mirrors/z3
3
0
Fork 0
mirror of https://github.com/Z3Prover/z3 synced 2025-11-04 13:29:11 +00:00
Code Activity

working on pb

Browse source 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2013-11-17 20:15:24 -08:00
parent 8cb959127f
commit 50cc852112
4 changed files with 366 additions and 161 deletions
Download patch file Download diff file Expand all files Collapse all files

4
src/smt/smt_context.h
View file

@ -332,6 +332,10 @@ namespace smt {
return get_assignment(literal(v));
}
literal_vector const & assigned_literals() const {
return m_assigned_literals;
}
lbool get_assignment(expr * n) const;
// Similar to get_assignment, but returns l_undef if n is not internalized.

2
src/smt/smt_justification.h
View file

@ -225,6 +225,7 @@ namespace smt {
virtual proof * mk_proof(conflict_resolution & cr) = 0;
virtual char const * get_name() const { return "simple"; }
};
class simple_theory_justification : public simple_justification {
@ -274,6 +275,7 @@ namespace smt {
virtual char const * get_name() const { return "theory-propagation"; }
};
class theory_conflict_justification : public simple_theory_justification {

484
src/smt/theory_pb.cpp
View file

@ -37,6 +37,156 @@ namespace smt {
SASSERT(well_formed());
}
void theory_pb::ineq::reset() {
m_max_coeff = 0;
m_watch_sz = 0;
m_sum = 0;
m_max_sum = 0;
m_num_propagations = 0;
m_compilation_threshold = UINT_MAX;
m_compiled = l_false;
m_args.reset();
m_k = 0;
}
theory_pb::numeral theory_pb::ineq::gcd(numeral a, numeral b) {
while (a != b) {
if (a == 0) return b;
if (b == 0) return a;
SASSERT(a != 0 && b != 0);
if (a < b) {
b %= a;
}
else {
a %= b;
}
}
return a;
}
lbool theory_pb::ineq::normalize() {
numeral& k = m_k;
arg_t& args = m_args;
// normalize first all literals to be positive:
// then we can compare them more easily.
for (unsigned i = 0; i < size(); ++i) {
if (lit(i).sign()) {
args[i].first.neg();
k -= coeff(i);
args[i].second = -coeff(i);
}
}
// remove constants
for (unsigned i = 0; i < size(); ++i) {
if (lit(i) == true_literal) {
k += coeff(i);
std::swap(args[i], args[size()-1]);
args.pop_back();
}
else if (lit(i) == false_literal) {
std::swap(args[i], args[size()-1]);
args.pop_back();
}
}
// sort and coalesce arguments:
std::sort(args.begin(), args.end());
for (unsigned i = 0; i + 1 < size(); ++i) {
if (lit(i) == args[i+1].first) {
args[i].second += coeff(i+1);
for (unsigned j = i+1; j + 1 < size(); ++j) {
args[j] = args[j+1];
}
args.pop_back();
}
if (coeff(i) == 0) {
for (unsigned j = i; j + 1 < size(); ++j) {
args[j] = args[j+1];
}
args.pop_back();
}
}
//
// Ensure all coefficients are positive:
// c*l + y >= k
// <=>
// c*(1-~l) + y >= k
// <=>
// c - c*~l + y >= k
// <=>
// -c*~l + y >= k - c
//
numeral sum = 0;
for (unsigned i = 0; i < size(); ++i) {
numeral c = coeff(i);
if (c < 0) {
args[i].second = -c;
args[i].first = ~lit(i);
k -= c;
}
sum += coeff(i);
}
// detect tautologies:
if (k <= 0) {
args.reset();
return l_true;
}
// detect infeasible constraints:
if (sum < k) {
args.reset();
return l_false;
}
// Ensure the largest coefficient is not larger than k:
for (unsigned i = 0; i < size(); ++i) {
numeral c = coeff(i);
if (c > k) {
args[i].second = k;
}
}
SASSERT(!args.empty());
// apply cutting plane reduction:
numeral g = 0;
for (unsigned i = 0; g != 1 && i < size(); ++i) {
numeral c = coeff(i);
if (c != k) {
g = gcd(g, c);
}
}
if (g == 0) {
// all coefficients are equal to k.
for (unsigned i = 0; i < size(); ++i) {
SASSERT(coeff(i) == k);
