CSCI (Math) 361

Due Date  To Turn In:  To Do On Own:  Solutions: 

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 ad, 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 ac, 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 dg  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 
11/58  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 2way 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 