Does an algorithm exist which can determine whether one regular language matches any input another regular language matches?

Question

Let\'s say we have regular expressions:

• Hello W.*rld
• Hello World
• .* World
• .* W.*

I would like to minimize the number

Answer 1

Yes.

The problem of equivalence of two regular languages is decidable.

Sketch of an algorithm:

• minimize both DFAs
• check if they are isomorph