  We convert, within polynomial-time and sequential processing, NP-Complete
Problems into a problem of deciding feasibility of a given system S of linear
equations with constants and coefficients of binary-variables that are 0, 1, or
-1. S is feasible, if and only if, the NP-Complete problem has a feasible
solution. We show separate polynomial-time conversions to S, from the
SUBSET-SUM and 3-SAT problems, both of which are NP-Complete. The number of
equations and variables in S is bounded by a polynomial function of the size of
the NP-Complete problem, showing that deciding the feasibility of S is
strongly-NP-Complete. We also show how to apply the approach used for the
SUBSET-SUM problem to decide the feasibility of Integer Linear Programs, as it
involves reducing the coefficient-magnitudes of variables to the logarithm of
their initial values, though the number of variables and equations are
increased.
