CS 162  Automata Theory Homework 5, 50 Points
Due: Friday, February 23, 11:55pm

10 points.
Consider the following grammar:
S > AB  BC
A > BA  a
B > CC  b
C > AB  a
Show the table that results from running the CYK algorithm discussed
in class to CFG membership for each of the following strings (and say
whether or not the string is in the language generated by the CFG above):
(a) baaab
(b) aabab

10 points.
Exercise 3.2(d,e) in Sipser.

10 points.
Exercise 3.8(b) in Sipser.

10 points.
Give a highlevel description of a Turing machine for deciding
the language of all strings of the form
a^{n}b^{n}c^{n}, where n is at least 1.

10 points.
Give a highlevel description of a Turing machine for deciding
the language of all strings of the form
a^{i}b^{j}, where j = i^{2} and i is at least 1.