Product Construction for Union (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 Union** is a formal method demonstrating that if two languages, L1 and L2, are regular, then their union (L1 U L2) 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 L1 and one for L2). The new DFA accepts a string if and only if *at least one* of the original DFAs would accept it, meaning the string belongs to L1 OR L2 (or both). Its states are pairs of states from the original DFAs, and a state is accepting if at least one component of the pair is an accepting state.