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add qe_arith routine for LW projection on monomomes

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2013-09-12 12:19:46 -07:00
parent 0aaa67fa7d
commit 4af4466821
7 changed files with 422 additions and 7 deletions
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22
src/muz/pdr/pdr_farkas_learner.cpp
View file

@ -151,6 +151,11 @@ namespace pdr {
public:
constr(ast_manager& m) : m(m), a(m), m_ineqs(m), m_time(0) {}
void reset() {
m_ineqs.reset();
m_coeffs.reset();
}
/** add a multiple of constraint c to the current constr */
void add(rational const & coef, app * c) {
bool is_pos = true;
@ -300,7 +305,6 @@ namespace pdr {
return r;
}
expr_ref extract_consequence(unsigned lo, unsigned hi) {
bool is_int = is_int_sort();
app_ref zero(a.mk_numeral(rational::zero(), is_int), m);
@ -373,6 +377,7 @@ namespace pdr {
farkas_learner::farkas_learner(smt_params& params, ast_manager& outer_mgr)
: m_proof_params(get_proof_params(params)),
m_pr(PROOF_MODE),
m_constr(0),
m_combine_farkas_coefficients(true),
p2o(m_pr, outer_mgr),
o2p(outer_mgr, m_pr)
@ -381,6 +386,10 @@ namespace pdr {
m_ctx = alloc(smt::kernel, m_pr, m_proof_params);
}
farkas_learner::~farkas_learner() {
dealloc(m_constr);
}
smt_params farkas_learner::get_proof_params(smt_params& orig_params) {
smt_params res(orig_params);
res.m_arith_bound_prop = BP_NONE;
@ -538,11 +547,14 @@ namespace pdr {
{
ast_manager& m = res.get_manager();
if (m_combine_farkas_coefficients) {
constr res_c(m);
for(unsigned i = 0; i < n; ++i) {
res_c.add(coeffs[i], lits[i]);
if (!m_constr) {
m_constr = alloc(constr, m);
}
res_c.get(res);
m_constr->reset();
for (unsigned i = 0; i < n; ++i) {
m_constr->add(coeffs[i], lits[i]);
}
m_constr->get(res);
}
else {
bool_rewriter rw(m);

3
src/muz/pdr/pdr_farkas_learner.h
View file

@ -42,6 +42,7 @@ class farkas_learner {
smt_params m_proof_params;
ast_manager m_pr;
scoped_ptr<smt::kernel> m_ctx;
constr* m_constr;
//
// true: produce a combined constraint by applying Farkas coefficients.
@ -80,6 +81,8 @@ class farkas_learner {
public:
farkas_learner(smt_params& params, ast_manager& m);
~farkas_learner();
/**
All ast objects have the ast_manager which was passed as
an argument to the constructor (i.e. m_outer_mgr)

2
src/muz/pdr/pdr_util.h
View file

@ -143,8 +143,6 @@ namespace pdr {
*/
void reduce_disequalities(model& model, unsigned threshold, expr_ref& fml);
/**
\brief hoist non-boolean if expressions.
*/

