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add hilbert basis utility for extracting auxiliary invariants

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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Nikolaj Bjorner 2013-02-12 14:58:44 -08:00
parent a14f29a4eb
commit 0fc44a43e1
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src/test/hilbert_basis.cpp Normal file
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#include "hilbert_basis.h"
static vector<rational> vec(int i, int j, int k) {
vector<rational> nv;
nv.resize(3);
nv[0] = rational(i);
nv[1] = rational(j);
nv[2] = rational(k);
return nv;
}
static vector<rational> vec(int i, int j, int k, int l) {
vector<rational> nv;
nv.resize(4);
nv[0] = rational(i);
nv[1] = rational(j);
nv[2] = rational(k);
nv[3] = rational(l);
return nv;
}
static vector<rational> vec(int i, int j, int k, int l, int x, int y, int z) {
vector<rational> nv;
nv.resize(7);
nv[0] = rational(i);
nv[1] = rational(j);
nv[2] = rational(k);
nv[3] = rational(l);
nv[4] = rational(x);
nv[5] = rational(y);
nv[6] = rational(z);
return nv;
}
static void saturate_basis(hilbert_sl_basis& hb) {
lbool is_sat = hb.saturate();
switch(is_sat) {
case l_true:
std::cout << "sat\n";
hb.display(std::cout);
break;
case l_false:
std::cout << "unsat\n";
break;
case l_undef:
std::cout << "undef\n";
break;
}
statistics st;
hb.collect_statistics(st);
st.display(std::cout);
}
static void saturate_basis(hilbert_basis& hb) {
lbool is_sat = hb.saturate();
switch(is_sat) {
case l_true:
std::cout << "sat\n";
hb.display(std::cout);
break;
case l_false:
std::cout << "unsat\n";
break;
case l_undef:
std::cout << "undef\n";
break;
}
statistics st;
hb.collect_statistics(st);
st.display(std::cout);
}
// example 9, Ajili, Contenjean
// x + y - 2z = 0
// x - z = 0
// -y + z <= 0
static void tst1() {
hilbert_basis hb;
hb.add_eq(vec(1,1,-2));
hb.add_eq(vec(1,0,-1));
hb.add_le(vec(0,1,-1));
saturate_basis(hb);
}
// example 10, Ajili, Contenjean
// 23x - 12y - 9z <= 0
// x - 8y - 8z <= 0
void tst2() {
hilbert_basis hb;
hb.add_eq(vec(-23,12,9));
hb.add_eq(vec(-1,8,8));
saturate_basis(hb);
}
// example 6, Ajili, Contenjean
// 3x + 2y - z - 2u <= 0
static void tst3() {
hilbert_basis hb;
hb.add_le(vec(3,2,-1,-2));
saturate_basis(hb);
}
#define R rational
// Sigma_1, table 1, Ajili, Contejean
static void tst4() {
hilbert_sl_basis hb;
hb.add_le(vec( 0,-2, 1, 3, 2,-2, 3), R(3));
hb.add_le(vec(-1, 7, 0, 1, 3, 5,-4), R(2));
hb.add_le(vec( 0,-1, 1,-1,-1, 0, 0), R(2));
hb.add_le(vec(-2, 0, 1, 4, 0, 0,-2), R(1));
hb.add_le(vec(-3, 2,-2, 2,-4,-1, 0), R(8));
hb.add_le(vec( 3,-2, 2,-2, 4, 1, 0), R(3));
hb.add_le(vec( 1, 0, 0,-1, 0, 1, 0), R(4));
hb.add_le(vec( 1,-2, 0, 0, 0, 0, 0), R(2));
hb.add_le(vec( 1, 1, 0, 0,-1, 0, 1), R(4));
hb.add_le(vec( 1, 0, 0, 0,-1, 0, 0), R(9));
saturate_basis(hb);
}
// Sigma_2 table 1, Ajili, Contejean
static void tst5() {
hilbert_sl_basis hb;
hb.add_le(vec( 1, 2,-1, 1), R(3));
hb.add_le(vec( 2, 4, 1, 2), R(12));
hb.add_le(vec( 1, 4, 2, 1), R(9));
hb.add_le(vec( 1, 1, 0,-1), R(10));
hb.add_le(vec( 1, 1,-1, 0), R(6));
hb.add_le(vec( 1,-1, 0, 0), R(0));
hb.add_le(vec( 0, 0, 1,-1), R(2));
saturate_basis(hb);
}
// Sigma_3 table 1, Ajili, Contejean
static void tst6() {
hilbert_sl_basis hb;
hb.add_le(vec( 4, 3, 0), R(6));
hb.add_le(vec(-3,-4, 0), R(-1));
hb.add_le(vec( 4, 0,-3), R(3));
hb.add_le(vec(-3, 0, 4), R(7));
hb.add_le(vec( 4, 0,-3), R(23));
hb.add_le(vec( 0,-3, 4), R(11));
saturate_basis(hb);
}
// Sigma_4 table 1, Ajili, Contejean
static void tst7() {
hilbert_sl_basis hb;
hb.add_le(vec( 2, 1, 0, 1), R(6));
hb.add_le(vec( 1, 2, 1, 1), R(7));
hb.add_le(vec( 1, 3,-1, 2), R(8));
hb.add_le(vec( 1, 2,-9,-12), R(-11));
hb.add_le(vec( 0, 0,-1, 3), R(10));
saturate_basis(hb);
}
void tst_hilbert_basis() {
std::cout << "hilbert basis test\n";
tst1();
tst2();
tst3();
#if 0
tst4();
tst5();
tst6();
tst7();
#endif
}