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simplify

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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2025-09-04 09:39:26 -10:00
parent af978d7c6e
commit ff39b47d1f
1 changed files with 194 additions and 210 deletions
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src/nlsat/levelwise.cpp
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@ -50,6 +50,7 @@ namespace nlsat {
pmanager& m_pm;
anum_manager& m_am;
std::vector<property> m_Q; // the set of properties to prove
std::vector<symbolic_interval> m_I; // intervals per level (indexed by variable/level)
bool m_fail = false;
bool m_Q_changed = false; // tracks mutations to m_Q for fixed-point iteration
// Property precedence relation stored as pairs (lesser, greater)
@ -147,14 +148,14 @@ namespace nlsat {
∪ { ord_inv(resultant(p_j,p_{j+1})) for adjacent roots }.
*/
// Helper 1: scan input polynomials, add sgn_inv / an_del properties and collect polynomials at level m_n
void collect_level_properties(std::vector<property> & Q, std::vector<poly*> & ps_of_n_level) {
void collect_level_properties(std::vector<poly*> & ps_of_n_level) {
for (unsigned i = 0; i < m_P.size(); ++i) {
poly* p = m_P[i];
unsigned level = max_var(p);
if (level < m_n)
Q.push_back(property(prop_enum::sgn_inv_irreducible, polynomial_ref(p, m_pm), /*s_idx*/0u, /* level */ level));
m_Q.push_back(property(prop_enum::sgn_inv_irreducible, polynomial_ref(p, m_pm), /*s_idx*/0u, /* level */ level));
else if (level == m_n){
Q.push_back(property(prop_enum::an_del, polynomial_ref(p, m_pm), /* s_idx */ -1, level));
m_Q.push_back(property(prop_enum::an_del, polynomial_ref(p, m_pm), /* s_idx */ -1, level));
ps_of_n_level.push_back(p);
}
else {
@ -180,7 +181,7 @@ namespace nlsat {
// Helper 3: given collected roots (possibly unsorted), sort them, and add ord_inv(resultant(...))
// for adjacent roots coming from different polynomials. Avoid adding the same unordered pair twice.
// Returns false on failure (e.g. when encountering an ambiguous zero resultant).
bool add_adjacent_resultants(std::vector<std::pair<scoped_anum, poly*>> & root_vals, std::vector<property> & Q) {
bool add_adjacent_resultants(std::vector<std::pair<scoped_anum, poly*>> & root_vals) {
if (root_vals.size() < 2) return true;
std::sort(root_vals.begin(), root_vals.end(), [&](auto const & a, auto const & b){ return m_am.lt(a.first, b.first); });
std::set<std::pair<unsigned,unsigned>> added_pairs;
@ -201,7 +202,7 @@ namespace nlsat {
NOT_IMPLEMENTED_YET();// ambiguous resultant - not handled yet
return false;
}
Q.push_back(property(prop_enum::ord_inv_irreducible, r, /*s_idx*/ -1, max_var(r)));
m_Q.push_back(property(prop_enum::ord_inv_irreducible, r, /*s_idx*/ -1, max_var(r)));
}
return true;
}
@ -211,29 +212,15 @@ namespace nlsat {
∪ { an_del(p) | level(p) == m_n }
∪ { ord_inv(resultant(p_j,p_{j+1})) for adjacent root functions }.
*/
std::vector<property> seed_properties() {
std::vector<property> Q;
void seed_properties() {
std::vector<poly*> ps_of_n_level;
collect_level_properties(Q, ps_of_n_level);
collect_level_properties(ps_of_n_level);
std::vector<std::pair<scoped_anum, poly*>> root_vals;
collect_roots_for_ps(ps_of_n_level, root_vals);
if (!add_adjacent_resultants(root_vals, Q)) {
if (!add_adjacent_resultants(root_vals))
m_fail = true;
return Q;
}
return Q;
}
struct result_struct {
symbolic_interval I;
// Set E of indexed root expressions at level i for P_non_null: the root functions from E pass throug s[i]
std::vector<indexed_root_expr> E;
// omega_buckets removed: sort roots by value instead of grouping into buckets
std::vector<property> Q;
bool fail = false;
};
// Internal carrier to keep root value paired with indexed root expr
struct root_item_t {
scoped_anum val;
@ -247,7 +234,7 @@ namespace nlsat {
root_item_t& operator=(root_item_t&& other) noexcept { val = other.val; ire = other.ire; return *this; }
};
// Compute symbolic interval I from sorted roots. Assumes roots are sorted.
