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Characteristic Equation

The Boolean function that determines the next state (QnextQ_{next}) of a sequential circuit based on the current state (QQ) and inputs (XX). For a flip-flop, Qnext=f(Q,X)Q_{next} = f(Q, X).
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The statement of the theorem

Let Q(t)Q(t) be the current state vector and X(t)X(t) be the input vector. The next state Q(t+1)Q(t+1) is determined by the Boolean function ff: Q(t+1)=f(Q(t),X(t))Q(t+1) = f(Q(t), X(t)) where f:Bn×Bm→Bnf: B^n \times B^m \to B^n. For a specific flip-flop type (e.g., JK), the characteristic equation defines the next state QnextQ_{next} based on the current state QQ and inputs XX: Qnext=f(Q,X)Q_{next} = f(Q, X).
Source: Wikipedia