A question regarding regular languages

[krumb]

hi!

I can't seem to answer the following question and i'd be very glad if someone could help me out:

 

is it possible that a regular language would be defined by an infinite regular expression? or, in other words, if L is a regular language, must the regular expression describing L be a finite one?

 

thanks!

[bascule]

I'm a bit unclear on what you're asking (probably because my background is somewhat informal). It's certainly possible for finite regular expressions to define infinite languages, but I don't know if regular languages must inherently be defined by a finite regular expression.

 

Any regular expression which has an underlying pattern should be expressible through the Kleene star operators * and +. If the regular expression is infinite and has no pattern, I don't think it's possible to decide whether a given string exists within the language.