# Decision Making

## Dependency Expression Evaluation

In terms of boolean logic, a dependency expression can be expressed in disjunctive normal form (DNF), which is a disjunction of conjunctive clauses. Each conjunctive clause represents one possible alternative combination of dependency atoms capable of satisfying the dependency expression.

### Delayed Evaluation of Disjunctive Dependency Choices

Disjunctive dependencies, of which virtuals are a special case, can be satisfied by multiple choices of dependency atoms. These choices are delayed until as late as possible in the dependency calculation, after packages have been selected to satisfy as many non-disjunctive dependencies as possible. As a consequence of this delayed evaluation, there is maximal information available which makes it possible to optimize choices such that the total number of packages required to satisfy all dependencies is minimized.

## Look-Ahead

When there are multiple combinations to choose from, a look-ahead mechanism will choose an optimal combination to satisfy constraints and minimize cost. The following package states influence the cost calculation for a given combination:

- installed

- selected (for installation)

- not selected (for installation)

In cost calculations, virtual packages by themselves are considered to cost nothing since they do not directly install anything. It is the dependencies of a virtual package that contribute to it's cost.

### Constraint Propagation

Combinations that include packages from the "installed" or "selected" categories are less costly than those that include packages from the "not selected" category. When a package is chosen for installation, it transitions to the "selected" state. This state change propagates to the cost calculations of later decisions, influencing later decisions to be consistent with earlier decisions. This feedback mechanism serves to propagate constraints and can influence the modeling process to converge on a more optimal final state.

### Expanded Search Space

When evaluating virtual atoms, an expanded search space is considered which recursively traverses the dependencies of virtual packages from all slots matching a given virtual atom. All combinations in this expanded search space are considered when choosing an optimal combination to satisfy constraints with minimal cost.