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Is it true that if a language is undecidable, then it must be infinite?
Yes, it is true that if a language is undecidable, then it must be infinite.
Is it true that if a language a is regular and language b reduces to a, then language b is also regular?
No, it is not necessarily true that if language A is regular and language B reduces to A, then language B is also regular.
How can you prove that the complement of a regular language is regular?
The complement of a regular language is regular because regular languages are closed under complementation. This means that if a language is regular, its complement is also regular.
What is the complement of a regular language and how does it relate to the concept of regular expressions?
The complement of a regular language is the set of all strings that are not in the original language. In terms of regular expressions, the complement of a regular language can be represented by negating the regular expression that defines the original language.
How can you prove that the reverse of a regular language is regular?
The reverse of a regular language is regular because for every string in the original language, there exists a corresponding string in the reversed language that is also regular. This is because regular languages are closed under the operation of reversal, meaning that if a language is regular, its reverse will also be regular.
