HW2 Outline solution and grading notes

Question 1. Problem 2.8.7

(a) (5 points)
	Definition of transition function of 2-D Turing machine
	
	This should be a simple answer, but some students complicate this
by anticipating the question of part (b).  That is, they
define "configuration" in terms of a string.  But of course,
the natural definition should be in terms of a matrix.
Otherwise, describing how to update "string configurations"
using the delta transition functions is a mess! 

(b) (15 points)
	Simulate a 2-D Turing machine with a 3-tape Turing machine
	in quadratic time.


Question 2 (10 points)
	Reprove corollary to Theorem 2.6 using "accepting complexity"
	instead of "decision complexity".


Question 3.

(a) 4 points: show that constant space languages are accepted
	by 2-way finite automata.

(b) 2 points: show a particular language is regular.

(c) 8+2 points: show that L is regular iff it has finitely
	many equivalence classes.  Give the number of
	equivalence classes in the language in (b).

(d) 14 points: show that 2-way finite automata accept only
	regular languages.