Mechanics Syllabus Assignments Supplemental

### Assignments

#### Assignment 0, due September 29, 2005

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 October 4, 2005

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 October 11, 2005

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]
5. 1.52 [1.35] (Please answer in your own words; the 2nd edition contains a sample solution.)

Assignment 3, due October 18, 2005

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 October 25, 2005

Sipser 2nd edition [first edition]:

1. 3.6 [3.6]

Assignment 5, due November 1, 2005

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 November 15, 2005

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 November 22, 2005

pdf file

Assignment 8, due December 1, 2005

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