CS 162  Automata Theory Homework 5, 25 Points
Due: Friday, February 17, 11:55pm

5 points.
Problem 2.26 in Sipser.

5 points.
Problem 2.31 in Sipser.

5 points.
Problem 2.32 in Sipser.

5 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

5 points.
In general, the intersection of two contextfree languages is not
a contextfree language,
as we showed in class. But sometimes it is.
Let L be the set of all strings of the form
a^{i}b^{j}c^{n}d^{m},
where i is greater than or equal to j
and n is greater than or equal to m,
and all of i, j, n, and m are at least 1.
Let M be the set of all strings of the form
a^{i}b^{j}c^{n}d^{m},
where i is less than or equal to j
and n is less than or equal to m,
and all of i, j, n, and m are at least 1.
Show that L, M, and the intersection of L and M are all contextfree languages.