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add clausal lookahead to arithmetic solver as part of portfolio

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have legacy qfbv-sls solver use nnf pre-processing. It relies on it for correctness of the score updates.
This commit is contained in:
Nikolaj Bjorner 2025-01-20 16:16:46 -08:00
parent a941f5ae84
commit 22e4054674
13 changed files with 678 additions and 92 deletions
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1
src/ast/sls/CMakeLists.txt
View file

@ -3,6 +3,7 @@ z3_add_component(ast_sls
bvsls_opt_engine.cpp
sat_ddfw.cpp
sls_arith_base.cpp
sls_arith_clausal.cpp
sls_arith_plugin.cpp
sls_array_plugin.cpp
sls_basic_plugin.cpp

21
src/ast/sls/sat_ddfw.cpp
View file

@ -99,6 +99,16 @@ namespace sat {
m_last_flips = m_flips;
}
sat::bool_var ddfw::bool_flip() {
flet<bool> _in_bool_flip(m_in_bool_flip, true);
double reward = 0;
bool_var v = pick_var(reward);
if (apply_flip(v, reward))
return v;
shift_weights();
return sat::null_bool_var;
}
bool ddfw::do_flip() {
double reward = 0;
bool_var v = pick_var(reward);
@ -125,7 +135,9 @@ namespace sat {
bool_var v0 = null_bool_var;
for (bool_var v : m_unsat_vars) {
r = reward(v);
if (r > 0.0)
if (m_in_bool_flip && m_plugin->is_external(v))
;
else if (r > 0.0)
sum_pos += score(r);
else if (r == 0.0 && sum_pos == 0 && (m_rand() % (n++)) == 0)
v0 = v;
@ -134,6 +146,8 @@ namespace sat {
double lim_pos = ((double) m_rand() / (1.0 + m_rand.max_value())) * sum_pos;
for (bool_var v : m_unsat_vars) {
r = reward(v);
if (m_in_bool_flip && m_plugin->is_external(v))
continue;
if (r > 0) {
lim_pos -= score(r);
if (lim_pos <= 0)
@ -146,6 +160,8 @@ namespace sat {
return v0;
if (m_unsat_vars.empty())
return null_bool_var;
if (m_in_bool_flip)
return false;
return m_unsat_vars.elem_at(m_rand(m_unsat_vars.size()));
}
@ -332,6 +348,7 @@ namespace sat {
m_vars[v].m_reward = 0;
}
m_unsat_vars.reset();
m_num_external_in_unsat_vars = 0;
m_unsat.reset();
unsigned sz = m_clauses.size();
for (unsigned i = 0; i < sz; ++i) {
@ -400,7 +417,7 @@ namespace sat {
for (unsigned i = 0; i < num_vars(); ++i)
m_model[i] = to_lbool(value(i));
save_priorities();
if (m_plugin)
if (m_plugin && !m_in_bool_flip)
m_last_result = m_plugin->on_save_model();
}

32
src/ast/sls/sat_ddfw.h
View file

@ -36,11 +36,10 @@ namespace sat {
class local_search_plugin {
public:
virtual ~local_search_plugin() {}
//virtual void init_search() = 0;
//virtual void finish_search() = 0;
virtual void on_rescale() = 0;
virtual lbool on_save_model() = 0;
virtual void on_restart() = 0;
virtual bool is_external(sat::bool_var v) = 0;
};
class ddfw {
@ -140,14 +139,26 @@ namespace sat {
unsigned select_max_same_sign(unsigned cf_idx);
unsigned m_num_external_in_unsat_vars = 0;
inline void inc_make(literal lit) {
bool_var v = lit.var();
if (make_count(v)++ == 0) m_unsat_vars.insert_fresh(v);
if (make_count(v)++ == 0) {
m_unsat_vars.insert_fresh(v);
if (m_plugin && m_plugin->is_external(v))
++m_num_external_in_unsat_vars;
}
}
inline void dec_make(literal lit) {
bool_var v = lit.var();
if (--make_count(v) == 0) m_unsat_vars.remove(v);
if (--make_count(v) == 0) {
if (m_unsat_vars.contains(v)) {
m_unsat_vars.remove(v);
if (m_plugin && m_plugin->is_external(v))
--m_num_external_in_unsat_vars;
}
}
}
inline void inc_reward(literal lit, double w) { m_vars[lit.var()].m_reward += w; }
@ -164,13 +175,12 @@ namespace sat {
bool apply_flip(bool_var v, double reward);
void save_best_values();
void save_model();
void save_priorities();
// shift activity
void shift_weights();
inline double calculate_transfer_weight(double w);
// reinitialize weights activity
@ -204,6 +214,8 @@ namespace sat {
bool_var_set m_rotate_tabu;
bool_var_vector m_new_tabu_vars;
bool m_in_bool_flip = false;
public:
ddfw() {}
@ -241,6 +253,10 @@ namespace sat {
indexed_uint_set const& unsat_set() const { return m_unsat; }
indexed_uint_set const& unsat_vars() const { return m_unsat_vars; }
unsigned num_external_in_unsat_vars() const { return m_num_external_in_unsat_vars; }
vector<clause_info> const& clauses() const { return m_clauses; }
clause_info& get_clause_info(unsigned idx) { return m_clauses[idx]; }
@ -251,6 +267,10 @@ namespace sat {
void flip(bool_var v);
sat::bool_var bool_flip();
void shift_weights();
inline double reward(bool_var v) const { return m_vars[v].m_reward; }
void set_reward(bool_var v, double r) { m_vars[v].m_reward = r; }

