Solving Linear Constraints in Elementary Abelian p-Groups of Symmetries
  Symmetries occur naturally in CSP or SAT problems and are not very difficult
to discover, but using them to prune the search space tends to be very
challenging. Indeed, this usually requires finding specific elements in a group
of symmetries that can be huge, and the problem of their very existence is
NP-hard. We formulate such an existence problem as a constraint problem on one
variable (the symmetry to be used) ranging over a group, and try to find
restrictions that may be solved in polynomial time. By considering a simple
form of constraints (restricted by a cardinality k) and the class of groups
that have the structure of Fp-vector spaces, we propose a partial algorithm
based on linear algebra. This polynomial algorithm always applies when k=p=2,
but may fail otherwise as we prove the problem to be NP-hard for all other
values of k and p. Experiments show that this approach though restricted should
allow for an efficient use of at least some groups of symmetries. We conclude
with a few directions to be explored to efficiently solve this problem on the
general case.
