  We propose an end-to-end approach for answer set programming (ASP) and linear
algebraically compute stable models satisfying given constraints. The idea is
to implement Lin-Zhao's theorem \cite{Lin04} together with constraints directly
in vector spaces as numerical minimization of a cost function constructed from
a matricized normal logic program, loop formulas in Lin-Zhao's theorem and
constraints, thereby no use of symbolic ASP or SAT solvers involved in our
approach. We also propose precomputation that shrinks the program size and
heuristics for loop formulas to reduce computational difficulty. We empirically
test our approach with programming examples including the 3-coloring and
Hamiltonian cycle problems. As our approach is purely numerical and only
contains vector/matrix operations, acceleration by parallel technologies such
as many-cores and GPUs is expected.
