patternModerate
Is every language with a finite number of strings regular?
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Problem
- Is every language with a finite number of strings regular?
- Is the language of all strings regular?
I am new to this topic and got confused. Can any one please help me with this?
Solution
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Yes. Assume the language is $L=\{w_1,w_2,\ldots, w_n\}$. then you can form the regular expression $w_1 + w_2 + \cdots + w_n$, which describes $L$.
You can also argue with finite automata or regular grammars.
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Yes, if your alphabet is $\Sigma=(a_1,\ldots,a_k)$ then the regular expression $(a_1+a_2+\cdots +a_k)^*$ describes the languages of all possible strings over $\Sigma$.
Yes. Assume the language is $L=\{w_1,w_2,\ldots, w_n\}$. then you can form the regular expression $w_1 + w_2 + \cdots + w_n$, which describes $L$.
You can also argue with finite automata or regular grammars.
-
Yes, if your alphabet is $\Sigma=(a_1,\ldots,a_k)$ then the regular expression $(a_1+a_2+\cdots +a_k)^*$ describes the languages of all possible strings over $\Sigma$.
Context
StackExchange Computer Science Q#9773, answer score: 11
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