By Torben Ægidius Mogensen
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4. The construction follows the structure of the regular expression by first making NFA fragments for the subexpressions and then joining these to form an NFA fragment for the whole regular expression. The NFA fragments for the subexpressions are shown as dotted ovals with the incoming half-transition on the left and the outgoing half-transition on the right. When an NFA fragment has been constructed for the whole regular expression, the construction is completed by connecting the outgoing half-transition to an accepting state.
All in all, DFAs are a lot faster to use than NFAs or regular expressions, so it is only when the size of the DFA is a real problem that one should consider using NFAs or regular expressions directly. 8 has only four states, it is not minimal. It is easy to see that states s0 and s2 are equivalent: Neither are accepting and they have identical transitions. We can hence collapse these states into a single state and get a three-state DFA. DFAs constructed from regular expressions through NFAs are often nonminimal, though they are rarely very far from being minimal.
The actions for these regular expressions are typically empty, meaning that white-space and comments are just ignored. An action can be more than just returning a token. If, for example, a language has a large number of keywords, then a DFA that recognises all of these individually can be fairly large. In such cases, the keywords are not described as separate regular expressions in the lexer definition but instead treated as special cases of the identifier token. The action for identifiers will then look the name up in a table of keywords and return the appropriate token type (or an identifier token if the name is not a keyword).