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I know that regular languages are those that can be described by regular expressions. For the language {0,1}*, is the corresponding regular expression (0∪1)* ? If so, does replacing braces with parentheses and commas with union always work when converting from regular language to regular expression?

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    $\begingroup$ There is no single syntax for regular languages. You are looking at two different ways of writing down regular expressions. $\endgroup$ – Raphael Sep 17 '15 at 21:22
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Regular expression represent one way of describing regular languages, but there are other notations which you can use to depict such formal languages. E.g. you can use the standard grammar notation ( $S \to aB, B \to bC, \ldots $) or you can use a nondeterministic finite automaton and therefor a deterministic finite automaton to describe a regular language.

Both of your given examples are of the notation-type "regular expression", which can have multiple forms. An 'or' can be e.g. represented as union ($u$), by square brackets ($[abc]$) or maybe a comma like you used in your first example. This is just a matter of what convention you agree to.

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