321
src/qe/qe_arith.cpp Normal file
View file

@ -0,0 +1,321 @@
/*++
Copyright (c) 2010 Microsoft Corporation
Module Name:
qe_arith.cpp
Abstract:
Simple projection function for real arithmetic based on Loos-W.
Author:
Nikolaj Bjorner (nbjorner) 2013-09-12
Revision History:
--*/
#include "qe_arith.h"
#include "qe_util.h"
#include "arith_decl_plugin.h"
#include "ast_pp.h"
#include "th_rewriter.h"
namespace qe {
class arith_project_util {
ast_manager& m;
arith_util a;
th_rewriter m_rw;
expr_ref_vector m_ineq_terms;
vector<rational> m_ineq_coeffs;
svector<bool> m_ineq_strict;
struct cant_project {};
// TBD: replace by "contains_x" class.
bool contains(app* var, expr* t) const {
ast_mark mark;
ptr_vector<expr> todo;
todo.push_back(t);
while (!todo.empty()) {
t = todo.back();
todo.pop_back();
if (mark.is_marked(t)) {
continue;
}
mark.mark(t, true);
if (var == t) {
return true;
}
SASSERT(is_app(t));
app* ap = to_app(t);
todo.append(ap->get_num_args(), ap->get_args());
}
return false;
}
void is_linear(app* var, rational const& mul, expr* t, rational& c, expr_ref_vector& ts) {
expr* t1, *t2;
rational mul1;
if (t == var) {
c += mul;
}
else if (a.is_mul(t, t1, t2) && a.is_numeral(t1, mul1)) {
is_linear(var, mul* mul1, t2, c, ts);
}
else if (a.is_mul(t, t1, t2) && a.is_numeral(t2, mul1)) {
is_linear(var, mul* mul1, t1, c, ts);
}
else if (a.is_add(t)) {
app* ap = to_app(t);
for (unsigned i = 0; i < ap->get_num_args(); ++i) {
is_linear(var, mul, ap->get_arg(i), c, ts);
}
}
else if (a.is_sub(t, t1, t2)) {
is_linear(var, mul, t1, c, ts);
is_linear(var, -mul, t2, c, ts);
}
else if (a.is_uminus(t, t1)) {
is_linear(var, -mul, t1, c, ts);
}
else if (a.is_numeral(t, mul1)) {
ts.push_back(a.mk_numeral(mul*mul1, m.get_sort(t)));
}
else if (contains(var, t)) {
IF_VERBOSE(1, verbose_stream() << mk_pp(t, m) << "\n";);
throw cant_project();
}
else if (mul.is_one()) {
ts.push_back(t);
}
else {
ts.push_back(a.mk_mul(a.mk_numeral(mul, m.get_sort(t)), t));
}
}
bool is_linear(app* var, expr* lit, rational& c, expr_ref& t, bool& is_strict) {
if (!contains(var, lit)) {
return false;
}
expr* e1, *e2;
c.reset();
sort* s;
expr_ref_vector ts(m);
bool is_not = m.is_not(lit, lit);
rational mul(1);
if (is_not) {
mul.neg();
}
SASSERT(!m.is_not(lit));
if (a.is_le(lit, e1, e2) || a.is_ge(lit, e2, e1)) {
is_linear(var, mul, e1, c, ts);
is_linear(var, -mul, e2, c, ts);
s = m.get_sort(e1);
is_strict = is_not;
}
else if (a.is_lt(lit, e1, e2) || a.is_gt(lit, e2, e1)) {
is_linear(var, mul, e1, c, ts);
is_linear(var, -mul, e2, c, ts);
s = m.get_sort(e1);
is_strict = !is_not;
}
else if (m.is_eq(lit, e1, e2) && !is_not) {
is_linear(var, mul, e1, c, ts);
is_linear(var, -mul, e2, c, ts);
s = m.get_sort(e1);
is_strict = false;
}
else {
throw cant_project();
}
if (ts.empty()) {
t = a.mk_numeral(rational(0), s);
}
else {
t = a.mk_add(ts.size(), ts.c_ptr());
}
return true;
}
void project(model& model, app* var, expr_ref_vector& lits) {
unsigned num_pos = 0, num_neg = 0;
expr_ref_vector new_lits(m);
for (unsigned i = 0; i < lits.size(); ++i) {
rational c(0);
expr_ref t(m);
bool is_strict;
if (is_linear(var, lits[i].get(), c, t, is_strict)) {
m_ineq_coeffs.push_back(c);
m_ineq_terms.push_back(t);
m_ineq_strict.push_back(is_strict);
if (c.is_pos()) {
++num_pos;
}
else {
--num_neg;
}
}
else {
new_lits.push_back(lits[i].get());
}
}
lits.reset();
lits.append(new_lits);
if (num_pos == 0 || num_neg == 0) {
return;
}
if (num_pos < num_neg) {
unsigned max_t = find_max(model);
for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
if (i != max_t) {
if (m_ineq_coeffs[i].is_pos()) {
lits.push_back(mk_le(i, max_t));
}
else {
lits.push_back(mk_lt(i, max_t));
}
}
}
}
else {
unsigned min_t = find_min(model);
for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
if (i != min_t) {
if (m_ineq_coeffs[i].is_neg()) {
lits.push_back(mk_le(min_t, i));
}
else {
lits.push_back(mk_lt(min_t, i));
}
}
}
}
}
unsigned find_max(model& mdl) {
return find_min_max(mdl, true);
}
unsigned find_min(model& mdl) {
return find_min_max(mdl, false);
}
unsigned find_min_max(model& mdl, bool do_max) {
unsigned result;
bool found = false;
rational found_val(0), r;
expr_ref val(m);
for (unsigned i = 0; i < m_ineq_terms.size(); ++i) {
rational const& ac = m_ineq_coeffs[i];
if (ac.is_pos() && do_max) {
VERIFY(mdl.eval(m_ineq_terms[i].get(), val));
VERIFY(a.is_numeral(val, r));
r /= ac;
if (!found || r > found_val) {
result = i;
found_val = r;
found = true;
}
}
else if (ac.is_neg() && !do_max) {
VERIFY(mdl.eval(m_ineq_terms[i].get(), val));
VERIFY(a.is_numeral(val, r));
r /= abs(ac); //// review.
if (!found || r < found_val) {
result = i;
found_val = r;
found = true;
}
}
}
SASSERT(found);
return result;
}
// ax + t <= 0
// bx + s <= 0
// a and b have different signs.
// Infer: a|b|x + |b|t + |a|bx + |a|s <= 0
// e.g. |b|t + |a|s <= 0
expr_ref mk_lt(unsigned i, unsigned j) {
rational const& ac = m_ineq_coeffs[i];
rational const& bc = m_ineq_coeffs[j];
SASSERT(ac.is_pos() != bc.is_pos());
SASSERT(ac.is_neg() != bc.is_neg());
expr* t = m_ineq_terms[i].get();
expr* s = m_ineq_terms[j].get();
expr_ref bt = mk_mul(abs(bc), t);
expr_ref as = mk_mul(abs(ac), s);
expr_ref ts = mk_add(bt, as);
expr* z = a.mk_numeral(rational(0), m.get_sort(t));
expr_ref result(m);
if (m_ineq_strict[i] || m_ineq_strict[j]) {
result = a.mk_lt(ts, z);
}
else {
result = a.mk_le(ts, z);
}
return result;
}
// ax + t <= 0
// bx + s <= 0
// a and b have same signs.
// encode:// t/|a| <= s/|b|
// e.g. |b|t <= |a|s
expr_ref mk_le(unsigned i, unsigned j) {
rational const& ac = m_ineq_coeffs[i];
rational const& bc = m_ineq_coeffs[j];
SASSERT(ac.is_pos() == bc.is_pos());
SASSERT(ac.is_neg() == bc.is_neg());
expr* t = m_ineq_terms[i].get();
expr* s = m_ineq_terms[j].get();
expr_ref bt = mk_mul(abs(bc), t);
expr_ref as = mk_mul(abs(ac), s);
if (m_ineq_strict[j] && !m_ineq_strict[i]) {
return expr_ref(a.mk_lt(bt, as), m);
}
else {
return expr_ref(a.mk_le(bt, as), m);
}
}
expr_ref mk_add(expr* t1, expr* t2) {
return expr_ref(a.mk_add(t1, t2), m);
}
expr_ref mk_mul(rational const& r, expr* t2) {
expr* t1 = a.mk_numeral(r, m.get_sort(t2));
return expr_ref(a.mk_mul(t1, t2), m);
}
public:
arith_project_util(ast_manager& m):
m(m), a(m), m_rw(m), m_ineq_terms(m) {}
expr_ref operator()(model& model, app_ref_vector& vars, expr_ref_vector const& lits) {
expr_ref_vector result(lits);
for (unsigned i = 0; i < vars.size(); ++i) {
project(model, vars[i].get(), result);
}
vars.reset();
expr_ref res1(m);
expr_ref tmp = qe::mk_and(result);
m_rw(tmp, res1);
return res1;
}
};
expr_ref arith_project(model& model, app_ref_vector& vars, expr_ref_vector const& lits) {
ast_manager& m = vars.get_manager();
arith_project_util ap(m);
return ap(model, vars, lits);
}
}