154
src/ast/sls/sls_arith_base.cpp
View file

@ -111,7 +111,8 @@ namespace sls {
arith_base<num_t>::arith_base(context& ctx) :
plugin(ctx),
a(m),
m_new_terms(m) {
m_new_terms(m),
m_clausal_sls(*this) {
m_fid = a.get_family_id();
}
@ -447,12 +448,12 @@ namespace sls {
delta_out = delta;
if (m_last_var == v && m_last_delta == -delta) {
TRACE("arith", tout << "flip back " << v << " " << delta << "\n";);
TRACE("arith_verbose", tout << "flip back " << v << " " << delta << "\n";);
return false;
}
if (m_use_tabu && vi.is_tabu(m_stats.m_num_steps, delta)) {
TRACE("arith", tout << "tabu\n");
if (m_use_tabu && vi.is_tabu(m_stats.m_steps, delta)) {
TRACE("arith_verbose", tout << "tabu v" << v << " delta:" << delta << "\n");
return false;
}
@ -545,8 +546,8 @@ namespace sls {
if (update(v, new_value)) {
m_last_delta = delta;
m_stats.m_num_steps++;
m_vars[v].set_step(m_stats.m_num_steps, m_stats.m_num_steps + 3 + ctx.rand(10), delta);
m_stats.m_steps++;
m_vars[v].set_step(m_stats.m_steps, m_stats.m_steps + 3 + ctx.rand(10), delta);
return true;
}
sum_score -= score;
@ -1106,6 +1107,7 @@ namespace sls {
// attach i to bv
m_ineqs.set(bv, &i);
m_bool_var_atoms.insert(bv);
}
template<typename num_t>
@ -1403,6 +1405,40 @@ namespace sls {
throw default_exception("repair is not supported for " + mk_pp(e, m));
}
}
for (unsigned v = 0; v < m_vars.size(); ++v)
initialize_bool_vars_of(v);
}
template<typename num_t>
void arith_base<num_t>::initialize_bool_vars_of(var_t v) {
if (!m_vars[v].m_bool_vars_of.empty())
return;
buffer<var_t> todo;
todo.push_back(v);
auto& vi = m_vars[v];
for (unsigned i = 0; i < todo.size(); ++i) {
var_t u = todo[i];
auto& ui = m_vars[u];
for (auto const& idx : ui.m_muls) {
auto& [x, monomial] = m_muls[idx];
if (all_of(todo, [x](var_t v) { return x != v; }))
todo.push_back(x);
}
for (auto const& idx : ui.m_adds) {
auto x = m_adds[idx].m_var;
if (all_of(todo, [x](var_t v) { return x != v; }))
todo.push_back(x);
}
for (auto const& [coeff, bv] : ui.m_linear_occurs)
vi.m_bool_vars_of.insert(bv);
}
;
for (auto bv : vi.m_bool_vars_of) {
for (auto i : ctx.get_use_list(sat::literal(bv, true)))
vi.m_clauses_of.insert(i);
for (auto i : ctx.get_use_list(sat::literal(bv, false)))
vi.m_clauses_of.insert(i);
}
}
template<typename num_t>
@ -2274,7 +2310,7 @@ namespace sls {
auto const& vi = m_vars[v];
if (vi.m_def_idx == UINT_MAX)
return true;
IF_VERBOSE(4, verbose_stream() << vi.m_op << " repair def " << mk_bounded_pp(vi.m_expr, m) << "\n");
IF_VERBOSE(10, verbose_stream() << vi.m_op << " repair def " << mk_bounded_pp(vi.m_expr, m) << "\n");
TRACE("sls", tout << "repair def " << mk_bounded_pp(vi.m_expr, m) << "\n");
switch (vi.m_op) {
case arith_op_kind::LAST_ARITH_OP:
@ -2398,13 +2434,12 @@ namespace sls {
template<typename num_t>
void arith_base<num_t>::collect_statistics(statistics& st) const {
st.update("sls-arith-flips", m_stats.m_num_steps);
st.update("sls-arith-moves", m_stats.m_moves);
st.update("sls-arith-steps", m_stats.m_steps);
}
template<typename num_t>
void arith_base<num_t>::reset_statistics() {
m_stats.m_num_steps = 0;
m_stats.m_steps = 0;
}
// global lookahead mode
@ -2708,7 +2743,6 @@ namespace sls {
template<typename num_t>
void arith_base<num_t>::lookahead_num(var_t v, num_t const& delta) {
num_t old_value = value(v);
expr* e = m_vars[v].m_expr;
if (m_last_expr != e) {
if (m_last_expr)
@ -2779,6 +2813,31 @@ namespace sls {
m_last_expr = nullptr;
}
template<typename num_t>
void arith_base<num_t>::add_lookahead(bool_info& i, sat::bool_var bv) {
if (!i.fixable_atoms.contains(bv))
return;
if (m_fixed_atoms.contains(bv))
return;
auto* ineq = get_ineq(bv);
if (!ineq)
return;
num_t na, nb;
for (auto const& [x, nl] : ineq->m_nonlinear) {
if (!i.fixable_vars.contains(x))
continue;
if (is_fixed(x))
continue;
if (is_linear(x, nl, nb))
find_linear_moves(*ineq, x, nb);
else if (is_quadratic(x, nl, na, nb))
find_quadratic_moves(*ineq, x, na, nb, ineq->m_args_value);
else
;
}
m_fixed_atoms.insert(bv);
}
// for every variable e, for every atom containing e
// add lookahead for e.
// m_fixable_atoms contains atoms that can be fixed.
@ -2786,33 +2845,6 @@ namespace sls {
template<typename num_t>
void arith_base<num_t>::add_lookahead(bool_info& i, expr* e) {
auto add_atom = [&](sat::bool_var bv) {
if (!i.fixable_atoms.contains(bv))
return;
if (m_fixed_atoms.contains(bv))
return;
auto a = ctx.atom(bv);
if (!a)
return;
auto* ineq = get_ineq(bv);
if (!ineq)
return;
num_t na, nb;
for (auto const& [x, nl] : ineq->m_nonlinear) {
