Prove property (12.3.4).
To Proof :The k-equivalance classes partition the set of all states of the automation into a union of mutually disjoint subsets for every integer
S is k-equivalance to t if and only if for all input string w of length less than or equal tok, N*(t,w) are both either accepting states or are both nonaccepting states.
let k be a nonnegative integer .Let A be an automation and let S bet the set of ststes of A.As its known that Rk is an equivalence relation.A theoram in state that the equivalence clases of an equivalence relation from a partition of the set on which the relation is defined .Thus the equivalence classes then from a partition of S,while the equivelence classes are the k-equivalence classes...
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