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better encodings for at-most-1, #755

Browse source 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2016-10-10 23:46:03 -07:00
parent 5d9820f3e2
commit 8d2b70a5e2
17 changed files with 232 additions and 253 deletions
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2
src/ast/pb_decl_plugin.h
View file

@ -119,6 +119,8 @@ public:
app* mk_fresh_bool();
expr_ref mk_at_most_1(unsigned num_args, expr * const * args);
private:
rational to_rational(parameter const& p) const;

5
src/opt/opt_solver.cpp
View file

@ -194,6 +194,11 @@ namespace opt {
}
}
lbool opt_solver::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return m_context.find_mutexes(vars, mutexes);
}
/**
\brief maximize the value of objective i in the current state.

1
src/opt/opt_solver.h
View file

@ -106,6 +106,7 @@ namespace opt {
virtual expr * get_assertion(unsigned idx) const;
virtual std::ostream& display(std::ostream & out) const;
virtual ast_manager& get_manager() const { return m; }
virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
void set_logic(symbol const& logic);
smt::theory_var add_objective(app* term);

12
src/sat/sat_solver.cpp
View file

@ -3053,6 +3053,12 @@ namespace sat {
return r;
}
// -----------------------
//
// Extraction of mutexes
//
// -----------------------
lbool solver::find_mutexes(literal_vector const& lits, vector<literal_vector> & mutexes) {
literal_vector ps(lits);
m_user_bin_clauses.reset();
@ -3111,6 +3117,12 @@ namespace sat {
}
}
// -----------------------
//
// Consequence generation.
//
// -----------------------
lbool solver::get_consequences(literal_vector const& asms, bool_var_vector const& vars, vector<literal_vector>& conseq) {
literal_vector lits;
lbool is_sat = check(asms.size(), asms.c_ptr());