if (!i.fixable_vars.contains(x))
continue;
if (is_fixed(x))
continue;
if (is_linear(x, nl, nb))
find_linear_moves(*ineq, x, nb);
else if (is_quadratic(x, nl, na, nb))
find_quadratic_moves(*ineq, x, na, nb, ineq->m_args_value);
else
;
}
m_fixed_atoms.insert(bv);
};
auto add_finite_domain = [&](var_t v) {
auto old_value = value(v);
for (auto const& n : m_vars[v].m_finite_domain)
@ -2832,13 +2864,8 @@ namespace sls {
add_finite_domain(v);
return;
}
for (auto const& [coeff, bv] : vi.m_linear_occurs)
add_atom(bv);
for (auto const& idx : vi.m_muls) {
auto const& [x, monomial] = m_muls[idx];
for (auto [coeff, bv] : m_vars[x].m_linear_occurs)
add_atom(bv);
}
for (auto bv : vi.m_bool_vars_of)
add_lookahead(i, bv);
}
}
@ -2927,7 +2954,7 @@ namespace sls {
add_lookahead(info, vars[(start + i) % sz]);
if (m_updates.empty())
return false;
unsigned idx = ctx.rand() % m_updates.size();
unsigned idx = ctx.rand(m_updates.size());
auto& [v, delta, score] = m_updates[idx];
m_best_expr = m_vars[v].m_expr;
if (false && !m_vars[v].m_finite_domain.empty())
@ -3015,13 +3042,13 @@ namespace sls {
void arith_base<num_t>::global_search() {
initialize_bool_assignment();
rescore();
m_config.max_moves = m_stats.m_moves + m_config.max_moves_base;
TRACE("arith", tout << "search " << m_stats.m_moves << " " << m_config.max_moves << "\n";);
IF_VERBOSE(3, verbose_stream() << "lookahead-search moves:" << m_stats.m_moves << " max-moves:" << m_config.max_moves << "\n");
m_config.max_moves = m_stats.m_steps + m_config.max_moves_base;
TRACE("arith", tout << "search " << m_stats.m_steps << " " << m_config.max_moves << "\n";);
IF_VERBOSE(3, verbose_stream() << "lookahead-search steps:" << m_stats.m_steps << " max-moves:" << m_config.max_moves << "\n");
TRACE("arith", display(tout));
while (ctx.rlimit().inc() && m_stats.m_moves < m_config.max_moves) {
m_stats.m_moves++;
while (ctx.rlimit().inc() && m_stats.m_steps < m_config.max_moves) {
m_stats.m_steps++;
check_restart();
auto t = get_candidate_unsat();
@ -3043,7 +3070,7 @@ namespace sls {
if (apply_move(t, vars, arith_move_type::random_update))
recalibrate_weights();
}
if (m_stats.m_moves >= m_config.max_moves)
if (m_stats.m_steps >= m_config.max_moves)
m_config.max_moves_base += 100;
finalize_bool_assignment();
}
@ -3098,11 +3125,11 @@ namespace sls {
if (old_value == new_value)
return true;
if (!vi.in_range(new_value)) {
TRACE("arith", tout << "Not in range v" << v << " " << new_value << "\n");
TRACE("arith_verbose", tout << "Not in range v" << v << " " << new_value << "\n");
return false;
}
if (!in_bounds(v, new_value) && in_bounds(v, old_value)) {
TRACE("arith", tout << "out of bounds v" << v << " " << new_value << "\n");
TRACE("arith_verbose", tout << "out of bounds v" << v << " " << new_value << "\n");
//verbose_stream() << "out of bounds v" << v << " " << new_value << "\n";
return false;
}
@ -3166,16 +3193,16 @@ namespace sls {
template<typename num_t>
void arith_base<num_t>::check_restart() {
if (m_stats.m_moves % m_config.restart_base == 0) {
if (m_stats.m_steps % m_config.restart_base == 0) {
ucb_forget();
rescore();
}
if (m_stats.m_moves < m_config.restart_next)
if (m_stats.m_steps < m_config.restart_next)
return;
++m_stats.m_restarts;
m_config.restart_next = std::max(m_config.restart_next, m_stats.m_moves);
m_config.restart_next = std::max(m_config.restart_next, m_stats.m_steps);
if (0x1 == (m_stats.m_restarts & 0x1))
m_config.restart_next += m_config.restart_base;
@ -3184,10 +3211,8 @@ namespace sls {
// reset_uninterp_in_false_literals
rescore();
}
template<typename num_t>
void arith_base<num_t>::ucb_forget() {
if (m_config.ucb_forget >= 1.0)
@ -3214,18 +3239,21 @@ namespace sls {
//m_config.ucb_forget = p.ucb_forget();
m_config.wp = p.wp();
m_config.restart_base = p.restart_base();
//m_config.restart_next = p.restart_next();
m_config.restart_next = p.restart_base();
//m_config.max_moves_base = p.max_moves_base();
//m_config.max_moves = p.max_moves();
m_config.arith_use_lookahead = p.arith_use_lookahead();
m_config.use_lookahead = p.arith_use_lookahead();
m_config.use_clausal_lookahead = p.arith_use_clausal_lookahead();
m_config.allow_plateau = p.arith_allow_plateau();
m_config.config_initialized = true;
}
template<typename num_t>
void arith_base<num_t>::start_propagation() {
updt_params();
if (m_config.arith_use_lookahead)
updt_params();
if (m_config.use_clausal_lookahead)
m_clausal_sls.search();
else if (m_config.use_lookahead)
global_search();
}

