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Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,

• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as

  • intersection,
  • complement,
  • homomorphism,
  • reversal,
  • left- or right-quotient,
  • regular transduction

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.

Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,

• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as

  • intersection,
  • complement,
  • homomorphism,
  • reversal,
  • left- or right-quotient,
  • regular transduction

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.

Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,

• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as

  • intersection,
  • complement,
  • homomorphism,
  • reversal,
  • left- or right-quotient,
  • regular transduction

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.

Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,

• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as

  • intersection,
  • complement,
  • homomorphism,
  • reversal,
  • left- or right-quotient,
  • regular transduction

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.

Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,
• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as
  • intersection,
  • complement,
  • homomorphism,
  • reversal

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.

Yes, if you can come up with any of the following:

• deterministic finite automaton (DFA),
• nondeterministic finite automaton (NFA),
• regular expression (regexp of formal languages) or
• regular grammar

for some language $L$, then $L$ is regular. There are more equivalent models, but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if

• it is finite,

• you can construct it by performing certain operations on regular languages, and those operations are closed for regular languages, such as

  • intersection,
  • complement,
  • homomorphism,
  • reversal,
  • left- or right-quotient,
  • regular transduction

and more, or

• using Myhill–Nerode theorem if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.