CS150 HW3
Set April 27
Due May 6 (at 9pm)
Total: 60 pts
Q1 [10 pts] Prove that the following languages are not regular:
(a) {0^n 1^m 2^n | n and m are arbitary (nonegative) integers}
(b) {0^{2n} 1^n | n > 0}
Q2 [10 pts] Prove that the following language (called squares) is not regular:
The set of binary strings of the form ww, that is, the same string repeated.
E.g., 00, 0101, 010010, 011011 are squares but 010, 0011, 0110 are not.
Q3 [10 pts] P. 147 (or P. 146 in 2nd ed) Ex.4.2.3.
If L is a language, and a is symbol, then a\L is the set of ...
You may consult Ex. 4.2.2 for ideas.
Q4 [10 pts] Give an algorithm to tell whether a regular language L
contains at least 100 strings.
Note that you may assume that the regular language is represented
as a DFA, and the pumping lemma constant n is the size of the DFA.
Hint: You may use the algorithm for Ex. 4.3.1 to decide if the
input DFA accepts an infinite language, and focus on the case when
the language is finite.
Q5 [20 pts] P. 165-166 (or P. 164 in 2nd ed) Ex.4.4.2.
Repeat Ex. 4.4.1 for the DFA of Fig. 4.15.