23
src/ast/sls/sls_arith_base.h
View file

@ -22,6 +22,7 @@ Author:
#include "ast/ast_trail.h"
#include "ast/arith_decl_plugin.h"
#include "ast/sls/sls_context.h"
#include "ast/sls/sls_arith_clausal.h"
namespace sls {
@ -36,6 +37,8 @@ namespace sls {
std::ostream& operator<<(std::ostream& out, arith_move_type mt);
static const unsigned null_arith_var = UINT_MAX;
// local search portion for arithmetic
template<typename num_t>
class arith_base : public plugin {
@ -66,13 +69,13 @@ namespace sls {
unsigned restart_base = 1000;
unsigned restart_next = 1000;
unsigned restart_init = 1000;
bool arith_use_lookahead = false;
bool use_lookahead = false;
bool use_clausal_lookahead = false;
bool allow_plateau = false;
};
struct stats {
unsigned m_num_steps = 0;
unsigned m_moves = 0;
unsigned m_steps = 0;
unsigned m_restarts = 0;
};
@ -116,6 +119,8 @@ namespace sls {
arith_op_kind m_op = arith_op_kind::LAST_ARITH_OP;
unsigned m_def_idx = UINT_MAX;
vector<std::pair<num_t, sat::bool_var>> m_linear_occurs;
indexed_uint_set m_bool_vars_of;
indexed_uint_set m_clauses_of;
unsigned_vector m_muls;
unsigned_vector m_adds;
optional<bound> m_lo, m_hi;
@ -154,6 +159,9 @@ namespace sls {
else
m_tabu_neg = tabu_step, m_last_neg = step;
}
unsigned last_step(num_t const& delta) const {
return delta > 0 ? m_last_pos : m_last_neg;
}
void out_of_range() {
++m_num_out_of_range;
if (m_num_out_of_range < 1000 * (1 + m_num_in_range))
@ -204,7 +212,10 @@ namespace sls {
bool m_use_tabu = true;
unsigned m_updates_max_size = 45;
arith_util a;
friend class arith_clausal<num_t>;
arith_clausal<num_t> m_clausal_sls;
svector<double> m_prob_break;
indexed_uint_set m_bool_var_atoms;
void invariant();
void invariant(ineq const& i);
@ -277,6 +288,7 @@ namespace sls {
double compute_score(var_t x, num_t const& delta);
void save_best_values();
void initialize_bool_vars_of(var_t v);
var_t mk_var(expr* e);
var_t mk_term(expr* e);
var_t mk_op(arith_op_kind k, expr* e, expr* x, expr* y);
@ -318,7 +330,7 @@ namespace sls {
double score = 0;
unsigned touched = 1;
lbool value = l_undef;
sat::bool_var_set fixable_atoms;
indexed_uint_set fixable_atoms;
uint_set fixable_vars;
ptr_vector<expr> fixable_exprs;
bool_info(unsigned w) : weight(w) {}
@ -335,6 +347,7 @@ namespace sls {
unsigned m_touched = 1;
sat::bool_var_set m_fixed_atoms;
uint64_t m_tabu_set = 0;
unsigned m_global_search_count = 0;
bool in_tabu_set(expr* e, num_t const& n);
void insert_tabu_set(expr* e, num_t const& n);
@ -344,6 +357,7 @@ namespace sls {
void set_bool_value(expr* e, bool v) { get_bool_info(e).value = to_lbool(v); }
bool get_basic_bool_value(app* e);
void initialize_bool_assignment();
void finalize_bool_assignment();
double old_score(expr* e) { return get_bool_info(e).score; }
double new_score(expr* e);
@ -366,6 +380,7 @@ namespace sls {
void lookahead_bool(expr* e);
double lookahead(expr* e, bool update_score);
void add_lookahead(bool_info& i, expr* e);
void add_lookahead(bool_info& i, sat::bool_var bv);
ptr_vector<expr> const& get_fixable_exprs(expr* e);
bool apply_move(expr* f, ptr_vector<expr> const& vars, arith_move_type t);
expr* get_candidate_unsat();

