Final answer:
The question pertains to automata theory, specifically regarding the decidable nature and emptiness property of SUBSETDFA. SUBSETDFA is decidable as we can check whether a combined DFA's language is empty. The emptiness property can also be checked for DFAs, hence the property SUBSETDFA EP is also decidable.
Step-by-step explanation:
In the context of automata theory, the question refers to DFA (Deterministic Finite Automata). Understanding whether SUBSETDFA, the language defined by pairs of DFAs (M1, M2) where the language of M1 is a subset of the language of M2, is decidable and shows an emptiness property is crucial.
a) SUBSETDFA is decidable because we know that for any two given DFAs, we can construct a new DFA to accept the difference of these two DFA's languages. Once we have this combined DFA, we can check if its language is empty. If it is, then L(M1) is a subset of L(M2), otherwise it isn't. The emptiness of a DFA's language is decidable, hence SUBSETDFA is decidable.
b) The emptiness property, typically denoted as EP, refers to the property that a language accepts no strings (i.e., empty). In this case, assuming SUBSETDFA = {(M1, M2) – M1, M2 are DFAs and L(M1) is a subset of L(M2)}, the question is equivalent to asking whether there exists a pair of DFAs that satisfy this property. This is an instance of non-emptiness problem, which is decidable for DFAs.
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