Mechanics Syllabus Assignments Supplemental CS 581: Fall 2010

### Assignments

#### Assignment 0, due at Lecture 2

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:

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 at Lecture 3

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 Lecture 5

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] Indistinguishable by L is an equivalence relation.
5. 1.52 [1.35] Myhill-Nerode theorem. Please answer in your own words; the 2nd edition contains a sample solution.

Assignment 3, due Lecture 7

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 Lecture 9

Sipser 2nd edition [first edition]:

1. 3.6 [3.6]

Assignment 5, due Lecture 13

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 Lecture 15 (may be supplemented)

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]

Assignment 7, due Lecture 17

New assignment 7: primrec.pdf MY.hs NaturalPR.hs

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

Assignment 8, due Lecture 19

Here is the updated pdf file.

Tim Sheard's calculator is http://hackage.haskell.org/package/LambdaCalculator