gorithm not only determines whether the string is accepted but also provides all possible paths through the automaton that lead to acceptance. If the result is an empty set, then the string is not in the language of the automaton.</p>
<p>For deterministic finite automata (DFAs), the algorithm simplifies because there are no epsilon transitions and each state has at most one transition on each symbol. In this case, there is at most one valid parse for any accepted string.</p>
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