368
src/ast/sls/sls_arith_clausal.cpp Normal file
View file

@ -0,0 +1,368 @@
/*++
Copyright (c) 2025 Microsoft Corporation
Module Name:
sls_arith_clausal
Abstract:
Theory plugin for arithmetic local search
based on clausal search as used in HybridSMT (nia_ls)
In contrast to HybridSMT/nia_ls we reuse ddfw
for everything Boolean. It requiers exposing the following:
- unsat_vars - Boolean variables that are in unsat clauses.
- num_external_vars_in_unsat - External variables in unsat clauses
- shift_weights - allow plugin to invoke shift-weights
Author:
Nikolaj Bjorner (nbjorner) 2025-01-16
--*/
#include "ast/sls/sls_arith_clausal.h"
#include "ast/sls/sls_arith_base.h"
namespace sls {
template<typename num_t>
arith_clausal<num_t>::arith_clausal(arith_base<num_t>& a) :
ctx(a.ctx),
a(a) {
}
template<typename num_t>
void arith_clausal<num_t>::search() {
num_t delta;
initialize();
TRACE("arith", ctx.display_all(tout));
a.m_config.max_moves = a.m_stats.m_steps + a.m_config.max_moves_base;
while (ctx.rlimit().inc() && a.m_stats.m_steps < a.m_config.max_moves && !ctx.unsat().empty()) {
a.m_stats.m_steps++;
check_restart();
unsigned vars_in_unsat = ctx.unsat_vars().size();
unsigned ext_in_unsat = ctx.num_external_in_unsat_vars();
unsigned bool_in_unsat = vars_in_unsat - ext_in_unsat;
bool time_up_bool = m_no_improve_bool * vars_in_unsat > 5 * bool_in_unsat;
bool time_up_arith = m_no_improve_arith * vars_in_unsat > 20 * ext_in_unsat;
if ((m_bool_mode && bool_in_unsat < vars_in_unsat && time_up_bool) || bool_in_unsat == 0)
enter_arith_mode();
else if ((!m_bool_mode && bool_in_unsat > 0 && time_up_arith) || vars_in_unsat == bool_in_unsat)
enter_bool_mode();
if (m_bool_mode) {
sat::bool_var v = ctx.bool_flip();
TRACE("arith", tout << "bool flip v:" << v << "\n";
tout << "unsat-vars " << vars_in_unsat << "\n";
tout << "bools: " << bool_in_unsat << " timeup-bool " << time_up_bool << "\n";
tout << "no-improve bool: " << m_no_improve_bool << "\n";
tout << "ext: " << ext_in_unsat << " timeup-arith " << time_up_arith << "\n";);
m_no_improve_bool = update_outer_best_solution() ? 0 : m_no_improve_bool + 1;
}
else {
move_arith_variable();
m_no_improve_arith = update_inner_best_solution() ? 0 : m_no_improve_arith + 1;
}
m_no_improve = update_best_solution() ? 0 : m_no_improve + 1;
}
if (a.m_stats.m_steps >= a.m_config.max_moves)
a.m_config.max_moves_base += 100;
}
template<typename num_t>
void arith_clausal<num_t>::move_arith_variable() {
var_t v = null_arith_var;
{
a.m_best_score = 1;
flet<bool> _use_tabu(a.m_use_tabu, true);
if (v == null_arith_var) {
add_lookahead_on_unsat_vars();
v = critical_move_on_updates(unsat_var_move);
}
if (v == null_arith_var) {
add_lookahead_on_false_literals();
v = critical_move_on_updates(false_literal_move);
}
}
// tabu flips were not possible
if (v == null_arith_var)
ctx.shift_weights();
if (v == null_arith_var) {
a.m_best_score = -1;
flet<bool> _use_tabu(a.m_use_tabu, false);
add_lookahead_on_unsat_vars();
v = random_move_on_updates();
}
}
template<typename num_t>
void arith_clausal<num_t>::add_lookahead_on_unsat_vars() {
a.m_updates.reset();
a.m_fixed_atoms.reset();
TRACE("arith_verbose", tout << "unsat-vars ";
for (auto v : ctx.unsat_vars())
if (a.get_ineq(v)) tout << mk_bounded_pp(ctx.atom(v), a.m) << " ";
tout << "\n";);
for (auto v : ctx.unsat_vars()) {
auto* ineq = a.get_ineq(v);
if (!ineq)
continue;
auto e = ctx.atom(v);
auto& i = a.get_bool_info(e);
auto const& vars = a.get_fixable_exprs(e);
for (auto v : vars)
a.add_lookahead(i, v);
}
}
/**
* \brief walk over literals that are false in some clause.
* Try to determine if flipping them to true improves the overall score.
*/
template<typename num_t>
void arith_clausal<num_t>::add_lookahead_on_false_literals() {
a.m_updates.reset();
a.m_fixed_atoms.reset();
for (auto bv : a.m_bool_var_atoms) {
if (ctx.unsat_vars().contains(bv))
continue;
auto* ineq = a.get_ineq(bv);
if (!ineq)
continue;
sat::literal lit(bv, !ineq->is_true());
auto const& ul = ctx.get_use_list(~lit);
if (ul.begin() == ul.end())
continue;
auto v = lit.var();
// literal is false in some clause but none of the clauses where it occurs false are unsat.
auto e = ctx.atom(v);
auto& i = a.get_bool_info(e);
a.add_lookahead(i, v);
}
}
template<typename num_t>
var_t arith_clausal<num_t>::critical_move_on_updates(move_t mt) {
if (a.m_updates.empty())
return null_arith_var;
std::stable_sort(a.m_updates.begin(), a.m_updates.end(), [](auto const& a, auto const& b) { return a.m_var < b.m_var || (a.m_var == b.m_var && a.m_delta < b.m_delta); });
m_last_var = null_arith_var;
m_last_delta = 0;
m_best_var = null_arith_var;
m_best_delta = 0;
m_best_abs_value = num_t(-1);
m_best_last_step = UINT_MAX;
for (auto const& u : a.m_updates)
lookahead(u.m_var, u.m_delta);
critical_move(m_best_var, m_best_delta, mt);
return m_best_var;
}
template<typename num_t>
var_t arith_clausal<num_t>::random_move_on_updates() {
if (a.m_updates.empty())
return null_arith_var;
unsigned idx = ctx.rand(a.m_updates.size());
auto& [v, delta, score] = a.m_updates[idx];
