Question

Converting a DFA such as the one below to a regular expression requires 0/1 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 below, determine the languages for the following limitations: 1.LAA = the set of path labels that go from A to A without passing through C or D. 2. LAB = the set of path labels that go from A to B without passing through Cor D. 3.LBA = the set of path labels that go from B to A without passing through C or D. 4.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. А B 0 0 0 BA = (01+0)* LAB = (0+10+01)*1 LAA = (0+1 (10)*0) LBA = 0(0+10)*

Answer 1

The correct option is (d)

LBA = 0(0+10) *

Here (0+10) * means 0 or more occurrence of 0 or 10.

Here let's say (0+10) doesn't exist.

Then there is transition from B on 0 which leads to A.

Now take it one occurrence.

So, 0(0+10 ) => 00 + 010

Either on 00 or 010 , the final state would be A if the initial state is B.

Let's take 2 occurrence of (0+10) *

=> 0(0+10) (0+10)

= (00+010) (0+10)

= 000 + 0010 + 0100 + 01010

On each of this symbol, the final state has to be A of initial state is B.

Thus the option D is correct by correctly examining it.

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