args[i].second = 1;
}
k = 1;
}
else if (g > 1) {
//
// Example 5x + 5y + 2z + 2u >= 5
// becomes 3x + 3y + z + u >= 3
//
numeral k_new = k / g;
if ((k % g) != 0) { // k_new is the ceiling of k / g.
k_new++;
}
for (unsigned i = 0; i < size(); ++i) {
numeral c = coeff(i);
if (c == k) {
c = k_new;
}
else {
c = c / g;
}
args[i].second = c;
}
k = k_new;
}
SASSERT(well_formed());
return l_undef;
}
bool theory_pb::ineq::well_formed() const {
SASSERT(k() > 0);
uint_set vars;
@ -57,7 +207,8 @@ namespace smt {
theory_pb::theory_pb(ast_manager& m):
theory(m.mk_family_id("card")),
m_util(m)
m_util(m),
m_lemma(null_literal)
{}
theory_pb::~theory_pb() {
@ -101,7 +252,7 @@ namespace smt {
args[i].second = -args[i].second;
}
k = -k;
lbool is_true = normalize_ineq(args, k);
lbool is_true = c->normalize();
literal lit(abv);
switch(is_true) {
@ -138,8 +289,9 @@ namespace smt {
++log;
n *= 2;
}
c->m_compilation_threshold = args.size()*log;
TRACE("card", tout << "compilation threshold: " << (args.size()*log) << "\n";);
unsigned th = 10*args.size()*log;
c->m_compilation_threshold = th;
TRACE("card", tout << "compilation threshold: " << th << "\n";);
}
else {
c->m_compilation_threshold = UINT_MAX;
@ -167,10 +319,34 @@ namespace smt {
ctx.set_var_theory(bv, get_id());
}
has_bv = (ctx.get_var_theory(bv) == get_id());
#if 0
TBD:
if (!has_bv) {
if (!ctx.e_internalized(arg)) {
ctx.internalize(arg, false);
SASSERT(ctx.e_internalized(arg));
}
enode* n = ctx.get_enode(arg);
theory_var v = mk_var(n);
ctx.attach_th_var(n, this, v);
}
#endif
}
else if (m.is_true(arg)) {
bv = true_bool_var;
has_bv = true;
}
else if (m.is_false(arg)) {
bv = true_bool_var;
has_bv = true;
negate = !negate;
}
// pre-processing should better remove negations under cardinality.
// assumes relevancy level = 2 or 0.
// TBD: should should have been like an uninterpreted
// function intenalize, where enodes for each argument
// is available.
if (!has_bv) {
expr_ref tmp(m), fml(m);
tmp = m.mk_fresh_const("card_proxy",m.mk_bool_sort());
@ -220,142 +396,8 @@ namespace smt {
ineqs->push_back(&c);
}
theory_pb::numeral theory_pb::gcd(numeral a, numeral b) {
while (a != b) {
if (a == 0) return b;
if (b == 0) return a;
SASSERT(a != 0 && b != 0);
if (a < b) {
b %= a;
}
else {
a %= b;
}
}
return a;
}
lbool theory_pb::normalize_ineq(arg_t& args, numeral& k) {
// normalize first all literals to be positive:
// then we can compare them more easily.
for (unsigned i = 0; i < args.size(); ++i) {
if (args[i].first.sign()) {
args[i].first.neg();
k -= args[i].second;
args[i].second = -args[i].second;
}
}
// remove constants
for (unsigned i = 0; i < args.size(); ++i) {
if (args[i].first == true_literal) {
k += args[i].second;
std::swap(args[i], args[args.size()-1]);
args.pop_back();
}
else if (args[i].first == false_literal) {
std::swap(args[i], args[args.size()-1]);
args.pop_back();
}
}
// sort and coalesce arguments:
std::sort(args.begin(), args.end());
for (unsigned i = 0; i + 1 < args.size(); ++i) {
if (args[i].first == args[i+1].first) {
args[i].second += args[i+1].second;
for (unsigned j = i+1; j + 1 < args.size(); ++j) {
args[j] = args[j+1];
}
args.resize(args.size()-1);
}
if (args[i].second == 0) {
for (unsigned j = i; j + 1 < args.size(); ++j) {
args[j] = args[j+1];
}
args.resize(args.size()-1);
}
}
//
// Ensure all coefficients are positive:
// c*l + y >= k
// <=>
// c*(1-~l) + y >= k
// <=>
// c - c*~l + y >= k
// <=>
// -c*~l + y >= k - c
//
numeral sum = 0;
