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Can we use DNF of the minterms to represent the transitions? 

eg: !p&!q&!Xp'&!Xq | etc..

Should we consider the input as well?

Can all automatons be represented like that? 

in # Study-Organisation (Master) by (2.7k points)

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You can list all transitions as minterms which results in a full DNF of the transition relation which is no better than the explicit listing of the transitions (thus not making use of the symbolic representation). You have to use inputs as well for doing so, and that can be done for all automata. As the state transition diagram shown has wildcard * transitions, you better use them also instead of listing all input combinations.
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I understood , Thanks for the clarification

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