Honors Theory of Computation, Spring'00.
HOMEWORK 2:
Out: Jan 31
Due: Feb 7
==================================================
IMPORTANT: you MUST answer each question
within the page limitation specified
(with reasonable size handwriting).
When necessary, summarize the method or arguments.
==================================================
YOU MUST CHOOSE TO HAND IN SOLUTIONS FOR
EITHER QUESTIONS (1) and (2)
OR QUESTION (3).
HOWEVER, I STRONGLY ENCOURAGE YOU TO SOLVE
TO YOUR OWN SATISFACTION THE OTHER
QUESTION(S) THAT YOU DO NOT HAND IN.
==================================================
(1) Solve Problem 2.8.7 (Chapter 2, page 53 of Text)
One page limit.
This concerns a 2-dimensional TM.
(2) Recall the corollary to Theorem 2.6 (page 47) that
if we can decide a language L in nondeterministic
time f then we can decide L in deterministic
time df for some d > 1
Prove the same result, except that we replace the
word ``decide'' by ``accept''.
NOTE: This is illustrates the remark that that ``acceptance
complexity'' and ``decision complexity'' usually have
equivalent theorems.
Half page limit.
(3) Solve Problem 2.8.11 (Chapter 2, page 54)
Two pages limit.
Do only parts (a) to (d).
This concerns Regular Languages, which I assume
you have seen in some previous course (any
undergraduate theory course will have this material).
This is a good chance to review regular languages
(these are favorite topics in exam questions).