for (unsigned i = 0; i < args.size(); ++i) {
numeral c = args[i].second;
if (c < 0) {
args[i].second = -c;
args[i].first = ~args[i].first;
k -= c;
}
sum += args[i].second;
}
// detect tautologies:
if (k <= 0) {
args.reset();
return l_true;
}
// detect infeasible constraints:
if (sum < k) {
args.reset();
return l_false;
}
// Ensure the largest coefficient is not larger than k:
for (unsigned i = 0; i < args.size(); ++i) {
numeral c = args[i].second;
if (c > k) {
args[i].second = k;
}
}
SASSERT(!args.empty());
// apply cutting plane reduction:
numeral g = 0;
for (unsigned i = 0; g != 1 && i < args.size(); ++i) {
numeral c = args[i].second;
if (c != k) {
g = gcd(g, c);
}
}
if (g == 0) {
// all coefficients are equal to k.
for (unsigned i = 0; i < args.size(); ++i) {
SASSERT(args[i].second == k);
args[i].second = 1;
}
k = 1;
}
else if (g > 1) {
//
// Example 5x + 5y + 2z + 2u >= 5
// becomes 3x + 3y + z + u >= 3
//
numeral k_new = k / g;
if ((k % g) != 0) { // k_new is the ceiling of k / g.
k_new++;
}
for (unsigned i = 0; i < args.size(); ++i) {
numeral c = args[i].second;
if (c == k) {
c = k_new;
}
else {
c = c / g;
}
args[i].second = c;
}
k = k_new;
}
return l_undef;
}
void theory_pb::collect_statistics(::statistics& st) const {
st.update("pb axioms", m_stats.m_num_axioms);
st.update("pb propagations", m_stats.m_num_propagations);
@ -384,6 +426,10 @@ namespace smt {
m_to_compile.reset();
}
void theory_pb::new_eq_eh(theory_var v1, theory_var v2) {
IF_VERBOSE(0, verbose_stream() << v1 << " = " << v2 << "\n";);
}
void theory_pb::assign_eh(bool_var v, bool is_true) {
context& ctx = get_context();
ptr_vector<ineq>* ineqs = 0;
@ -461,7 +507,7 @@ namespace smt {
if (maxsum < c.k()) {
literal_vector& lits = get_unhelpful_literals(c, true);
lits.push_back(~c.lit());
add_clause(c, lits);
add_clause(c, c.lit(), lits);
return;
}
@ -514,7 +560,7 @@ namespace smt {
//
literal_vector& lits = get_unhelpful_literals(c, false);
lits.push_back(~c.lit());
add_clause(c, lits);
add_clause(c, literal(v, !is_true), lits);
}
else if (c.max_sum() < k + c.max_coeff()) {
//
@ -804,9 +850,14 @@ namespace smt {
std::ostream& theory_pb::display(std::ostream& out, ineq& c) const {
ast_manager& m = get_manager();
context& ctx = get_context();
expr_ref tmp(m);
ctx.literal2expr(c.lit(), tmp);
out << tmp << "\n";
if (c.lit() != null_literal) {
expr_ref tmp(m);
ctx.literal2expr(c.lit(), tmp);
out << tmp << "\n";
}
else {
out << "null\n";
}
for (unsigned i = 0; i < c.size(); ++i) {
out << c.coeff(i) << "*" << c.lit(i);
if (i + 1 < c.size()) {
@ -829,6 +880,17 @@ namespace smt {
return m_literals;
}
class theory_pb::pb_justification : public theory_propagation_justification {
ineq& m_ineq;
public:
pb_justification(ineq& c, family_id fid, region & r,
unsigned num_lits, literal const * lits, literal consequent):
theory_propagation_justification(fid, r, num_lits, lits, consequent),
m_ineq(c)
{}
ineq& get_ineq() { return m_ineq; }
};
void theory_pb::add_assign(ineq& c, literal_vector const& lits, literal l) {
inc_propagations(c);
m_stats.m_num_propagations++;
@ -841,13 +903,13 @@ namespace smt {
display(tout, c););
ctx.assign(l, ctx.mk_justification(
theory_propagation_justification(
get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), l)));
pb_justification(
c, get_id(), ctx.get_region(), lits.size(), lits.c_ptr(), l)));
}
void theory_pb::add_clause(ineq& c, literal_vector const& lits) {
void theory_pb::add_clause(ineq& c, literal conseq, literal_vector const& lits) {