// Compute symbolic interval from sorted roots. Assumes roots are sorted.
void compute_interval_from_sorted_roots(unsigned i,
std::vector<root_item_t>& roots,
symbolic_interval& I) {
@ -298,172 +285,173 @@ namespace nlsat {
// directly on a sorted vector<root_item_t>.
// Part A of construct_interval: apply pre-conditions (line 8-11 scaffolding)
bool apply_property_rules(unsigned i, prop_enum prop_to_avoid, result_struct* rs) {
// Iterate until no mutation to m_Q occurs (fixed-point). We avoid copying m_Q
// by using a change flag that is set by mutating helpers (add_to_Q_if_new / erase_from_Q).
if (m_fail) return false;
do {
m_Q_changed = false;
std::vector<property> to_refine = greatest_to_refine(i, prop_to_avoid);
for (const auto& p : to_refine) {
apply_pre(p, rs);
if (m_fail) return false;
}
} while (m_Q_changed && !m_fail);
return !m_fail;
}
bool apply_property_rules(unsigned i, prop_enum prop_to_avoid, bool has_repr) {
// Iterate until no mutation to m_Q occurs (fixed-point). We avoid copying m_Q
// by using a change flag that is set by mutating helpers (add_to_Q_if_new / erase_from_Q).
if (m_fail) return false;
do {
m_Q_changed = false;
std::vector<property> to_refine = greatest_to_refine(i, prop_to_avoid);
for (const auto& p : to_refine) {
apply_pre(p, has_repr);
if (m_fail) return false;
}
} while (m_Q_changed && !m_fail);
return !m_fail;
}
// Part B of construct_interval: build (I, E, ≼) representation for level i
void build_representation(unsigned i, result_struct& ret) {
std::vector<const poly*> p_non_null;
for (const auto & pr: m_Q) {
if (pr.prop_tag == prop_enum::sgn_inv_irreducible && max_var(pr.poly) == i &&
!coeffs_are_zeroes_on_sample(pr.poly, m_pm, sample(), m_am ))
p_non_null.push_back(pr.poly.get());
}
std::vector<root_item_t> roots;
collect_E_and_roots(p_non_null, i, ret.E, roots);
// Do not use omega_buckets: sort roots by their algebraic value and compute the interval
std::sort(roots.begin(), roots.end(), [&](root_item_t const& a, root_item_t const& b){
return m_am.lt(a.val, b.val);
});
compute_interval_from_sorted_roots(i, roots, ret.I);
}
// Part B of construct_interval: build (I, E, ≼) representation for level i
void build_representation(unsigned i) {
std::vector<const poly*> p_non_null;
for (const auto & pr: m_Q) {
if (pr.prop_tag == prop_enum::sgn_inv_irreducible && max_var(pr.poly) == i &&
!coeffs_are_zeroes_on_sample(pr.poly, m_pm, sample(), m_am ))
p_non_null.push_back(pr.poly.get());
}
std::vector<root_item_t> roots;
std::vector<indexed_root_expr> E;
collect_E_and_roots(p_non_null, i, E, roots);
// Ensure m_I can hold interval for this level
if (m_I.size() <= i) m_I.resize(i+1);
std::sort(roots.begin(), roots.end(), [&](root_item_t const& a, root_item_t const& b){
return m_am.lt(a.val, b.val);
});
compute_interval_from_sorted_roots(i, roots, m_I[i]);
}
std::vector<property> greatest_to_refine(unsigned level, prop_enum prop_to_avoid) {
// Collect candidates on current level, excluding sgn_inv_irreducible
std::vector<property> cand;
cand.reserve(m_Q.size());
for (const auto& q : m_Q)
if (q.level == level && q.prop_tag != prop_to_avoid)
