2. (10 points) Consider the following computational problems:

EQDF A = {hA, Bi | A and B are DFAs and L(A) = L(B)}

SUBDF A = {hA, Bi | A and B are DFAs and L(A) L(B)}

DISJDF A = {hA, Bi | A and B are DFAs and L(A) L(B) = }.

Prove that SUBDF A and DISJDF A are each Turing-decidable.

You may (and should) use high-level descriptions of any Turing machines you define. Make sure to provide both a machine definition and a proof of correctness.

2. (10 points) Consider the following computational problems: EQDFA = {(A,B) | A and B are DFAs and L(A) = L(B)) SUBDFA = {(A,B) | A and B are DFAs and L(A) L(B)) DISJDFA = {(A,B) | A and B are DFAs and L(A) L(B) = } Prove that SUBDFA and DISJDFA are each Turing-decidable. You may (and should) use high-level descriptions of any Turing machines you define. Make sure to provide both a machine definition and a proof of correctness