T heory of Cornpiit,at,ion
18.404/6.840
Fall. 2001
hlichacl Sipscr
S ample MidTerm Examination Questions
1. (30 points)
( a) (15 point,^) Let A = cfw_a'jc" i j j j 2i).
Prowe t,llat A is not a cont,cxt,-frcc language
( h) (15 point,^) Let B = cfw_a%7 i
18.404/6.840
Theory of Computation
Due by 11:00am sharp, Thursday, September 21, 2006
Michael Sipser
Problem Set 1
Please turn in each problem on a separate page with your name.
NOTE: All problems are from the 2nd edition of the textb ook.
0.1 Read and so
18.404/6.840
Theory of Computation
Due by 11:00am sharp, Thursday, October 5, 2006
Michael Sipser
Problem Set 2 revised version
Please turn in each problem on a separate page with your name.
1. Book, 2.32 . [proving nonCFL]
(Note that the result of this
18.404/6.840
Theory of Computation
Due by 11:00am sharp, Thursday, November 2, 2006
Michael Sipser
Problem Set 4 revised version
Please turn in each problem on a separate page with your name.
1. Book, 7.12 .
[MODEXP P]
2. Book, 7.14 .
[P is closed under s
18.404/6.840
Theory of Computation
Due by 11:00am sharp, Thursday, October 19, 2006
Michael Sipser
Problem Set 3
Please turn in each problem on a separate page with your name.
1. Book, 5.22 and 5.23 . [Trecog i A m ATM and decidable i A m 0 1 ]
2. Book, 5
18.404/6.840 Fall 2006
Theory of Computation
Michael Sipser
FINAL EXAM SAMPLE PROBLEMS and SOLUTIONS
1. For each of the following statements, answer True, False or Open question according to our
current state of knowledge of complexity theory, as describe
Theory of Computation
18.404/6.840
Fall, 2006
Michael Sipser
Sample MidTerm Examination Questions
1. (a) Let = cfw_a, b, c and let A = cfw_ai bj ck | i, j, k 0, and i = j or i = k .
Describe (in English) a pushdown automaton that recognizes A.
(b) Let R
18.404/6.840
Theory of Computation
Due by 11:00am sharp, Thursday, November 16, 2006
Michael Sipser
Problem Set 5
Please turn in each problem on a separate page with your name.
1. Book, 7.24 .
[=SAT is NPcomplete]
2. Book, 7.25 .
[MAXCUT is NPcomplete]
3.