Converting a DFA such as the following: to a regular expression requires us to develop regular expressions for limited sets of paths --- those that take the automaton from one particular state to another particular state, without passing through some set of states. For the automaton above, determine the languages for the following limitations: LAA = the set of path labels that go from A to A without passing through C or D. LAB = the set of path labels that go from A to B without passing through C or D. LBA = the set of path labels that go from B to A without passing through C or D. LBB = the set of path labels that go from B to B without passing through C or D. Then, identify a correct regular expression from the list below. Note: there are several different regular expressions possible for each of these languages. However, each of the correct answers can be thought of as built from more limited components. For example, the regular expression 1 is the set of path labels that go from A to B without passing through any of the four states.

		a)	LBA = (00*1+10)*0
		b)	LAB = 0*1(00*1)*
		c)	LBB = (0*1)*
		d)	LBA = 0(00*10)*