XSAT of Linear CNF Formulas
  Open questions with respect to the computational complexity of linear CNF
formulas in connection with regularity and uniformity are addressed. In
particular it is proven that any l-regular monotone CNF formula is
XSAT-unsatisfiable if its number of clauses m is not a multiple of l. For exact
linear formulas one finds surprisingly that l-regularity implies k-uniformity,
with m = 1 + k(l-1)) and allowed k-values obey k(k-1) = 0 (mod l). Then the
computational complexity of the class of monotone exact linear and l-regular
CNF formulas with respect to XSAT can be determined: XSAT-satisfiability is
either trivial, if m is not a multiple of l, or it can be decided in
sub-exponential time, namely O(exp(n^^1/2)). Sub-exponential time behaviour for
the wider class of regular and uniform linear CNF formulas can be shown for
certain subclasses.
