Question:
Suppose a language \(L_1\) has 2 states and \(L_2\) has 2 states. After using the cross product construction method, we have a machine \(M\). The total number of states in \(M\) are
Suppose a language \(L_1\) has 2 states and \(L_2\) has 2 states. After using the cross product construction method, we have a machine \(M\). The total number of states in \(M\) are
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Cross Product Construction:
If DFA\(_1\) has \(m\) states and DFA\(_2\) has \(n\) states,
then product DFA has
\[
m\times n
\]
states.
Updated On: Jun 25, 2026
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The Correct Option is B
Solution and Explanation
Concept:
Cross-product construction is used when combining two finite automata.
If
\[
M_1
\]
has \(m\) states and
\[
M_2
\]
has \(n\) states, then the product automaton contains
\[
m\times n
\]
states.
Step 1: Write the formula.
Number of states in product machine: \[ m\times n \]
Step 2: Substitute values.
Given: \[ m=2,\quad n=2. \] Hence \[ 2\times2=4. \]
Step 3: Determine the result.
The machine obtained after cross-product construction contains \[ 4 \] states.
Step 4: Write the answer.
Therefore, \[ \boxed{4} \] Hence option (B) is correct.
Step 1: Write the formula.
Number of states in product machine: \[ m\times n \]
Step 2: Substitute values.
Given: \[ m=2,\quad n=2. \] Hence \[ 2\times2=4. \]
Step 3: Determine the result.
The machine obtained after cross-product construction contains \[ 4 \] states.
Step 4: Write the answer.
Therefore, \[ \boxed{4} \] Hence option (B) is correct.
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