**RGPV PYQ 2010**

**Ans. ** If a transition leads to a state from which it can never escape. such a state is called a trap state.

Trap state is also known as Dead state.

For example:

In DFA below, state C is a trap state.

From C no input is going to another state.

## Q1.: What is a trape state in an automaton?

**Ans:** A trape state is a state in a finite automaton that cannot transition to any other state, but is not an accepting state. It is also known as a dead state or a sink state.

## Q2: Why do we need trape states in an automaton?

**Ans:** Trape states are used to ensure that the automaton always has a transition for every input symbol. They can be used to simplify the design of the automaton and make it more efficient.

## Q3: How do you identify trape states in an automaton?

**Ans:** Trape states can be identified by looking at the transitions from each state in the automaton. If a state has no outgoing transitions for any input symbol, and is not an accepting state, then it is a trape state.

## Q4: How do you handle trape states in automata?

**Ans:** One way to handle trape states is to remove them from the automaton. This can be done by merging them with another state, or by creating a new accepting state that transitions to the trape state for all input symbols. Another way to handle trape states is to leave them in the automaton and treat them as special cases in the implementation of the automaton.

## Q5: Can an automaton have more than one trape state?

**Ans:** Yes, an automaton can have more than one trape state.

## Q6: How do trape states affect the complexity of an automaton?

**Ans:** Trape states can increase the number of states in an automaton, which can increase the complexity of the automaton. However, they can also simplify the design of the automaton by ensuring that it always has a transition for every input symbol.

## Q7: How do you minimize an automaton with trape states?

**Ans:** To minimize an automaton with trape states, we can use an algorithm such as Hopcroft’s algorithm or Moore’s algorithm. These algorithms group together states that are indistinguishable and create a new automaton with fewer states.

## Q8: Can a trape state be an accepting state?

**Ans:** Yes, a trape state can be an accepting state if it is the only accepting state in the automaton. However, if there are other accepting states in the automaton, a trape state cannot be an accepting state.