Boolean minimization

Logic optimization, a part of logic synthesis in electronics, is the process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. Generally the circuit is constrained to minimum chip area meeting a prespecified delay.

With the advent of logic synthesis, one of the biggest challenges faced by the electronic design automation (EDA) industry was to find the best netlist representation of the given design description. While two-level logic optimization had long existed in the form of the Quine–McCluskey algorithm, later followed by the Espresso heuristic logic minimizer, the rapidly improving chip densities, and the wide adoption of HDLs for circuit description, formalized the logic optimization domain as it exists today.

Today, logic optimization is divided into various categories:

Based on circuit representation

Based on circuit characteristics

Based on type of execution

While a two-level circuit representation of circuits strictly refers to the flattened view of the circuit in terms of SOPs (sum-of-products) — which is more applicable to a PLA implementation of the design — a multi-level representation is a more generic view of the circuit in terms of arbitrarily connected SOPs, POSs (product-of-sums), factored form etc. Logic optimization algorithms generally work either on the structural (SOPs, factored form) or functional (BDDs, ADDs) representation of the circuit.

If we have two functions F₁ and F₂:

...
Wikipedia