cand.push_back(q);
if (cand.empty()) return {};
std::vector<property> greatest_to_refine(unsigned level, prop_enum prop_to_avoid) {
// Collect candidates on current level, excluding sgn_inv_irreducible
std::vector<property> cand;
cand.reserve(m_Q.size());
for (const auto& q : m_Q)
if (q.level == level && q.prop_tag != prop_to_avoid)
cand.push_back(q);
if (cand.empty()) return {};
// Determine maxima w.r.t. ▹ using the transitive closure matrix
// Dominance requires the same polynomial in both compared properties
std::vector<bool> dominated(cand.size(), false);
for (size_t i = 0; i < cand.size(); ++i) {
for (size_t j = 0; j < cand.size(); ++j) {
if (i != j && dominates(cand[j], cand[i])) {
dominated[i] = true;
break;
}
}
}
auto poly_id = [cand](unsigned i) { return cand[i].poly == nullptr? UINT_MAX: polynomial::manager::id(cand[i].poly);};
// Extract non-dominated (greatest) candidates; keep deterministic order by (poly id, prop enum)
struct Key { unsigned pid; unsigned pprop; size_t idx; };
std::vector<Key> keys;
keys.reserve(cand.size());
for (size_t i = 0; i < cand.size(); ++i) {
if (!dominated[i]) {
keys.push_back(Key{ poly_id(i), static_cast<unsigned>(cand[i].prop_tag), i });
}
}
std::sort(keys.begin(), keys.end(), [](Key const& a, Key const& b){
if (a.pid != b.pid) return a.pid < b.pid;
return a.pprop < b.pprop;
});
std::vector<property> ret;
ret.reserve(keys.size());
for (auto const& k : keys) ret.push_back(cand[k.idx]);
return ret;
}
// Determine maxima w.r.t. ▹ using the transitive closure matrix
// Dominance requires the same polynomial in both compared properties
std::vector<bool> dominated(cand.size(), false);
for (size_t i = 0; i < cand.size(); ++i) {
for (size_t j = 0; j < cand.size(); ++j) {
if (i != j && dominates(cand[j], cand[i])) {
dominated[i] = true;
break;
}
}
}
auto poly_id = [cand](unsigned i) { return cand[i].poly == nullptr? UINT_MAX: polynomial::manager::id(cand[i].poly);};
// Extract non-dominated (greatest) candidates; keep deterministic order by (poly id, prop enum)
struct Key { unsigned pid; unsigned pprop; size_t idx; };
std::vector<Key> keys;
keys.reserve(cand.size());
for (size_t i = 0; i < cand.size(); ++i) {
if (!dominated[i]) {
keys.push_back(Key{ poly_id(i), static_cast<unsigned>(cand[i].prop_tag), i });
}
}
std::sort(keys.begin(), keys.end(), [](Key const& a, Key const& b){
if (a.pid != b.pid) return a.pid < b.pid;
return a.pprop < b.pprop;
});
std::vector<property> ret;
ret.reserve(keys.size());
for (auto const& k : keys) ret.push_back(cand[k.idx]);
return ret;
}
// Step 1a: collect E and root values
void collect_E_and_roots(std::vector<const poly*> const& P_non_null,
unsigned i,
std::vector<indexed_root_expr>& E,
std::vector<root_item_t>& roots_out) {
var y = i;
for (auto const* p0 : P_non_null) {
auto* p = const_cast<poly*>(p0);
if (m_pm.max_var(p) != y)
continue;
scoped_anum_vector roots(m_am);
m_am.isolate_roots(polynomial_ref(p, m_pm), undef_var_assignment(sample(), y), roots);
// Step 1a: collect E and root values
void collect_E_and_roots(std::vector<const poly*> const& P_non_null,
unsigned i,
std::vector<indexed_root_expr>& E,
