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When we converting from nfa to dfa there may be result like the image below… My question is, is it necessary to write that from state {4} it’s going to Zero state? I mean that without showing the input symbol 1 of {4} is the same with picture below right? or no?
It’s a matter of convention. Personally, I prefer not to clutter my DFA with unnecessary states, especially since DFAs obtained via transformation from NFAs tend to become quite complex anyway, and since it’s deterministic we know that any non-displayed transition must be invalid.
However, I’ve experienced that many people in academia teach / use the other convention, and require all transitions to be explicitly shown. When working as a TA (tutor) I’ve actually had a discussion with a professor about this – he wanted us tutors to deduct points on the final tests for missing transitions in DFAs but I convinced him that deducting points for this was unfair.