if (!a.can_update_num(v, delta))
return null_arith_var;
critical_move(v, delta, random_move);
return v;
}
template<typename num_t>
void arith_clausal<num_t>::lookahead(var_t v, num_t const& delta) {
if (v == m_last_var && delta == m_last_delta)
return;
if (delta == 0)
return;
m_last_var = v;
m_last_delta = delta;
if (!a.can_update_num(v, delta))
return;
auto score = get_score(v, delta);
auto& vi = a.m_vars[v];
num_t abs_value = abs(vi.value() + delta);
unsigned last_step = vi.last_step(delta);
if (score < a.m_best_score)
return;
if (score > a.m_best_score ||
(m_best_abs_value == -1) ||
(abs_value < m_best_abs_value) ||
(abs_value == m_best_abs_value && last_step < m_best_last_step)) {
a.m_best_score = score;
m_best_var = v;
m_best_delta = delta;
m_best_last_step = last_step;
m_best_abs_value = abs_value;
}
}
template<typename num_t>
void arith_clausal<num_t>::critical_move(var_t v, num_t const& delta, move_t mt) {
if (v == null_arith_var)
return;
a.m_last_delta = delta;
a.m_last_var = v;
TRACE("arith", tout << mt << " v" << v << " " << mk_bounded_pp(a.m_vars[v].m_expr, a.m)
<< " += " << delta << " score:" << a.m_best_score << "\n");
a.m_vars[v].set_step(a.m_stats.m_steps, a.m_stats.m_steps + 3 + ctx.rand(10), delta);
VERIFY(a.update_num(v, delta));
for (auto bv : a.m_vars[v].m_bool_vars_of)
if (a.get_ineq(bv) && a.get_ineq(bv)->is_true() != ctx.is_true(bv))
ctx.flip(bv);
DEBUG_CODE(
for (sat::bool_var bv = 0; bv < ctx.num_bool_vars(); ++bv) {
if (a.get_ineq(bv) && a.get_ineq(bv)->is_true() != ctx.is_true(bv)) {
TRACE("arith", tout << bv << " " << *a.get_ineq(bv) << "\n";
tout << a.m_vars[v].m_bool_vars_of << "\n");
}
VERIFY(!a.get_ineq(bv) || a.get_ineq(bv)->is_true() == ctx.is_true(bv));
});
}
template<typename num_t>
double arith_clausal<num_t>::get_score(var_t v, num_t const& delta) {
auto& vi = a.m_vars[v];
VERIFY(a.update_num(v, delta));
double score = 0;
for (auto ci : vi.m_clauses_of) {
auto const& c = ctx.get_clause(ci);
unsigned num_true = 0;
for (auto lit : c) {
auto bv = lit.var();
auto ineq = a.get_ineq(bv);
if (ineq) {
if (ineq->is_true() != lit.sign())
++num_true;
}
else if (ctx.is_true(lit))
++num_true;
}
CTRACE("arith_verbose", c.m_num_trues != num_true && (c.m_num_trues == 0 || num_true == 0),
tout << "clause: " << c
<< " v" << v << " += " << delta
<< " new-true lits: " << num_true
<< " old-true lits: " << c.m_num_trues
<< " w: " << c.m_weight << "\n";
for (auto lit : c)
if (a.get_ineq(lit.var()))
tout << lit << " " << *a.get_ineq(lit.var()) << "\n";);
if (c.m_num_trues > 0 && num_true == 0)
score -= c.m_weight;
else if (c.m_num_trues == 0 && num_true > 0)
score += c.m_weight;
}
// revert the update
VERIFY(a.update_num(v, -delta));
return score;
}
template<typename num_t>
void arith_clausal<num_t>::check_restart() {
if (m_no_improve <= 500000)
return;
IF_VERBOSE(2, verbose_stream() << "restart sls-arith\n");
TRACE("arith", tout << "restart\n";);
// reset values of (arithmetical) variables at bounds.
for (auto& vi : a.m_vars) {
if (vi.m_lo && !vi.m_lo->is_strict && vi.m_lo->value > 0)
vi.set_value(vi.m_lo->value);
else if (vi.m_hi && !vi.m_hi->is_strict && vi.m_hi->value < 0)
vi.set_value(vi.m_hi->value);
else
vi.set_value(num_t(0));
vi.m_bool_vars_of.reset();
vi.m_clauses_of.reset();
}
initialize();
}
template<typename num_t>
void arith_clausal<num_t>::initialize() {
a.initialize_bool_assignment();
for (sat::bool_var v = 0; v < ctx.num_bool_vars(); ++v)
a.init_bool_var_assignment(v);
m_best_found_cost_bool = ctx.unsat().size();
m_best_found_cost_arith = ctx.unsat().size();
m_best_found_cost_restart = ctx.unsat().size();
m_no_improve = 0;
m_no_improve_bool = 0;
m_no_improve_arith = 0;
}
template<typename num_t>
bool arith_clausal<num_t>::update_outer_best_solution() {
if (ctx.unsat().size() >= m_best_found_cost_bool)
return false;
m_best_found_cost_bool = ctx.unsat().size();
return true;
}
template<typename num_t>
void arith_clausal<num_t>::enter_bool_mode() {
CTRACE("arith", !m_bool_mode, tout << "enter bool mode\n";);
m_best_found_cost_bool = ctx.unsat().size();
if (!m_bool_mode)
m_no_improve_bool = 0;
m_bool_mode = true;
}
template<typename num_t>
bool arith_clausal<num_t>::update_inner_best_solution() {
if (ctx.unsat().size() >= m_best_found_cost_arith)
return false;
m_best_found_cost_arith = ctx.unsat().size();
return true;
}
template<typename num_t>
void arith_clausal<num_t>::enter_arith_mode() {
CTRACE("arith", m_bool_mode, tout << "enter arith mode\n";);
m_best_found_cost_arith = ctx.unsat().size();
if (m_bool_mode)
m_no_improve_arith = 0;
m_bool_mode = false;
}
template<typename num_t>
bool arith_clausal<num_t>::update_best_solution() {
bool improved = false;
if (ctx.unsat().size() < m_best_found_cost_restart) {
improved = true;
m_best_found_cost_restart = ctx.unsat().size();
}
if (ctx.unsat().size() < m_best_found_cost) {
improved = true;
m_best_found_cost = ctx.unsat().size();
}
return improved;
}
}
template class sls::arith_clausal<checked_int64<true>>;
template class sls::arith_clausal<rational>;