16
src/qe/qe_arith.h Normal file
View file

@ -0,0 +1,16 @@
#ifndef __QE_ARITH_H_
#define __QE_ARITH_H_
#include "model.h"
namespace qe {
/**
Loos-Weispfenning model-based projection for a basic conjunction.
Lits is a vector of literals.
return vector of variables that could not be projected.
*/
expr_ref arith_project(model& model, app_ref_vector& vars, expr_ref_vector const& lits);
};
#endif

1
src/test/main.cpp
View file

@ -214,6 +214,7 @@ int main(int argc, char ** argv) {
TST(quant_solve);
TST(rcf);
TST(polynorm);
TST(qe_arith);
}
void initialize_mam() {}

64
src/test/qe_arith.cpp Normal file
View file

@ -0,0 +1,64 @@
#include "qe_arith.h"
#include "th_rewriter.h"
#include "smt2parser.h"
#include "arith_decl_plugin.h"
#include "reg_decl_plugins.h"
#include "arith_rewriter.h"
#include "ast_pp.h"
#include "qe_util.h"
#include "smt_context.h"
static expr_ref parse_fml(ast_manager& m, char const* str) {
expr_ref result(m);
cmd_context ctx(false, &m);
ctx.set_ignore_check(true);
std::ostringstream buffer;
buffer << "(declare-const x Real)\n"
<< "(declare-const y Real)\n"
<< "(declare-const z Real)\n"
<< "(declare-const a Real)\n"
<< "(declare-const b Real)\n"
<< "(assert " << str << ")\n";
std::istringstream is(buffer.str());
VERIFY(parse_smt2_commands(ctx, is));
SASSERT(ctx.begin_assertions() != ctx.end_assertions());
result = *ctx.begin_assertions();
return result;
}
static char const* example1 = "(and (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
static char const* example2 = "(and (<= z x) (<= x 3.0) (<= (* 3.0 x) y) (<= z y))";
static char const* example3 = "(and (<= z x) (<= x 3.0) (< (* 3.0 x) y) (<= z y))";
static char const* example4 = "(and (<= z x) (<= x 3.0) (not (>= (* 3.0 x) y)) (<= z y))";
static void test(char const *ex) {
smt_params params;
params.m_model = true;
ast_manager m;
reg_decl_plugins(m);
arith_util a(m);
expr_ref fml = parse_fml(m, ex);
app_ref_vector vars(m);
expr_ref_vector lits(m);
vars.push_back(m.mk_const(symbol("x"), a.mk_real()));
qe::flatten_and(fml, lits);
smt::context ctx(m, params);
ctx.assert_expr(fml);
lbool result = ctx.check();
SASSERT(result == l_true);
ref<model> md;
ctx.get_model(md);
expr_ref pr = qe::arith_project(*md, vars, lits);
std::cout << mk_pp(fml, m) << "\n";
std::cout << mk_pp(pr, m) << "\n";
}
void tst_qe_arith() {
test(example1);
test(example2);
test(example3);
test(example4);
}