James A. Foster

Course Details for CS490

Homework
bullet Homework 8, due last class: 12.1, 12.3, 12.5, and 14.1a.
bullet Homework 7, due LN 39 (6 Dec): 9.15 a,b,f; 9.33; 9.37. Here are the answers: page 1, page 2, page 3
bullet Homework 6, due LN 31 (13 Nov): 9.1; 9.2 a,b; 9.4 a,b; 9.14; 9.7. Here are the answers: page 1, page 2, page 3, page 4
bullet Homework 5: 7.3; 7.5a,c (diagrams only); 7.6; 7.11; 7.14; 7.24; 8.1 a,c,b; 8.2. Here are the answers: page 1, page 2, page 3, page 4, page 5, page 6, page 7, page 8.
bullet Homework 4, due LN 25 (30 Oct): 6.1; 6.4; 6.11; 6.17 a,b,c; 7.1; 7.2; 5.35 b,e,f; Find context free grammars for La union Lb, LbLc, and Lb* where Lx is the language described in 6.1x. Here are the answers: page 1, page 2, page 3, page 4, page 5, page 6, page 7.
bullet Homework 3, due LN 22 (20 Oct): 5.1; 5.24 a,b,c; 5.25 a,b; 5.27 a,b,c; 5.30 a (a,b,c), b; 5.34 a,c,d,e; 5.35 a,d,g. Here are the answers: page 1, page 2, page 3, page 4, page 5, page 6.
bullet Homework 2, due LN 16 (4 Oct): 4.40 a,b; 4.33; 4.35; 3.30; 3.31; 3.32. Here are the answers: page 1, page 2, page 3, page 4, page 5.
bullet Homework 1, due LN 13 (27 Sept): 4.1; 4.14; 4.31; 4.32; 4.39; 3.41; 3.1; 3.2.  Here are the answers: page 1, page 2, page 3, page 4, page 5, page 6, page 7, page 8, page 9, page 10, page 11, page 12, page 13.

Scores
HW 1

HW 2

Grade Score Grade Score
A 100-84 A 70-58
B 83-67 B 57-45
C 66-50 C 44-32
D 49-33 D 31-20
F 32-0 F 19-0
Average 73.4 Average 54.8
Std Dev 15.6 Std Dev 11.9

Remember, homework grades will only be used as a "tie breaker" if your test scores

Tests

Tests for this semester

Here are solutions to the first version of test 1 (pdf) and the second version of test 2 (pdf)--there were two versions.

Grades for Tests
Test
Grade Score 1 2 3
A 100-110
B 90-99
C 80-89
D 70-79
F 60-0
Average
Std Dev
Final grades
Grade Score Distribution
A
B
C
D
F
Average
Std Dev

Old Tests

Beware. There are errors in some answers on old tests (due to changes in include files before formatting them for the web). 
bullet 1996 Test 1 (in pdf format)
bullet 1996 Test 2 (in pdf format)
bullet 1996 Test 3 (in pdf format)
bullet 1994 Test 1 (in pdf format)
bullet 1994 Test 2 (in pdf format)
bullet 1994 Test 3 (in pdf format)
bullet 1992 Midterm Examination (in pdf format)
bullet 1992 Final Examination (in pdf format)
bullet 1990 Final Examination (in pdf format)

Old Homework

See old webpages (Fall 1996, Fall 1994).

Here is homework from Fall 1996:

Homework 1: 4.3, 4.4, 4.5, 4.10, 4.15, 4.17, 4.19 (note that this is identical to Homework 2 (pdf) from 1994, which is where the solutions are). Some other good exercises to try: 

