You actually can parse an arithmetic expression with a "regular" expression if it uses a stack automata.
Just think that a regular language can't even check if there is a correct number of parenthesis if the maximum depth is undefined, as such, strictly speaking that is not so much regular...
Re: RFC: Perl regex to validate arithmetic expressions
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Since 5.10, Perl regular expressions can match anything that's matched by a context-free grammar - and then some (backreferences add even more power). Matching balanced parenthesis is easy in 5.10 and later: /^(\((?1)*\))$/.