Question: Generalize the preceding argument to prove that we cannot merge states , f there exists a string such that (,) and (,) . (Hint: Induct

Generalize the preceding argument to prove that we cannot merge states , f there exists a string such that (,) and (,) . (Hint: Induct on the length of .) As we will see, it turns out that this yields a condition that is both necessary and sufficient for merging states. Formally, if :((,) (,) ), then , are equivalent and can be merged. We begin by formalizing the notion of equivalent states.

Generalize the preceding argument to prove that we cannot merge states ,

Part 3. (5 points) Generalize the preceding argument to prove that we cannot merge states p, q if there exists a string x * such that A(p, x) E F and A(q,x) & F. (Hint: Induct on the length of x.) As we will see, it turns out that this yields a condition that is both necessary and sufficient for merging states. Formally, if Vx *:(^(p, x) EF AA(q,x) E F), then p, q are equivalent and can be merged. We begin by formalizing the notion of equivalent states

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