  We present a general framework for good CNF-representations of boolean
constraints, to be used for translating decision problems into SAT problems
(i.e., deciding satisfiability for conjunctive normal forms). We apply it to
the representation of systems of XOR-constraints, also known as systems of
linear equations over the two-element field, or systems of parity constraints.
  The general framework defines the notion of "representation", and provides
several methods to measure the quality of the representation by the complexity
("hardness") needed for making implicit "knowledge" of the representation
explicit (to a SAT-solving mechanism). We obtain general upper and lower
bounds.
  Applied to systems of XOR-constraints, we show a super-polynomial lower bound
on "good" representations under very general circumstances. A corresponding
upper bound shows fixed-parameter tractability in the number of constraints.
  The measurement underlying this upper bound ignores the auxiliary variables
needed for shorter representations of XOR-constraints. Improved upper bounds
(for special cases) take them into account, and a rich picture begins to
emerge, under the various hardness measurements.
