Product Construction for Intersection (L1 ∩L2 )
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Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
The **Product Construction for Intersection** is a formal method to prove that if two languages, $L_1$ and $L_2$, are regular, then their intersection ($L_1 \cap L_2$) is also regular. It achieves this by constructing a new Deterministic Finite Automaton (DFA) that simulates the parallel operation of two original DFAs (one for $L_1$ and one for $L_2$). The new DFA accepts a string if and only if *both* original DFAs would accept it, meaning the string belongs to both $L_1$ and $L_2$. Its states are pairs of states from the original DFAs, and a state is accepting only if both components of the pair are accepting states.