90
src/ast/sls/sls_arith_clausal.h Normal file
View file

@ -0,0 +1,90 @@
/*++
Copyright (c) 2025 Microsoft Corporation
Module Name:
sls_arith_clausal
Abstract:
Theory plugin for arithmetic local search
based on clausal search as used in HybridSMT
Author:
Nikolaj Bjorner (nbjorner) 2025-01-16
--*/
#pragma once
#include "util/checked_int64.h"
#include "util/optional.h"
#include "ast/ast_trail.h"
#include "ast/arith_decl_plugin.h"
#include "ast/sls/sls_context.h"
namespace sls {
template<typename num_t>
class arith_base;
using var_t = unsigned;
template<typename num_t>
class arith_clausal {
context& ctx;
class arith_base<num_t>& a;
void check_restart();
void initialize();
enum move_t {
unsat_var_move,
false_literal_move,
random_move
};
friend std::ostream& operator<<(std::ostream& out, move_t mt) {
return out << (mt == unsat_var_move ?
"unsat-var" : mt == false_literal_move ?
"false-literal" : "random");
}
void enter_arith_mode();
void enter_bool_mode();
bool update_outer_best_solution();
bool update_inner_best_solution();
bool update_best_solution();
void move_arith_variable();
var_t critical_move_on_updates(move_t mt);
var_t random_move_on_updates();
void add_lookahead_on_unsat_vars();
void add_lookahead_on_false_literals();
void critical_move(var_t v, num_t const& delta, move_t mt);
void lookahead(var_t v, num_t const& delta);
double get_score(var_t v, num_t const& delta);
unsigned m_no_improve_bool = 0;
unsigned m_no_improve_arith = 0;
unsigned m_no_improve = 0;
bool m_bool_mode = true;
unsigned m_best_found_cost_bool = 0;
unsigned m_best_found_cost_arith = 0;
unsigned m_best_found_cost_restart = 0;
unsigned m_best_found_cost = 0;
num_t m_best_abs_value;
num_t m_best_delta;
var_t m_best_var = UINT_MAX;
unsigned m_best_last_step = 0;
// avoid checking the same updates twice
var_t m_last_var = UINT_MAX;
num_t m_last_delta;
public:
arith_clausal(arith_base<num_t>& a);
void search();
};
}

23
src/ast/sls/sls_context.cpp
View file

@ -112,6 +112,18 @@ namespace sls {
if (p)
p->on_restart();
}
bool context::is_external(sat::bool_var v) {
auto a = atom(v);
if (!a)
return false;
family_id fid = get_fid(a);
if (fid == basic_family_id)
return false;
auto p = m_plugins.get(fid, nullptr);
CTRACE("sls_verbose", p != nullptr, tout << "external " << mk_bounded_pp(a, m) << "\n");
return p != nullptr;
}
lbool context::check() {
//
@ -438,6 +450,7 @@ namespace sls {
sat::literal context::mk_literal(expr* e) {
expr_ref _e(e, m);
SASSERT(!m_input_assertions.contains(e));
sat::literal lit;
bool neg = false;
expr* a, * b, * c;
@ -528,8 +541,11 @@ namespace sls {
for (unsigned i = 0; i < m_atoms.size(); ++i)
if (m_atoms.get(i))
register_terms(m_atoms.get(i));
for (auto e : m_input_assertions)
register_terms(e);
{
flet<bool> _is_input_assertion(m_is_input_assertion, true);
for (auto e : m_input_assertions)
register_terms(e);
}
for (auto p : m_plugins)
if (p)
p->initialize();
@ -564,7 +580,7 @@ namespace sls {
m_parents.reserve(arg->get_id() + 1);
m_parents[arg->get_id()].push_back(e);
}
if (m.is_bool(e))
if (m.is_bool(e) && !m_is_input_assertion)
mk_literal(e);
visit(e);
}
@ -629,7 +645,6 @@ namespace sls {
m_visited.reset();
m_root_literals.reset();
for (auto const& clause : s.clauses()) {
bool has_relevant = false;
unsigned n = 0;