244
src/smt/smt_consequences.cpp
View file

@ -251,191 +251,6 @@ namespace smt {
expr_ref_vector& conseq,
expr_ref_vector& unfixed) {
m_antecedents.reset();
pop_to_base_lvl();
lbool is_sat = check(assumptions.size(), assumptions.c_ptr());
if (is_sat != l_true) {
return is_sat;
}
obj_map<expr, expr*> var2val;
index_set _assumptions;
for (unsigned i = 0; i < assumptions.size(); ++i) {
_assumptions.insert(get_literal(assumptions[i]).var());
}
model_ref mdl;
get_model(mdl);
ast_manager& m = m_manager;
expr_ref_vector trail(m);
model_evaluator eval(*mdl.get());
expr_ref val(m);
TRACE("context", model_pp(tout, *mdl););
for (unsigned i = 0; i < vars.size(); ++i) {
eval(vars[i], val);
if (m.is_value(val)) {
trail.push_back(val);
var2val.insert(vars[i], val);
}
else {
unfixed.push_back(vars[i]);
}
}
unsigned num_units = 0;
extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
app_ref eq(m);
TRACE("context",
tout << "vars: " << vars.size() << "\n";
tout << "lits: " << num_units << "\n";);
m_case_split_queue->init_search_eh();
unsigned num_iterations = 0;
unsigned model_threshold = 2;
unsigned num_fixed_eqs = 0;
unsigned num_reiterations = 0;
while (!var2val.empty()) {
obj_map<expr,expr*>::iterator it = var2val.begin();
expr* e = it->m_key;
expr* val = it->m_value;
TRACE("context", tout << "scope level: " << get_scope_level() << "\n";);
SASSERT(!inconsistent());
//
// The current variable is checked to be a backbone
// We add the negation of the reference assignment to the variable.
// If the variable is a Boolean, it means adding literal that has
// the opposite value of the current reference model.
// If the variable is a non-Boolean, it means adding a disequality.
//
literal lit = mk_diseq(e, val);
mark_as_relevant(lit);
push_scope();
assign(lit, b_justification::mk_axiom(), true);
flet<bool> l(m_searching, true);
//
// We check if the current assignment stack can be extended to a
// satisfying assignment. bounded search may decide to restart,
// in which case it returns l_undef and clears search failure.
//
while (true) {
is_sat = bounded_search();
TRACE("context", tout << "search result: " << is_sat << "\n";);
if (is_sat != l_true && m_last_search_failure != OK) {
return is_sat;
}
if (is_sat == l_undef) {
TRACE("context", tout << "restart\n";);
inc_limits();
continue;
}
break;
}
//
// If the state is satisfiable with the current variable assigned to
// a different value from the reference model, it is unfixed.
//
// If it is assigned above the search level we can't conclude anything
// about its value.
// extract_fixed_consequences pops the assignment stack to the search level
// so this sets up the state to retry finding fixed values.
//
// Otherwise, the variable is fixed.
// - it is either assigned at the search level to l_false, or
// - the state is l_false, which means that the variable is fixed by
// the background constraints (and does not depend on assumptions).
//
if (is_sat == l_true && get_assignment(lit) == l_true && is_relevant(lit)) {
var2val.erase(e);
unfixed.push_back(e);
SASSERT(!are_equal(e, val));
TRACE("context", tout << mk_pp(e, m) << " is unfixed\n";
display_literal_verbose(tout, lit); tout << "\n";
tout << "relevant: " << is_relevant(lit) << "\n";
display(tout););
}
else if (is_sat == l_true && (get_assign_level(lit) > get_search_level() || !is_relevant(lit))) {
TRACE("context", tout << "Retry fixing: " << mk_pp(e, m) << "\n";);
extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
++num_reiterations;
continue;
}
else {
//
// The state can be labeled as inconsistent when the implied consequence does
// not depend on assumptions, then the conflict level sits at the search level
// which causes the conflict resolver to decide that the state is unsat.
//
if (l_false == is_sat) {
SASSERT(inconsistent());
m_conflict = null_b_justification;
m_not_l = null_literal;
}
TRACE("context", tout << "Fixed: " << mk_pp(e, m) << " " << is_sat << "\n";
if (is_sat == l_false) display(tout););
}
++num_iterations;
//
// Check the slow pass: it retrieves an updated model and checks if the
// values in the updated model differ from the values in the reference
// model.
//
bool apply_slow_pass = model_threshold <= num_iterations || num_iterations <= 2;
if (apply_slow_pass && is_sat == l_true) {
delete_unfixed(var2val, unfixed);
// The next time we check the model is after 1.5 additional iterations.
model_threshold *= 3;
model_threshold /= 2;
}
//
// Walk the assignment stack at level 1 for learned consequences.
// The current literal should be assigned at the search level unless
// the state is is_sat == l_true and the assignment to lit is l_true.
// This condition is checked above.
//
extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
//
// Fixed equalities can be extracted by walking all variables and checking
// if the congruence roots are equal at the search level.
//
if (apply_slow_pass) {
num_fixed_eqs += extract_fixed_eqs(var2val, conseq);
IF_VERBOSE(1, display_consequence_progress(verbose_stream(), num_iterations, var2val.size(), conseq.size(),
unfixed.size(), num_fixed_eqs););
TRACE("context", display_consequence_progress(tout, num_iterations, var2val.size(), conseq.size(),
unfixed.size(), num_fixed_eqs););
}
TRACE("context", tout << "finishing " << mk_pp(e, m) << "\n";);
SASSERT(!inconsistent());
//
// This becomes unnecessary when the fixed consequence are
// completely extracted.
//
if (var2val.contains(e)) {
TRACE("context", tout << "Fixed value to " << mk_pp(e, m) << " was not processed\n";);
expr_ref fml(m);
fml = m.mk_eq(e, var2val.find(e));
if (!m_antecedents.contains(lit.var())) {
extract_fixed_consequences(lit, var2val, _assumptions, conseq);
}
fml = m.mk_implies(antecedent2fml(m_antecedents[lit.var()]), fml);
conseq.push_back(fml);
var2val.erase(e);
}
}
end_search();
DEBUG_CODE(validate_consequences(assumptions, vars, conseq, unfixed););
return l_true;
}
lbool context::get_consequences2(expr_ref_vector const& assumptions,
expr_ref_vector const& vars,
expr_ref_vector& conseq,
expr_ref_vector& unfixed) {
m_antecedents.reset();
pop_to_base_lvl();
lbool is_sat = check(assumptions.size(), assumptions.c_ptr());
@ -552,6 +367,65 @@ namespace smt {
}
lbool context::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
index_set lits;
for (unsigned i = 0; i < vars.size(); ++i) {
expr* n = vars[i];
bool neg = m_manager.is_not(n, n);
if (b_internalized(n)) {
lits.insert(literal(get_bool_var(n), !neg).index());
}
}
while (!lits.empty()) {
literal_vector mutex;
index_set other(lits);
while (!other.empty()) {
index_set conseq;
literal p = to_literal(*other.begin());
other.erase(p.index());
mutex.push_back(p);
if (other.empty()) {
break;
}
get_reachable(p, other, conseq);
other = conseq;
}
if (mutex.size() > 1) {
expr_ref_vector mux(m_manager);
for (unsigned i = 0; i < mutex.size(); ++i) {
expr_ref e(m_manager);
literal2expr(mutex[i], e);
mux.push_back(e);
}
mutexes.push_back(mux);
}
for (unsigned i = 0; i < mutex.size(); ++i) {
lits.remove(mutex[i].index());
}
}
return l_true;
}
void context::get_reachable(literal p, index_set& goal, index_set& reachable) {
index_set seen;
literal_vector todo;
todo.push_back(p);
while (!todo.empty()) {
p = todo.back();
todo.pop_back();
if (seen.contains(p.index())) {
continue;
}
seen.insert(p.index());
literal np = ~p;
if (goal.contains(np.index())) {
reachable.insert(np.index());
}
watch_list & w = m_watches[np.index()];
todo.append(static_cast<unsigned>(w.end_literals() - w.begin_literals()), w.begin_literals());
}
}
//
// Validate, in a slow pass, that the current consequences are correctly
// extracted.

