Mechanics Syllabus Assignments Supplemental CS 581: Spring 2008

### Assignments

#### Assignment 0, due April 2, 2008

All problems are from Sipser: (All six of these are the same in both editions.)

1. Sipser 0.1 d,e,f
2. 0.2 d,e,f
3. 0.3 f
4. 0.6 e
5. 0.7
6. 0.8

Assignment 1, due April 7, 2008

Sipser:

1. 0.10 [0.10 in 1st edition] (Critique proof)
2. 0.11 [0.11] (Horses all same color)
3. 1.3 [1.3] (Draw DFA)
4. 1.4g [new] (Construct intersection)
5. 1.5d [new] (Complement)
6. 1.31 [1.24] (Closed under reverse)
7. 1.32 [1.25] (Correct sums)

Assignment 2, due April 14, 2008

Sipser:

1. 1.16 (b) [1.12(b) in 1st edition]
2. 1.21(a) [1.16(a)]
3. 1.46(a) [not in 1st edition]
4. 1.51 [1.34]

Assignment 3, due April 21, 2008

Sipser 2nd edition [first edition]:

1. 2.2 [2.2]
2. 2.18 [2.17]
3. 2.30 a,d [2.18 a,d]
4. 2.35 [2.20]
5. 2.22 [2.26] Hint: Focus on how two strings can be different. Two strings can be different if they are different lengths, or if there is some corresponding position where they differ. Your solution only needs to find a single difference. I have seen understandable solutions that use either a PDA or a grammar to define the language. As a warm up problem it may be useful to find a description for w#x#y#z such that |w| = |y|.

Assignment 4, due April 28, 2008

Sipser 2nd edition [first edition]:

1. 3.6 [3.6]

Assignment 5, due May 5, 2008

Sipser 2nd edition

1. 3.18 [3.16]
2. 4.6 [4.7] (diagonalization, {0,1}^\omega is not countable)
3. 4.17 [4.17] (C is Turing-recognizable if there is a decidable language D such that C = {x| \exists y . <x,y> \in D})
4. 4.18 [4.18] (any two disjoint co-Turing-recognizable languages are separated by a decidable language)
5. 5.13 [5.13]

Assignment 6, due May 12, 2008 (assignment may be revised)

Sipser 2nd edition [1st edition]

1. 5.28 [5.22] (Note: sample solution is given in 2nd edition; however collaboration policy applies!)
2. 5.30 [not in 1st edition]
3. 7.14 [7.13] P closed under star.
4. 7.17 [7.17] Almost all of P is NP complete if P = NP
5. 7.39 [7.32] Window size in Cook Levin proof

Assignment 7, due May 19, 2008

pdf file [assignment may be revised for this class offering]

Assignment 8, due May 28, 2008

pdf file (note: A sample solution for an earlier version of this assignment is available here; however the collaboration policy applies!)

New! Supplemental assignment pdf file.