Explanation:

NFA (Non-Deterministic Finite Automata) and DFA (Deterministic Finite Automata) are two types of finite automata used in computer science to recognize regular languages. The main difference between the two is that NFA can have multiple transitions for a single input symbol while DFA has only one transition for a single input symbol.

Statement: If K is the number of states in NFA, the DFA simulating the same language would have states less than 2k.

This statement is true. The reason behind this is that in NFA, a state can have multiple transitions for a single input symbol, whereas in DFA, a state can have only one transition for a single input symbol. Therefore, the number of states in DFA would be less than or equal to the number of states in NFA.

Let's take an example to understand this statement better.

Example:

Consider an NFA with K states. Let's say the language recognized by this NFA is L. Now, we need to construct a DFA that simulates the same language L.

To construct a DFA, we need to follow the subset construction algorithm. In this algorithm, we start with the initial state of the NFA and find the set of all possible states that can be reached from this state for each input symbol. We repeat this process for all the sets until we get all the possible sets of states in the DFA.

Now, the number of states in DFA would be equal to the number of possible sets of states in the DFA. The maximum number of possible sets of states in the DFA would be 2^K (as each state in NFA can be either present or absent in each set). However, some of these sets may be unreachable or redundant. Hence, the actual number of states in DFA would be less than or equal to 2^K.

Therefore, the statement "If K is the number of states in NFA, the DFA simulating the same language would have states less than 2K" is true.

Conclusion:

In conclusion, the statement "If K is the number of states in NFA, the DFA simulating the same language would have states less than 2K" is true. The reason behind this is that the number of states in DFA would be less than or equal to the number of states in NFA due to the deterministic nature of DFA.