std::vector<root_item_t>& roots_out) {
var y = i;
for (auto const* p0 : P_non_null) {
auto* p = const_cast<poly*>(p0);
if (m_pm.max_var(p) != y)
continue;
scoped_anum_vector roots(m_am);
m_am.isolate_roots(polynomial_ref(p, m_pm), undef_var_assignment(sample(), y), roots);
unsigned num_roots = roots.size();
TRACE(levelwise,
tout << "roots (" << num_roots << "):";
for (unsigned kk = 0; kk < num_roots; ++kk) {
tout << " "; m_am.display(tout, roots[kk]);
}
tout << std::endl;
);
for (unsigned k = 0; k < num_roots; ++k) {
E.push_back(indexed_root_expr{ p, k + 1 });
roots_out.emplace_back(m_am, p, k + 1, roots[k]);
}
}
}
unsigned num_roots = roots.size();
TRACE(levelwise,
tout << "roots (" << num_roots << "):";
for (unsigned kk = 0; kk < num_roots; ++kk) {
tout << " "; m_am.display(tout, roots[kk]);
}
tout << std::endl;
);
for (unsigned k = 0; k < num_roots; ++k) {
E.push_back(indexed_root_expr{ p, k + 1 });
roots_out.emplace_back(m_am, p, k + 1, roots[k]);
}
}
}
// Helper: add a property to m_Q if an equivalent one is not already present.
// Equivalence: same prop_tag and same level; if pr.poly is non-null, require the same poly as well.
void add_to_Q_if_new(const property & pr) {
for (auto const & q : m_Q) {
if (q.prop_tag != pr.prop_tag) continue;
if (q.level != pr.level) continue;
if (pr.poly) {
if (q.poly == pr.poly) return;
else continue;
}
// pr.poly is null -> match by prop_tag + level only
return;
}
m_Q.push_back(pr);
m_Q_changed = true;
}
// Helper: add a property to m_Q if an equivalent one is not already present.
// Equivalence: same prop_tag and same level; if pr.poly is non-null, require the same poly as well.
void add_to_Q_if_new(const property & pr) {
for (auto const & q : m_Q) {
if (q.prop_tag != pr.prop_tag) continue;
if (q.level != pr.level) continue;
if (pr.poly) {
if (q.poly == pr.poly) return;
else continue;
}
// pr.poly is null -> match by prop_tag + level only
return;
}
m_Q.push_back(pr);
m_Q_changed = true;
}
void remove_level_i_from_Q(std::vector<property> & Q, unsigned i) {
Q.erase(std::remove_if(Q.begin(), Q.end(),
[i](const property &p) { return p.level == i; }),
Q.end());
}
void remove_level_i_from_Q(std::vector<property> & Q, unsigned i) {
Q.erase(std::remove_if(Q.begin(), Q.end(),
[i](const property &p) { return p.level == i; }),
Q.end());
}
void erase_from_Q(const property& p) {
auto it = std::find_if(m_Q.begin(), m_Q.end(), [&](const property & q) {
return q.prop_tag == p.prop_tag && q.poly == p.poly && q.level == p.level && q.s_idx == p.s_idx;
});
SASSERT(it != m_Q.end());
m_Q.erase(it);
m_Q_changed = true;
}
void erase_from_Q(const property& p) {
auto it = std::find_if(m_Q.begin(), m_Q.end(), [&](const property & q) {
return q.prop_tag == p.prop_tag && q.poly == p.poly && q.level == p.level && q.s_idx == p.s_idx;
});
SASSERT(it != m_Q.end());
m_Q.erase(it);
m_Q_changed = true;
}
result_struct construct_interval(unsigned i) {
result_struct ret;
if (!apply_property_rules(i, prop_enum::sgn_inv_irreducible, nullptr)) {
ret.fail = true;
return ret;
// construct_interval: compute representation for level i and apply post rules.
