User:Tizio/Minimization of Boolean formulae

In computer science, the minimization of Boolean formulae is the problem of finding a Boolean formula of minimal size that is equivalent to another given Boolean formula or represents another given Boolean function. A manual method for solving this problem is that of Karnaugh maps; automated algorithms include the Quine–McCluskey algorithm and is variant Petrick's method.

The decision problem corresponding to minimization is that of establishing whether a formula is of mimimal size. This problem appears to be harder than NP-complete and coNP-complete problems (and in some subcases has been proved so); this was the original motivation behind the introduction of the polynomial hierarchy. The exact complexity of this problem in its general form is currently unknown, but complete characterizations for some subcases have been established.

To do

 * Example: two equivalent formulae of different size
 * Methods for DNF
 * Various notions of minimality
 * Complexity known (NP-complete) for the Horn case
 * Hemaspaandra, E. and Wechsung, G. (1997)

Related problems

 * Minimal unsatisfiability/leanness
 * Redundancy