10
src/ast/sls/sls_context.h
View file

@ -69,12 +69,16 @@ namespace sls {
virtual sat::clause_info const& get_clause(unsigned idx) const = 0;
virtual ptr_iterator<unsigned> get_use_list(sat::literal lit) = 0;
virtual void flip(sat::bool_var v) = 0;
virtual sat::bool_var bool_flip() = 0;
virtual bool try_rotate(sat::bool_var v, sat::bool_var_set& rotated, unsigned& budget) = 0;
virtual double reward(sat::bool_var v) = 0;
virtual double get_weigth(unsigned clause_idx) = 0;
virtual bool is_true(sat::literal lit) = 0;
virtual unsigned num_vars() const = 0;
virtual indexed_uint_set const& unsat() const = 0;
virtual indexed_uint_set const& unsat_vars() const = 0;
virtual void shift_weights() = 0;
virtual unsigned num_external_in_unsat_vars() const = 0;
virtual void on_model(model_ref& mdl) = 0;
virtual sat::bool_var add_var() = 0;
virtual void add_clause(unsigned n, sat::literal const* lits) = 0;
@ -136,6 +140,7 @@ namespace sls {
void init();
expr_ref_vector m_todo;
bool m_is_input_assertion = false;
void register_terms(expr* e);
void register_term(expr* e);
@ -162,6 +167,7 @@ namespace sls {
void register_atom(sat::bool_var v, expr* e);
lbool check();
bool is_external(sat::bool_var v);
void on_restart();
void updt_params(params_ref const& p);
params_ref const& get_params() const { return m_params; }
@ -183,9 +189,13 @@ namespace sls {
void add_theory_axiom(expr* f) { add_assertion(f, false); }
void add_clause(sat::literal_vector const& lits);
void flip(sat::bool_var v) { s.flip(v); }
sat::bool_var bool_flip() { return s.bool_flip(); }
void shift_weights() { s.shift_weights(); }
bool try_rotate(sat::bool_var v, sat::bool_var_set& rotated, unsigned& budget) { return s.try_rotate(v, rotated, budget); }
double reward(sat::bool_var v) { return s.reward(v); }
indexed_uint_set const& unsat() const { return s.unsat(); }
indexed_uint_set const& unsat_vars() const { return s.unsat_vars(); }
unsigned num_external_in_unsat_vars() const { return s.num_external_in_unsat_vars(); }
unsigned rand() { return m_rand(); }
unsigned rand(unsigned n) { return m_rand(n); }
reslimit& rlimit() { return s.rlimit(); }

12
src/ast/sls/sls_smt_plugin.h
View file

@ -124,6 +124,8 @@ namespace sls {
m_ddfw->reinit();
}
void shift_weights() override { m_ddfw->shift_weights(); }
lbool on_save_model() override;
void on_model(model_ref& mdl) override {
@ -131,6 +133,14 @@ namespace sls {
m_sls_model = mdl;
}
sat::bool_var bool_flip() override {
return m_ddfw->bool_flip();
}
bool is_external(sat::bool_var v) override {
return m_context.is_external(v);
}
void on_rescale() override {}
reslimit& rlimit() override { return m_ddfw->rlimit(); }
@ -160,6 +170,8 @@ namespace sls {
}
unsigned num_vars() const override { return m_ddfw->num_vars(); }
indexed_uint_set const& unsat() const override { return m_ddfw->unsat_set(); }
indexed_uint_set const& unsat_vars() const override { return m_ddfw->unsat_vars(); }
unsigned num_external_in_unsat_vars() const override { return m_ddfw->num_external_in_unsat_vars(); }
sat::bool_var add_var() override {
return m_ddfw->add_var();
}

10
src/ast/sls/sls_smt_solver.cpp
View file

@ -67,10 +67,14 @@ namespace sls {
return r;
}
void on_model(model_ref& mdl) override {
void on_model(model_ref& mdl) override {
m_model = mdl;
}
bool is_external(sat::bool_var v) override {
return m_context.is_external(v);
}
void register_atom(sat::bool_var v, expr* e) {
m_context.register_atom(v, e);
}
@ -85,15 +89,19 @@ namespace sls {
sat::clause_info const& get_clause(unsigned idx) const override { return m_ddfw.get_clause_info(idx); }
ptr_iterator<unsigned> get_use_list(sat::literal lit) override { return m_ddfw.use_list(lit); }
void flip(sat::bool_var v) override { if (m_dirty) m_ddfw.reinit(), m_dirty = false; m_ddfw.flip(v); }
sat::bool_var bool_flip() override { if (m_dirty) m_ddfw.reinit(), m_dirty = false; return m_ddfw.bool_flip(); }
bool try_rotate(sat::bool_var v, sat::bool_var_set& rotated, unsigned& budget) override { if (m_dirty) m_ddfw.reinit(), m_dirty = false; return m_ddfw.try_rotate(v, rotated, budget); }
double reward(sat::bool_var v) override { return m_ddfw.reward(v); }
double get_weigth(unsigned clause_idx) override { return m_ddfw.get_clause_info(clause_idx).m_weight; }
bool is_true(sat::literal lit) override { return m_ddfw.get_value(lit.var()) != lit.sign(); }
unsigned num_vars() const override { return m_ddfw.num_vars(); }
indexed_uint_set const& unsat() const override { return m_ddfw.unsat_set(); }
indexed_uint_set const& unsat_vars() const override { return m_ddfw.unsat_vars(); }
unsigned num_external_in_unsat_vars() const override { return m_ddfw.num_external_in_unsat_vars(); }
sat::bool_var add_var() override { m_dirty = true; return m_ddfw.add_var(); }
void add_input_assertion(expr* f) { m_context.add_input_assertion(f); }
reslimit& rlimit() { return m_ddfw.rlimit(); }
void shift_weights() override { m_ddfw.shift_weights(); }
void force_restart() override { m_ddfw.force_restart(); }