  Generalised Satisfiability Problems (or Boolean Constraint Satisfaction
Problems), introduced by Schaefer in 1978, are a general class of problem which
allow the systematic study of the complexity of satisfiability problems with
different types of constraints. In 1979, Valiant introduced the complexity
class parity P, the problem of counting the number of solutions to NP problems
modulo two. Others have since considered the question of counting modulo other
integers.
  We give a dichotomy theorem for the complexity of counting the number of
solutions to Generalised Satisfiability Problems modulo integers. This follows
from an earlier result of Creignou and Hermann which gave a counting dichotomy
for these types of problem, and the dichotomy itself is almost identical.
Specifically, counting the number of solutions to a Generalised Satisfiability
Problem can be done in polynomial time if all the relations are affine.
Otherwise, except for one special case with k = 2, it is #_kP-complete.
