@arr = split /(&&|\|\|)/, $str;
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But it included && and || in the array.

That's because you used capturing parentheses.

Then if there is many separators how to with that?

You use the pipe "|" character to separate multiple options, like so:

@arr = split /foo|bar|meh/, $str;
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That would split the string on any occurrences of "foo", "bar" or "meh" without including them in the resultant list.
This may not be clear in your original example, as one of the strings you are splitting on is a double-pipe "||", so the escaping of those adds a bit of "noise" to the split expression :)