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<chapter id='dependency-resolution-decision-making'>
<title>Decision Making</title>
<sect1 id='dependency-resolution-decision-making-dependency-expression-evaluation'>
<title>Dependency Expression Evaluation</title>
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.
<sect2 id='dependency-resolution-decision-making-dependency-expression-evaluation-delayed-disjunction'>
<title>Delayed Evaluation of Disjunctive Dependency Choices</title>
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.
<sect1 id='dependency-resolution-decision-making-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:
<para>selected (for installation)</para>
<para>not selected (for installation)</para>
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.
<sect2 id='dependency-resolution-decision-making-look-ahead-constraint-propagation'>
<title>Constraint Propagation</title>
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.
<sect2 id='dependency-resolution-decision-making-look-ahead-expanded-search-space'>
<title>Expanded Search Space</title>
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.