and b | Solutions |
10/4 | 2.2.6, 2.2.10 | 2.2.7, 2.2.9. Also give an NFA that accepts the language (a | b)* a b+ a (a | b) a b*, and find an equivalent DFA. [Note that this was the language for which you implemented an acceptor in HW1.] | Solutions |
10/6 | 2.3.3 [Give the construction and the proof of correctness.] | 2.3.1, 2.3.2, 2.3.5, 2.3.6 a and f, 2.3.10 | Solutions |
10/8 | none | 2.3.4, 2.3.7 b [from left to right, label states 2, 1, 3] | Solutions |
10/13 | 2.4.3 a, c, f, 2.4.5 a, 2.4.8 a, b, c | 2.4.2, 2.4.3 d, e, 2.4.4, 2.4.7, 2.4.8 d-g | Solutions |
10/20 | minimize the DFA given in class | Solutions | |
10/22 | 3.1.4, 3.1.7 [Make a claim about what L(G) is and then prove it; then show that L(G) is regular.], 3.1.9 a and d | 3.1.2, 3.1.3, 3.1.5 | Solutions |
10/25 | 3.1.10 c, d [give constructions and sketch pf of correctness] | 3.1.10 a | Solutions |
10/27 | none | 3.2.2, 3.2.3, 3.2.4b | Solutions |
10/29 | 3.3.2 b, 3.3.3 (see class notes for explanation) | 3.3.1 (see class notes for typo in text), 3.3.2 a, c, d | Solutions |
11/1 | Handout | 3.4.1 | Solutions |
11/3 | 3.5.1 a and b, 3.5.3 a | 3.5.1 c, d, e | Solutions |
11/5-8 | 3.5.2 c, 3.5.8, 3.5.14 b | 3.5.2 d, 3.5.7, 3.5.14 a, c | Solutions |
11/10 | none | 3.7.5 a | |
11/15 | 4.1.4, 4.1.7 | 4.1.1, 4.1.2, 4.1.3, 4.1.5 | Solutions |
11/17 | none | 4.1.8, 4.1.9, 4.1.10 | Solutions |
11/19 | 4.2.1, 4.2.2, 4.2.3 | none | Solutions |
11/22 | 4.3.1 a, Let M be a Turing Machine with 2-way infinite tape. Define the relation |- formally, as was done for standard Turing Machines. | 4.3.3 | Solutions |
11/29 | 4.5.1 a, 4.5.3 | 4.5.1 b, 4.5.2 | Solutions |
12/6 | 5.3.3 (don't do Kleene *; give deterministic constructions) | 5.3.2 | |
12/8 | 5.4.1 b, 5.4.2 a and d | rest of 5.4.1 and 5.4.2 | Solutions |