Get A New Canonical Form For Fast Boolean Matching In Logic ... - Atrak Usc

Two dual canonical forms of any Boolean function are a "sum of minterms" and a "product of maxterms." The term "Sum of Products" (SoP or SOP) is widely used for the canonical form that is a disjunction (OR) of minterms.

A canonical form is an element of a set of representatives of equivalence classes of forms such that there is a function or procedure which projects every element of each equivalence class onto that one element, the canonical form of that equivalence class.

one gets a new representation of the same state. This is often referred to as a “Gauge” freedom. We will use it to convert our Matrix Product States into Canonical forms. There are four forms worth considering: the left, right, mixed, and symmetric forms.

There are two types of canonical forms: SOP: Sum of products or sum of min terms.

There are two types of canonical forms of a Boolean expression. The first one is called sum of products or “SoP“ and the second one is called product of sums or “PoS”.

A canonical form may simply be a convention, or a deep theorem. For example, polynomials are conventionally written with the terms in descending powers: it is more usual to write x2 + x + 30 than x + 30 + x2, although the two forms define the same polynomial.

In the first canonical form, SoP (Sum of Products) is obtained by adding all the minterms that give 1 as output. In a minterm 0 is assigned to the inversed variable and 1 to the direct variable (Shannon Theorem).