Automata Theory - Quiz II

K. Subramani LCSEE, West Virginia University, Morgantown, WV {ksmani@csee.wvu.edu}

1 Instructions

1. Attempt as many problems as you can. You will be given partial credit.

2 Problems

1. Let L_{1} and L_{2} be 2 regular languages, over the same alphabet Σ and let them be respectively represented by DFAs A_{1} and A_{2}. Discuss a strategy by which you could check whether there is a string in Σ^{∗}, that is neither in L_{1} nor in L_{2}. (3 points)

2. Consider the grammar G = ({S}, {a, b}, P, S), where P is defined as the following set of rules:

S → aSbS | bSaS | ϵ

Argue using mathematical induction, that L(G) is the set of all strings with an equal number of a′s and b′s. (4 points)

3. Write a CFG for the following language: L = {a^{i}b^{j}| i, j ≥ 1, j = i + 1}. (3 points)