  1. Prove that the class of regular languages is closed under union and kleene star. Try doing this for intersection and difference. 
  2. Prove that the class of finite sets is closed under union, intersection, and difference, but not under kleene star. 
Homework 2 (Due Lecture 15, 30 Sept): 5.1, 5.2, 5.4, 5.12, 5.15, 5.17; 6.6, 6.7, 6.8 (note that this is identical to Homework 3 (pdf) from 1994, which is where the solutions are). Some other good exercises to try: 
  1. Formulate the idea of a team DFA, which is a finite set of DFAs which accepts when at least one member of the team accepts. Can team DFAs compute more than individuals? (Does teamwork help?) Can individuals compute more? (Is rugged individualism better than teamwork?) 
  2. Formulate the idea of a multstart DFA, which is a DFA with (possibly) more than one start state. How does it compare with the other variations? 
  3. Formulate the idea of a unique accepting DFA, which is a DFA with a single accepting state. How does it compare with the other variations? 
Homework 3 (Due Lecture 18, 7 October): 7.10, 7.11, 7.12, 7.14, 8.1, 8.2, 8.4, 8.6 (note that this is identical to Homework 4 (pdf) from 1994, which is where the solutions are). Some other good exercises to try: 
  1. The {\em regular expression equivalence} problem is: given two regular expressions A and B, determine whether or not they are equivalent (that is, LA=LB). Is this problem solvable (in the intuitive sense that you could come up with an algorithm for it)? 
  2. Consider an infinite complete binary tree, with left branches labeled 0 and right branches labeled 1. There is an obvious one to one correpondence between the nodes in this tree and the binary words. For example, the root corresponds to lambda; by going right, left, left, right you get to the node for 1001; and so on. Notice that, for any language L, you can partition this tree into disjoint trees where all the nodes in each partition are indistinguishable wrt to L. Try this with a regular and with a non-regular language. How does this observation relate to the Myhill-Nerode theorem? 
Homework 4 (Due Lecture 23, 18 October): 9.4b, 9.11 a,c, 9.12 acfi, 9.15, 9.18 1de (note that this is identical to Homework 5 (pdf) from 1994, which is where the solutions are). Here is an interesting question to think about: 
  1. Which is a more intuitively appealing way to define languages which have recognition algorithms---expressions, grammars, or automata? 
  2. Can you come up with a more general type of grammar than the ones we see in Chapter 9? (Don't look ahead first!) Describe the languages which can be generated by your more general grammar informally, then formally (eg., give a definition for it, like that for context free languages.) 
Homework 5 (Due Lecture 27, 30 October): 12.3, 12.5ab, 12.6ab, 12.12; 13.1b; 15.1ac, 15.2ac (note that this is identical to Homework 6 (pdf) from 1994, which is where the solutions are). Here is some interesting questions to think about: 
  1. Suppose you have two stacks on your NPDA. Can you recognize any languages that you cannot recognize with one stack? If so, how do you do it? 
  2. Suppose you have three stacks on your NPDA. Can you recognize any languages that you cannot recognize with two stacks? How about four, or five, or six stacks? Can you generalize from this? 
  3. Suppose you have a DPDA with two stacks. How does the ability of this model to recognize language compare to the other variations of PDA? 
Homework 6 (Due Lecture 33, 13 November): 16.3ae, 16.6a, 16.9ce, 17.1, 17.5, 17.12, (look at 17.9,10) (note that this is identical to Homework 7 (pdf) from 1994, which is where the solutions are). 

Homework 7 (Due Lecture 38, 4 December): 18.3, 18.5, 18.7, 18.12, 20.1, 20.2, 20.4) (note that this is identical to Homework 8 (pdf) from 1994, which is where the solutions are).

Here is the suggested homework and solutions from 1994:
bullet Homework 1 (pdf): 3.2,3.6.3.9 b,c,e,h, 3.1 
bullet Homework 2 (pdf): 4.3, 4.4, 4.5, 4.10, 4.15, 4.17, 4.19 
bullet Homework 3 (pdf): 5.1, 5.2, 5.4, 5.12, 5.15, 5.17; 6.6, 6.7, 6.8 
bullet Homework 4 (pdf): 7.10, 7.11, 7.12, 7.14, 8.1, 8.2, 8.4, 8.6 
bullet Homework 5 (pdf): 9.4b, 9.11 a,c, 9.12 acfi, 9.15, 9.18 1de 
bullet Homework 6 (pdf): 12.3, 12.5ab, 12.6ab, 12.12; 13.1b; 15.1ac, 15.2ac 
bullet Homework 7 (pdf): 16.3ae, 16.6a, 16.9ce, 17.1, 17.5, 17.12, (look at 17.9,10) 
bullet Homework 8 (pdf): 18.3, 18.5, 18.7, 18.12, 20.1, 20.2, 20.4 
bullet Homework 9 (pdf): 23.2, 23.14, 23.15, 23.16, (try 23.6) 
bullet Homework 10: Practice with oracles and NP

Newsgroups

bullet uidaho.cs.theory
bullet comp.theory
bullet sci.logic
 

Last Updated 01/13/2003 15:56 -0800