// Returns true on failure.
bool construct_interval(unsigned i) {
if (!apply_property_rules(i, prop_enum::sgn_inv_irreducible, false)) {
return true;
}
build_representation(i, ret);
apply_property_rules(i, prop_enum(prop_enum::holds), & ret);
build_representation(i);
// apply post-processing that may rely on the representation being present
if (!apply_property_rules(i, prop_enum(prop_enum::holds), true))
return true;
// (moved Rule 1.1 precondition handling into apply_pre_connected)
ret.Q = m_Q;
ret.fail = m_fail;
remove_level_i_from_Q(ret.Q, i);
return ret;
}
// Extracted helper: handle ord_inv(discriminant_{x_{i+1}}(p)) for an_del pre-processing
void add_ord_inv_discriminant_for(const property& p) {
polynomial_ref disc(m_pm);
disc = discriminant(p.poly, p.level);
TRACE(levelwise, ::nlsat::display(tout << "discriminant: ", m_solver, disc) << "\n";);
if (!is_const(disc)) {
if (coeffs_are_zeroes_on_sample(disc, m_pm, sample(), m_am)) {
m_fail = true; // ambiguous multiplicity -- not handled yet
NOT_IMPLEMENTED_YET();
return;
}
else {
unsigned lvl = max_var(disc);
add_to_Q_if_new(property(prop_enum::ord_inv_irreducible, disc, /*s_idx*/ 0u, lvl));
}
}
// remove properties at level i from m_Q (they are consumed by this level)
remove_level_i_from_Q(m_Q, i);
return m_fail;
}
// Extracted helper: handle ord_inv(discriminant_{x_{i+1}}(p)) for an_del pre-processing
void add_ord_inv_discriminant_for(const property& p) {
polynomial_ref disc(m_pm);
disc = discriminant(p.poly, p.level);
TRACE(levelwise, ::nlsat::display(tout << "discriminant: ", m_solver, disc) << "\n";);
if (!is_const(disc)) {
if (coeffs_are_zeroes_on_sample(disc, m_pm, sample(), m_am)) {
m_fail = true; // ambiguous multiplicity -- not handled yet
NOT_IMPLEMENTED_YET();
return;
}
else {
unsigned lvl = max_var(disc);
add_to_Q_if_new(property(prop_enum::ord_inv_irreducible, disc, /*s_idx*/ 0u, lvl));
}
}
}
// Extracted helper: handle sgn_inv(leading_coefficient_{x_{i+1}}(p)) for an_del pre-processing
void add_sgn_inv_leading_coeff_for(const property& p) {
@ -522,7 +510,7 @@ namespace nlsat {
}
// Pre-processing for connected(i) (Rule 4.11)
void apply_pre_connected(const property & p, result_struct* rs) {
void apply_pre_connected(const property & p, bool has_repr) {
TRACE(levelwise, tout << "connected:";
if (p.level != static_cast<unsigned>(-1)) tout << " level=" << p.level;
tout << std::endl;);
@ -536,7 +524,7 @@ namespace nlsat {
}
// p.level > 0
if (!rs) return; // no change since the interval etc is not there
if (!has_repr) return; // no change since the interval etc is not there
// Rule 1.1 precondition: when processing connected(i) we must ensure the next lower level
// has connected(i-1) and repr(I,s) available. Add those markers to m_Q so they propagate.
@ -554,7 +542,7 @@ namespace nlsat {
if (p.level != static_cast<unsigned>(-1)) tout << " level=" << p.level;
tout << std::endl;);
// First try subrule 1 of Rule 4.2. If it succeeds we do not apply the fallback (subrule 2).
if (try_non_null_via_coeffs(p, nullptr))
if (try_non_null_via_coeffs(p))
return;
// fallback: apply the first subrule
apply_pre_non_null_fallback(p);
@ -574,13 +562,13 @@ namespace nlsat {
// if c_j evaluates non-zero at the sample and we already have sgn_inv(c_j) in m_Q,
// then non_null(p) holds on the region represented by 'rs' (if provided).