inc_propagations(c);
m_stats.m_num_axioms++;
context& ctx = get_context();
@ -857,11 +919,139 @@ namespace smt {
}
tout << "\n";
display(tout, c););
// DEBUG_CODE(resolve_conflict(conseq, c););
justification* js = 0;
ctx.mk_clause(lits.size(), lits.c_ptr(), js, CLS_AUX_LEMMA, 0);
IF_VERBOSE(2, ctx.display_literals_verbose(verbose_stream(),
lits.size(), lits.c_ptr());
verbose_stream() << "\n";);
// ctx.mk_th_axiom(get_id(), lits.size(), lits.c_ptr());
}
void theory_pb::process_antecedent(literal l, numeral coeff) {
context& ctx = get_context();
bool_var v = l.var();
unsigned lvl = ctx.get_assign_level(v);
IF_VERBOSE(0, verbose_stream() << l << "*" << coeff << " marked: " << ctx.is_marked(v) << " lvl: " << lvl << "\n";);
if (!ctx.is_marked(v) && lvl > ctx.get_base_level()) {
ctx.set_mark(v);
if (lvl == m_conflict_lvl) {
++m_num_marks;
}
else {
m_lemma.m_args.push_back(std::make_pair(l, coeff));
}
}
}
void theory_pb::process_ineq(ineq& c) {
// TBD: create CUT.
context& ctx = get_context();
for (unsigned i = 0; i < c.size(); ++i) {
process_antecedent(c.lit(i), c.coeff(i));
}
process_antecedent(~c.lit(), 1);
}
//
// modeled after sat_solver/smt_context
//
void theory_pb::resolve_conflict(literal conseq, ineq& c) {
bool_var v;
context& ctx = get_context();
unsigned& lvl = m_conflict_lvl = ctx.get_assign_level(c.lit());
for (unsigned i = 0; i < c.size(); ++i) {
IF_VERBOSE(0, verbose_stream() << "conflict level: " << m_conflict_lvl << "\n";);
v = c.lit(i).var();
if (ctx.get_assignment(v) != l_undef) {
lvl = std::max(lvl, ctx.get_assign_level(v));
}
}
if (lvl == ctx.get_base_level()) {
return;
}
b_justification js(ctx.mk_justification(
pb_justification(c, get_id(), ctx.get_region(),
0, 0, c.lit())));
m_lemma.reset();
m_num_marks = 0;
// point into stack of assigned literals
literal_vector const& lits = ctx.assigned_literals();
SASSERT(!lits.empty());
unsigned idx = lits.size()-1;
do {
//
// Resolve selected conseq with antecedents.
//
switch(js.get_kind()) {
case b_justification::CLAUSE: {
clause* cls = js.get_clause();
unsigned num_lits = cls->get_num_literals();
for (unsigned i = 0; i < num_lits; ++i) {
process_antecedent(cls->get_literal(i), 1);
}
justification* cjs = cls->get_justification();
if (cjs) {
// TBD
NOT_IMPLEMENTED_YET();
}
break;
}
case b_justification::BIN_CLAUSE:
SASSERT(conseq.var() != js.get_literal().var());
process_antecedent(~js.get_literal(), 1);
break;
case b_justification::AXIOM:
break;
case b_justification::JUSTIFICATION: {
justification& j = *js.get_justification();
// only process pb justifications.
if (j.get_from_theory() != get_id()) break;
pb_justification& pbj = dynamic_cast<pb_justification&>(j);
// weaken the lemma and resolve.
process_ineq(pbj.get_ineq());
break;
}
default:
UNREACHABLE();
}
//
// find the next marked variable in the assignment stack
//
SASSERT(idx > 0);
SASSERT(m_num_marks > 0);
do {
conseq = lits[idx];
v = conseq.var();
--idx;
}
while (!ctx.is_marked(v));
js = ctx.get_justification(v);
--m_num_marks;
ctx.unset_mark(v);
IF_VERBOSE(0, verbose_stream() << "unmark: " << v << "\n";);
}
while (m_num_marks > 0);
// unset the marks on lemmas
for (unsigned i = 0; i < m_lemma.size(); ++i) {
bool_var v = m_lemma.lit(i).var();
if (ctx.is_marked(v)) {
IF_VERBOSE(0, verbose_stream() << "unmark: " << v << "\n";);
ctx.unset_mark(v);
}
}
TRACE("card", display(tout, m_lemma););
IF_VERBOSE(1, display(verbose_stream(), m_lemma););
}
}

