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Space Explosion: How it really relates to regular expression

In my mini thesis, I concentrating on pattern matching algorithm which relates to packet payload processing. During my literature reviews, I came across to regular expression "space explosion". The phrase rather seems remind me to inter galactic war in Star Trek, Starwars, Battlestar Galactica or things like that.

Dealing with regular expression led me to read more: time & space consideration. Somehow it led me to think about Quantum Physic (which unfortunately I never learn pure sciences subject during my secondary school, so I'll avoid to elaborate things I didn't know).

I did google to the Internet and try to use "space explosion" and pair with regular expression phrase.

Quoting this paper:

Pattern matching using regular expressions is distinct from static pattern
matching, where the input string is matched against other literal strings. In regular expressions, meta-characters with special meaning are used, and a single regular expression can represent several strings. Regular expressions augment the challenges of static pattern matching (e.g., overlapped matching) with other ones, such as space explosion (regular expressions can represent very large strings in a very compact form)

So I guess "space explosion" means character such as asterisk(*) or decimal/period(.) which led to many pattern being greedily grabbed and fetch either to standard output or input.

Am I correct here?

*pix taken from here