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Sequential Circuit Minimization (K-Maps/Quine-McCluskey)

Algorithmic methods (like Karnaugh Maps or Quine-McCluskey) used to simplify the Boolean expressions defining the next-state logic and output functions.
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The statement of the theorem

Circuit minimization aims to find the minimal Boolean function fminf_{min} equivalent to the original function ff. For sequential logic, this involves minimizing both the next-state function fnext(Q,X)f_{next}(Q, X) and the output function Y(Q,X)Y(Q, X). Methods like the Quine-McCluskey algorithm systematically identify prime implicants (PIs) that cover the required minterms, ensuring that the resulting simplified expression fminf_{min} maintains logical equivalence: fmin=⋁iMif_{min} = \bigvee_{i} M_i where MiM_i are the selected prime implicants.