37
src/smt/theory_pb.h
View file

@ -28,6 +28,7 @@ namespace smt {
class theory_pb : public theory {
struct sort_expr;
class pb_justification;
typedef int64 numeral;
typedef svector<std::pair<literal, numeral> > arg_t;
@ -57,16 +58,9 @@ namespace smt {
unsigned m_compilation_threshold;
lbool m_compiled;
ineq(literal l):
m_lit(l),
m_max_coeff(0),
m_watch_sz(0),
m_sum(0),
m_max_sum(0),
m_num_propagations(0),
m_compilation_threshold(UINT_MAX),
m_compiled(l_false)
{}
ineq(literal l) : m_lit(l) {
reset();
}
literal lit() const { return m_lit; }
numeral const & k() const { return m_k; }
@ -90,9 +84,16 @@ namespace smt {
return begin;
}
void reset();
void negate();
lbool normalize();
bool well_formed() const;
static numeral gcd(numeral a, numeral b);
};
typedef ptr_vector<ineq> watch_list;
@ -109,8 +110,6 @@ namespace smt {
ptr_vector<ineq> m_to_compile; // inequalities to compile.
// internalize_atom:
lbool normalize_ineq(arg_t& args, numeral& k);
static numeral gcd(numeral a, numeral b);
literal compile_arg(expr* arg);
void add_watch(ineq& c, unsigned index);
void del_watch(watch_list& watch, unsigned index, ineq& c, unsigned ineq_index);
@ -120,7 +119,7 @@ namespace smt {
std::ostream& display(std::ostream& out, ineq& c) const;
virtual void display(std::ostream& out) const;
void add_clause(ineq& c, literal_vector const& lits);
void add_clause(ineq& c, literal conseq, literal_vector const& lits);
void add_assign(ineq& c, literal_vector const& lits, literal l);
literal_vector& get_lits();
@ -134,6 +133,16 @@ namespace smt {
void compile_ineq(ineq& c);
void inc_propagations(ineq& c);
unsigned get_compilation_threshold(ineq& c);
//
// Conflict resolution, cutting plane derivation.
//
unsigned m_num_marks;
unsigned m_conflict_lvl;
ineq m_lemma;
void resolve_conflict(literal conseq, ineq& c);
void process_antecedent(literal l, numeral coeff);
void process_ineq(ineq& c);
public:
theory_pb(ast_manager& m);
@ -142,7 +151,7 @@ namespace smt {
virtual theory * mk_fresh(context * new_ctx);
virtual bool internalize_atom(app * atom, bool gate_ctx);
virtual bool internalize_term(app * term) { UNREACHABLE(); return false; }
virtual void new_eq_eh(theory_var v1, theory_var v2) { }
virtual void new_eq_eh(theory_var v1, theory_var v2);
virtual void new_diseq_eh(theory_var v1, theory_var v2) { }
virtual bool use_diseqs() const { return false; }
virtual bool build_models() const { return false; }