Please note: I may revise any assignment with one week's notice.
Assignment 0, Self-assessment.
All problems are from Sipser: (All six of these are the same in both editions.) If any of the following problems require unfamiliar concepts or are difficult to complete please see the instructor as you may not be prepared to take the course:
- Sipser 0.1 d,e,f
- 0.2 d,e,f
- 0.3 f
- 0.6 e
- 0.7
- 0.8
Assignment 1, due October 6, 2008
Sipser:
- 0.10 [0.10 in 1st edition] (Critique proof)
- 0.11 [0.11] (Horses all same color)
- 1.3 [1.3] (Draw DFA)
- 1.4g [new] (Construct intersection)
- 1.5d [new] (Complement)
- 1.31 [1.24] (Closed under reverse)
- 1.32 [1.25] (Correct sums)
Assignment 2, due October 13, 2008
Sipser:
- 1.16 (b) [1.12(b) in 1st edition]
- 1.21(a) [1.16(a)]
- 1.46(a) [not in 1st edition]
- 1.51 [1.34]
Indistinguishable by L is an equivalence relation.
- 1.52 [1.35] Myhill-Nerode theorem. Please answer in your own words; the 2nd edition contains a sample solution.
Assignment 3, due October 20, 2008
Sipser 2nd edition [first edition]:
- 2.2 [2.2]
- 2.18 [2.17]
- 2.30 a,d [2.18 a,d]
- 2.35 [2.20]
- 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 27, 2008
Sipser 2nd edition [first edition]:
- 3.6 [3.6]
Assignment 5, due November 3, 2008
Sipser 2nd edition
- 3.18 [3.16]
- 4.6 [4.7] (diagonalization, {0,1}^\omega is not countable)
- 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})
- 4.18 [4.18] (any two disjoint co-Turing-recognizable languages are separated by a decidable language)
- 5.13 [5.13]
Assignment 6, due November 10, 2008 (assignment may be revised)
Sipser 2nd edition [1st edition]
- 5.28 [5.22] (Note: sample solution is given in 2nd edition; however collaboration policy applies!)
- 5.30 [not in 1st edition]
- 7.14 [7.13] P closed under star.
- 7.17 [7.17] Almost all of P is NP complete if P = NP
- 7.39 [7.32] Window size in Cook Levin proof
Assignment 7, due November 17, 2008
pdf file [assignment may be revised for this class offering]
Assignment 8, due November 24, 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.
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