Syntax error Find the regular expression for the given Finite automata with state elimination method

Find the regular expression for the given Finite automata with state elimination method

Problem

Generate RE for a given finite automata by using the state elimination method.

Solution

There are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE).

  • Arden's Theorem Method.
  • State Elimination Method.

The given automata is as follows−

Step 1

Initial state is A that has an incoming edge.

So, we have to create a new initial state qi as follows−

Step 2

Initial state is B that has an incoming edge.

So, we have to create a new final state qf as given below−

Step 3

Now, try to eliminate all intermediate states one by one.

First eliminate state A

There is a path from state qi to B via A.

So, after eliminating state A, we can connect a direct path from qi to B having cost.

ε.0=0

There is a loop on state B using State A.

So, after eliminating state A, we can draw a direct loop on state B having cost.

1.0=10

After eliminating A, we get the following −

Step 4

Now eliminate State B

There is a path from state qi to qf via state B.

So, after eliminating B, we can draw a direct path from qi to state qf having cost

0.(10)* ε=0(10)*

Final Regular Expression is = 0(10)*

Updated on: 2021-06-11T12:58:59+05:30

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