// Returns true if non_null was established and the property p was removed.
bool try_non_null_via_coeffs(const property& p, result_struct* rs) {
bool try_non_null_via_coeffs(const property& p) {
if (have_non_zero_const(p.poly, p.level)) {
TRACE(levelwise, tout << "have a non-zero const coefficient\n";);
erase_from_Q(p);
return true;
}
poly* pp = p.poly.get();
unsigned deg = m_pm.degree(pp, p.level);
for (unsigned j = 0; j <= deg; ++j) {
@ -596,17 +584,17 @@ namespace nlsat {
continue;
auto it = std::find_if(m_Q.begin(), m_Q.end(), [&](const property & q) {
return (q.prop_tag == prop_enum::sgn_inv_irreducible || q.prop_tag == prop_enum::sgn_inv_reducible)
&& q.poly == p.poly;
});
if (it != m_Q.end()) {
erase_from_Q(p);
return true;
}
return (q.prop_tag == prop_enum::sgn_inv_irreducible || q.prop_tag == prop_enum::sgn_inv_reducible)
&& q.poly == p.poly;
});
if (it != m_Q.end()) {
erase_from_Q(p);
return true;
}
add_to_Q_if_new(property(prop_enum::sgn_inv_reducible, coeff, 0u, max_var(coeff)));
erase_from_Q(p);
return true;
add_to_Q_if_new(property(prop_enum::sgn_inv_reducible, coeff, 0u, max_var(coeff)));
erase_from_Q(p);
return true;
}
return false;
}
@ -654,39 +642,35 @@ namespace nlsat {
erase_from_Q(p);
}
void apply_pre(const property& p, result_struct* rs) {
void apply_pre(const property& p, bool has_repr) {
TRACE(levelwise, display(tout << "property p:", p) << std::endl;);
if (p.prop_tag == prop_enum::an_del)
apply_pre_an_del(p);
else if (p.prop_tag == prop_enum::connected)
apply_pre_connected(p, rs );
apply_pre_connected(p, has_repr );
else if (p.prop_tag == prop_enum::non_null)
apply_pre_non_null(p);
else
NOT_IMPLEMENTED_YET();
}
}
// return an empty vector on failure, otherwise returns the cell representations with intervals
std::vector<symbolic_interval> single_cell() {
TRACE(levelwise,
m_solver.display_assignment(tout << "sample()") << std::endl;
tout << "m_P:\n";
for (const auto & p: m_P) {
::nlsat::display(tout, m_solver, polynomial_ref(p, m_pm)) << std::endl;
tout << "max_var:" << m_pm.max_var(p) << std::endl;
}
);
std::vector<symbolic_interval> ret;
m_Q = seed_properties(); // Q is the set of properties on level m_n
apply_property_rules(m_n, prop_enum::_count, nullptr); // reduce the level by one to be consumed by construct_interval
m_solver.display_assignment(tout << "sample()") << std::endl;
tout << "m_P:\n";
for (const auto & p: m_P) {
::nlsat::display(tout, m_solver, polynomial_ref(p, m_pm)) << std::endl;
tout << "max_var:" << m_pm.max_var(p) << std::endl;
}
);
seed_properties(); // initializes m_Q as the set of properties on level m_n
apply_property_rules(m_n, prop_enum::_count, false); // reduce the level by one to be consumed by construct_interval
for (unsigned i = m_n; --i > 0; ) {
auto result = construct_interval(i);
if (result.fail)
if (!construct_interval(i))
return std::vector<symbolic_interval>(); // return empty
ret.push_back(result.I);
m_Q = result.Q;
}
return ret; // the order is reversed!
return m_I; // the order of intervals is reversed
}
bool dominates(const property& a, const property& b) const {