12
src/smt/smt_context.h
View file

@ -1344,6 +1344,9 @@ namespace smt {
literal lit, context& src_ctx, context& dst_ctx,
vector<bool_var> b2v, ast_translation& tr);
/*
\brief Utilities for consequence finding.
*/
typedef hashtable<unsigned, u_hash, u_eq> index_set;
//typedef uint_set index_set;
u_map<index_set> m_antecedents;
@ -1358,11 +1361,17 @@ namespace smt {
expr_ref antecedent2fml(index_set const& ante);
literal mk_diseq(expr* v, expr* val);
void validate_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars,
expr_ref_vector const& conseq, expr_ref_vector const& unfixed);
/*
\brief Auxiliry function for mutex finding.
*/
void get_reachable(literal p, index_set& goal, index_set& reached);
public:
context(ast_manager & m, smt_params & fp, params_ref const & p = params_ref());
@ -1404,7 +1413,8 @@ namespace smt {
lbool check(unsigned num_assumptions = 0, expr * const * assumptions = 0, bool reset_cancel = true);
lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed);
lbool get_consequences2(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed);
lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
lbool setup_and_check(bool reset_cancel = true);

10
src/smt/smt_kernel.cpp
View file

@ -112,7 +112,11 @@ namespace smt {
}
lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed) {
return m_kernel.get_consequences2(assumptions, vars, conseq, unfixed);
return m_kernel.get_consequences(assumptions, vars, conseq, unfixed);
}
lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return m_kernel.find_mutexes(vars, mutexes);
}
void get_model(model_ref & m) const {
@ -272,6 +276,10 @@ namespace smt {
return m_imp->get_consequences(assumptions, vars, conseq, unfixed);
}
lbool kernel::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return m_imp->find_mutexes(vars, mutexes);
}
void kernel::get_model(model_ref & m) const {
m_imp->get_model(m);
}

5
src/smt/smt_kernel.h
View file

@ -132,6 +132,11 @@ namespace smt {
lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars,
expr_ref_vector& conseq, expr_ref_vector& unfixed);
/*
\brief find mutually exclusive variables.
*/
lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
/**
\brief Return the model associated with the last check command.
*/

5
src/smt/smt_solver.cpp
View file

@ -73,6 +73,10 @@ namespace smt {
return m_context.get_consequences(assumptions, vars, conseq, unfixed);
}
virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return m_context.find_mutexes(vars, mutexes);
}
virtual void assert_expr(expr * t) {
m_context.assert_expr(t);
}
@ -160,6 +164,7 @@ namespace smt {
SASSERT(idx < get_num_assertions());
return m_context.get_formulas()[idx];
}
};
};

7
src/smt/theory_pb.cpp
View file

@ -519,6 +519,7 @@ namespace smt {
c->m_compilation_threshold = th;
IF_VERBOSE(2, verbose_stream() << "(smt.pb setting compilation threhshold to " << th << ")\n";);
TRACE("pb", tout << "compilation threshold: " << th << "\n";);
compile_ineq(*c);
}
else {
c->m_compilation_threshold = UINT_MAX;
@ -1216,7 +1217,7 @@ namespace smt {
void theory_pb::inc_propagations(ineq& c) {
++c.m_num_propagations;
if (c.m_compiled == l_false && c.m_num_propagations > c.m_compilation_threshold) {
if (c.m_compiled == l_false && c.m_num_propagations >= c.m_compilation_threshold) {
c.m_compiled = l_undef;
m_to_compile.push_back(&c);
}
@ -1263,12 +1264,14 @@ namespace smt {
n -= rational::one();
}
}
if (ctx.get_assignment(thl) == l_true &&
ctx.get_assign_level(thl) == ctx.get_base_level()) {
psort_expr ps(ctx, *this);
psort_nw<psort_expr> sortnw(ps);
sortnw.m_stats.reset();
at_least_k = sortnw.ge(false, k, in.size(), in.c_ptr());
at_least_k = sortnw.ge(false, k, in.size(), in.c_ptr());
ctx.mk_clause(~thl, at_least_k, justify(~thl, at_least_k));
m_stats.m_num_compiled_vars += sortnw.m_stats.m_num_compiled_vars;
m_stats.m_num_compiled_clauses += sortnw.m_stats.m_num_compiled_clauses;

