# CSCI (Math) 361 Theory of Computation

## Homework Assignments Fall, 1999

Homework is generally assigned two class periods before it is due. Please note that homework is due at the beginning of class and no late homework will be accepted. The two homeworks to be dropped are to cover situations like illness or other circumstances that prevent you from attending class or doing homework.

Due Date To Turn In: To Do On Own: Solutions:
9/15 1.3.5, 1.3.7, 1.6.2 + program 1.3.1abc, 1.3.2a, 1.3.9, 1.6.1, 1.6.5 Solutions 1
9/17 1.4.1, 1.5.2, 1.5.5, 1.5.6 1.4.2ab, 1.5.3, 1.5.7, 1.5.8 Solutions 2
9/20 1.7.2c, 1.7.4ab 1.7.3, 1.7.5, 1.7.6 Solutions 3
9/22 1.8.3ab 1.8.2abcd,1.8.5abcd Solutions 4
9/24 2.1.2d, 2.1.3ad, 2.1.4a(i+ii) 2.1.1, 2.1.2abc, 2.1.3bc Solutions 5
9/27 2.2.2b, 2.2.3ac 2.2.1ab, 2.2.2a, 2.2.4, create ndfa accepting (a U b)*ab+(aaa U aba)b* Solutions 6
9/29 2.2.6, create dfa accepting (a U b)*ab+(aaa U aba)b* 2.2.7, 2.2.9b, 2.2.10 Solutions 7
10/1 2.3.3, 2.3.6ag, 2.3.11a 2.3.1, 2.3.2, 2.3.5, 2.3.6f Solutions 8
10/4 2.3.7b 2.3.4b,2.3.7a Solutions 9
10/6 2.4.3ad, 2.4.4, 2.4.5a, 2.4.8ac 2.4.2,2.4.3bce,2.4.8b Solutions 10
10/8 2.5.2, Find min state dfa equiv to dfa here 2.5.1(i)(iii), both parts a and b Solutions 11
10/11 Describe an algorithm to determine, given M1 and M2, if L(M1) and L(M2) are disjoint. Solutions 12
10/13 3.1.3ab, 3.1.5b,3.1.7 3.1.2, 3.1.3c, 3.1.4, 3.1.5a, 3.1.9ad Solutions 13
10/15 3.2.2 3.2.3,3.2.4b Solutions 14
10/20 3.3.2b,3.3.3 3.3.1,3.3.2acd,3.4.1 Solutions 15
10/25 No homework because of take-home test
10/27 3.5.1ab, 3.5.2cd, show {aibjcidj | i,j >= 0} is not a cfl 3.5.1cd Solutions 16
10/29 3.5.3a, 3.7.5a 3.7.1a Solutions 17
11/1 4.1.5 4.1.1, 4.1.4 Solutions 18
11/3 4.2.1 4.2.2 Solutions 19
11/5 4.3.3 4.3.1a Solutions 20
11/8 4.5.3 4.5.1, 4.5.2 Solutions 21
11/10 4.7.1 (do carefully - no handwaving!) 4.7.2bc Solutions 22
11/12 4.7.3 Solutions 23
11/15 (1) Prove for all n succ n = n+1. (2) Prove for all m, n, Plus m n = m+n. (Use induction on m.) Solutions 24
11/17 Define monus in the lambda calculus. Define rem(m,n) in the lambda calculus. Solutions 25
11/19 None: Midterm 2 due
11/29 5.4.1 5.4.2a-d Solutions 26
12/1 5.4.3, 5.7.7e Solutions 27
12/3 Let G be cfg. Show L(G) is infinite iff there is a w in L(G) s.t. n<=|w|<2n, where n is the number given by the pumping lemma. Solutions 28
12/6 5.4.2eh Solutions 29
12/8 Show the computation of Ref(r,w,i) | client(r,w,v). Show the interference that can occur when running Ref(r,w,i) | client(r,w,v) | client(r,w,v'), i.e., show the client sending v can actually get back v'.