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compound autometa

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In compound automta we doing cross product for and/or opearion

My doubt is that supose there is lang L1 which we can drw DFA for tht & another lang for which we r unable to draw dfa but draw nfa is possible.

 While performing cross product is necessery that cross product are performing on nfa-nfa/dfa-dfa or we can perform nfa- dfa/dfa-nfa??

Another doubt is that in dfa there is Dead state is also so what about Dead state??

Is dead state is participating on cross product of FA???
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