Still better is:

print "quoted\n" if /^'([^'].*)'$/ and ($1 !~ /[^\\]'/);
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That makes sure the string starts and ends with a quote (as the previous one does), and that there are no unescaped quotes in the string apart from the first and last.

This makes more assumptions about what your string looks like; it assumes you're using MySQL-style quoting---quote char is single-quote, escape char is backslash. I don't think there's a way around hardcoding your knowledge of your database's quoting into your script; the previous post.

And you still don't know for sure if 'hello' is a quoted string or an unquoted string containing quotes at the beginning and end; you need some kind of meta-information for that.