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Are regular languages regular under reunion?

User Mike Moore
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Final answer:

Regular languages are closed under the union operation, which means the union of two regular languages is also a regular language, confirmable by constructing a finite automaton that recognizes the union.

Step-by-step explanation:

Yes, regular languages are closed under the operation of union (reunion).

In other words, if you have two regular languages, their union will also be a regular language.

This is one of the closure properties of regular languages in formal language theory, a subject studied in computer science.

To provide an example, let's say you have two regular languages L1 and L2.

Representing each with their respective finite automata, you can construct a new finite automaton that recognizes L1 ∪ L2 simply by introducing a new start state that non-deterministically transitions to the start states of the automata for L1 and L2.

The resulting automaton will accept a string if it belongs to either L1 or L2, hence recognizing the union of the two languages.

User Saturnian
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