Final answer:
Designing a DFA or NFA to accept binary strings divisible by 3 requires tracking remainders, and it is not feasible to create a two-state DFA or a three-state NFA for this purpose. A four-state DFA or a five-state NFA could be designed with each state corresponding to the remainders of division by 3 and an appropriate error state.
Step-by-step explanation:
The question requires the design of deterministic finite automata (DFA) and nondeterministic finite automata (NFA) that accept binary strings representing numbers divisible by 3. Designing such automata involves understanding the concepts of state transitions based on input symbols and how these transitions relate to the divisibility of binary numbers.
Design DFA with Two States:
It is not possible to design a DFA with only two states that accepts binary strings divisible by 3. This is because we need to track the remainder when dividing by 3, and there are 3 possible remainders (0, 1, 2), which necessitates at least three states.
NFA with Three States:
Similarly, it is challenging and nonintuitive to create an NFA with exactly three states for this language. The complexity arises from having to track remainders as mentioned before, and three states would not provide enough differentiations between the remainders of the number being divided by 3.
DFA with Four States:
This is a more plausible scenario. A DFA designed to accept binary strings divisible by 3 would need one state for each remainder (0, 1, 2) and an additional error state for the cases where input doesn't start with a proper binary digit. State transitions are then determined by the addition of each binary digit to the current total.
NFA with Five States:
An NFA can be more flexible than a DFA, allowing for multiple transitions for each input symbol. A five-state NFA could have extra states to allow for nondeterministic choices that eventually lead to an accept state if the string represents a number divisible by 3.