What is the language accepted by a DFA with no states that are drawn as $\circledcirc$ (double circle)? Assume language is $\Sigma = \{0, 1\}$.

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BlackTom AI · Accepted Answer

Question restatement: What is the language accepted by a DFA with no states that are drawn as a double circle (i.e., with no accepting states)? The alphabet is Σ = {0, 1}.

Option a: Strings with an odd number of symbols. This would require at least one accepting state to distinguish odd from even length strings. If there are no accepting states, the machine cannot accept any string, so this option does not hold.

Option b: Strings containing the substring "11". Accepting such a language would again require at least one path that ends in an accepting state after reading a string with "11" somewhere. With no accepting states at all, no string can be accepted, so this option is incorrect.

Option c: ∅ (the empty set). A DFA accepts a string only if the resulting state after processing the string is an accepting state. If no states are accepting (no double circles), then no input string can be accepted, so the language is exactly the empty set. This matches the given description of having no accepting states.

Option d: All strings in the alphabet. This would require that every possible input is accepted, i.e., that every reachable state from the start is accepting or that all computation paths end in accepting states. Since there are no accepting states at all, this cannot be the case, so this option is incorrect.

Summary of reasoning: In a DFA, acceptance requires finishing in an accepting state. If there are no accepting states (no double circles), no input string can be accepted, yielding the empty language. Therefore, options a, b, and d describe nonempty languages that would require at least one accepting state, which contradicts the given condition. Option c correctly reflects the situation where the language accepted is the empty set.

CSC 333 (002) SPRG 2025 MCQ2

What is the language accepted by a DFA with no states that are drawn as \(\circledcirc\) (double circle)? Assume language is \(\Sigma = \{0, 1\}\).

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