57
src/solver/solver.cpp
View file

@ -138,63 +138,6 @@ lbool solver::get_consequences_core(expr_ref_vector const& asms, expr_ref_vector
lbool solver::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return l_true;
#if 0
// complete for literals, but inefficient.
// see more efficient (incomplete) version in sat_solver
mutexes.reset();
ast_manager& m = vars.get_manager();
typedef obj_hashtable<expr> expr_set;
expr_set A, P;
for (unsigned i = 0; i < vars.size(); ++i) {
A.insert(vars[i]);
}
while (!A.empty()) {
P = A;
expr_ref_vector mutex(m);
while (!P.empty()) {
expr_ref_vector asms(m);
expr* p = *P.begin();
P.remove(p);
if (!is_literal(m, p)) {
break;
}
mutex.push_back(p);
asms.push_back(p);
expr_set Q;
expr_set::iterator it = P.begin(), end = P.end();
for (; it != end; ++it) {
expr* q = *it;
scoped_assumption_push _scoped_push(asms, q);
if (is_literal(m, q)) {
lbool is_sat = check_sat(asms);
switch (is_sat) {
case l_false:
Q.insert(q);
break;
case l_true:
break;
case l_undef:
return l_undef;
}
}
}
P = Q;
}
if (mutex.size() > 1) {
mutexes.push_back(mutex);
}
for (unsigned i = 0; i < mutex.size(); ++i) {
A.remove(mutex[i].get());
}
}
return l_true;
#endif
}
bool solver::is_literal(ast_manager& m, expr* e) {

6
src/solver/solver_na2as.cpp
View file

@ -22,6 +22,7 @@ Notes:
#include"solver_na2as.h"
#include"ast_smt2_pp.h"
solver_na2as::solver_na2as(ast_manager & m):
m(m),
m_assumptions(m) {
@ -71,6 +72,11 @@ lbool solver_na2as::get_consequences(expr_ref_vector const& asms, expr_ref_vecto
return get_consequences_core(m_assumptions, vars, consequences);
}
lbool solver_na2as::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
return l_true;
}
void solver_na2as::push() {
m_scopes.push_back(m_assumptions.size());
push_core();

1
src/solver/solver_na2as.h
View file

@ -46,6 +46,7 @@ public:
virtual unsigned get_num_assumptions() const { return m_assumptions.size(); }
virtual expr * get_assumption(unsigned idx) const { return m_assumptions[idx]; }
virtual lbool get_consequences(expr_ref_vector const& asms, expr_ref_vector const& vars, expr_ref_vector& consequences);
virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
protected:
virtual lbool check_sat_core(unsigned num_assumptions, expr * const * assumptions) = 0;
virtual void push_core() = 0;

40
src/tactic/arith/card2bv_tactic.cpp
View file

@ -168,13 +168,39 @@ namespace pb {
return BR_FAILED;
}
expr_ref card2bv_rewriter::mk_atmost1(unsigned sz, expr * const* args) {
expr_ref f1(m), f2(m), f3(m), result(m);
f1 = bv.mk_bv(sz, args);
f2 = bv.mk_bv_sub(f1, bv.mk_numeral(rational(1), sz));
f3 = m.mk_app(bv.get_fid(), OP_BAND, f1, f2);
result = m.mk_eq(f3, bv.mk_numeral(rational(0), sz));
return result;
expr_ref card2bv_rewriter::mk_atmost1(unsigned n, expr * const* xs) {
expr_ref_vector result(m), in(m);
in.append(n, xs);
unsigned inc_size = 4;
while (!in.empty()) {
expr_ref_vector ors(m);
unsigned i = 0;
unsigned n = in.size();
bool last = n <= inc_size;
for (; i + inc_size < n; i += inc_size) {
mk_at_most_1_small(last, inc_size, in.c_ptr() + i, result, ors);
}
if (i < n) {
mk_at_most_1_small(last, n - i, in.c_ptr() + i, result, ors);
}
if (last) {
break;
}
in.reset();
in.append(ors);
}
return mk_and(result);
}
void card2bv_rewriter::mk_at_most_1_small(bool last, unsigned n, literal const* xs, expr_ref_vector& result, expr_ref_vector& ors) {
if (!last) {
ors.push_back(m.mk_or(n, xs));
}
for (unsigned i = 0; i < n; ++i) {
for (unsigned j = i + 1; j < n; ++j) {
result.push_back(m.mk_not(m.mk_and(xs[i], xs[j])));
}
}
}
bool card2bv_rewriter::is_atmost1(func_decl* f, unsigned sz, expr * const* args, expr_ref& result) {

