Final answer:
The student is asking for an NFA that recognizes strings containing either an even number of 0's or exactly two 1's over the alphabet {0,1}. An NFA that satisfies these conditions would have separate branches for each: one tracking the number of 0's and another counting the number of 1's, with appropriate accept states for each. A detailed state diagram cannot be provided due to format restrictions, but the conceptual approach to designing such an NFA is described.
Step-by-step explanation:
The student's question pertains to constructing a state diagram for a nondeterministic finite automaton (NFA) that recognizes the language A, where A consists of strings over the alphabet {0,1} that either contain an even number of 0's or exactly two 1's. To design this NFA, one could create separate branches for each condition (an even number of 0's and exactly two 1's) and merge them such that if either condition is met, the NFA accepts the string.
For the even number of 0's, we can construct a loop between two states that switch with each occurrence of 0, starting and ending with an accept state. For the condition of exactly two 1's, we can create a series of transitions that count the number of 1's and enter an accept state after the second 1 is read, while any subsequent 1 would lead to a dead state. Since an NFA can be in multiple states at once, we structure it in a way to accept strings that satisfy either condition.
Unfortunately, due to the format restriction, I cannot depict the state diagram here. However, I can describe the process: one could imagine states q0, q1, and q2 where q0 and q2 are accept states for the even number of 0's condition. For the two 1's condition, we might use states q0, r1, and r2, where r2 is an accept state, and any further 1's from r2 would transition to a non-acceptance trap state. Transitions will happen from q0 to r1 on input 1, then from r1 to r2 on the next input of 1, and between q0 and q1 on input 0, back and forth to account for an even number of 0's.