Construction of a handle-recognising DFA

To construct a handle-recognising DFA from a context-free grammar, perform the following:

1. Prepare the grammar by:
   1. Eliminating any $\varepsilon$-productions
   2. If $S$ is the start symbol, add a new rule to the grammar $S'\, \rightarrow\, S$.

2. The start state of the DFA is ${\sf closure}\{S'\, \rightarrow\, {}_{\triangle} S\}$

3. Each time we create a new state in the DFA perform the following:
   For each grammar symbol (terminal or non-terminal):
   work out the closure of the move operation applied to newly created state and this symbol; this may create new states.

Note the similarities between this and the "subset construction" algorithm which we used to convert a NFA to a DFA.