1
src/tactic/arith/card2bv_tactic.h
View file

@ -54,6 +54,7 @@ namespace pb {
bool is_and(func_decl* f);
bool is_atmost1(func_decl* f, unsigned sz, expr * const* args, expr_ref& result);
expr_ref mk_atmost1(unsigned sz, expr * const* args);
void mk_at_most_1_small(bool last, unsigned n, literal const* xs, expr_ref_vector& result, expr_ref_vector& ors);
public:
card2bv_rewriter(ast_manager& m);

25
src/test/sorting_network.cpp
View file

@ -332,7 +332,32 @@ void test_sorting5(unsigned n, unsigned k) {
test_sorting_ge(n, k);
}
void test_at_most_1(unsigned n) {
ast_manager m;
reg_decl_plugins(m);
expr_ref_vector in(m), out(m);
for (unsigned i = 0; i < n; ++i) {
in.push_back(m.mk_fresh_const("a",m.mk_bool_sort()));
}
ast_ext2 ext(m);
psort_nw<ast_ext2> sn(ext);
expr_ref result(m);
result = sn.le(false, 1, in.size(), in.c_ptr());
std::cout << result << "\n";
std::cout << ext.m_clauses << "\n";
}
void tst_sorting_network() {
test_at_most_1(1);
test_at_most_1(2);
test_at_most_1(3);
test_at_most_1(4);
test_at_most_1(5);
test_at_most_1(10);
return;
test_sorting_eq(11,7);
for (unsigned n = 3; n < 20; n += 2) {
for (unsigned k = 1; k < n; ++k) {

52
src/util/sorting_network.h
View file

@ -201,7 +201,11 @@ Notes:
if (dualize(k, n, xs, in)) {
return ge(full, k, n, in.c_ptr());
}
else if (k == 1) {
return mk_at_most_1(full, n, xs);
}
else {
std::cout << "sort " << k << "\n";
SASSERT(2*k <= n);
m_t = full?LE_FULL:LE;
card(k + 1, n, xs, out);
@ -230,6 +234,54 @@ Notes:
private:
literal mk_at_most_1(bool full, unsigned n, literal const* xs) {
literal_vector in(n, xs);
literal result = ctx.fresh();
unsigned inc_size = 4;
while (!in.empty()) {
literal_vector ors;
unsigned i = 0;
unsigned n = in.size();
bool last = n <= inc_size;
for (; i + inc_size < n; i += inc_size) {
mk_at_most_1_small(full, last, inc_size, in.c_ptr() + i, result, ors);
}
if (i < n) {
mk_at_most_1_small(full, last, n - i, in.c_ptr() + i, result, ors);
}
if (last) {
break;
}
in.reset();
in.append(ors);
ors.reset();
}
return result;
}
void mk_at_most_1_small(bool full, bool last, unsigned n, literal const* xs, literal result, literal_vector& ors) {
if (!last) {
literal ex = ctx.fresh();
for (unsigned j = 0; j < n; ++j) {
add_clause(ctx.mk_not(xs[j]), ex);
}
if (full) {
literal_vector lits(n, xs);
lits.push_back(ctx.mk_not(ex));
add_clause(lits.size(), lits.c_ptr());
}
ors.push_back(ex);
}
for (unsigned i = 0; i < n; ++i) {
for (unsigned j = i + 1; j < n; ++j) {
add_clause(ctx.mk_not(result), ctx.mk_not(xs[i]), ctx.mk_not(xs[j]));
}
if (full) {
add_clause(result, xs[i]);
}
}
}
std::ostream& pp(std::ostream& out, unsigned n, literal const* lits) {
for (unsigned i = 0; i < n; ++i) ctx.pp(out, lits[i]) << " ";
return out;