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Minimal SOP/POS Form

The most simplified algebraic representation of a Boolean function, ensuring the minimal number of literals and terms are used, crucial for hardware efficiency.
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The statement of the theorem

Let ff be a Boolean function. The minimal SOP form is defined as f=∑Pif = \sum P_i, where PiP_i are prime implicants, and the set of PiP_i is minimal such that ∑Pi\sum P_i covers all minterms where f=1f=1. The minimal POS form is defined as f=∏Qjf = \prod Q_j, where QjQ_j are prime implicants (maxterms), and the set of QjQ_j is minimal such that ∏Qj\prod Q_j covers all maxterms where f=0f=0. Minimality requires that no prime implicant can be removed without changing the function's truth value.
Source: Wikipedia