From 0210156bf0c59844a65aacb4957ce49cd65e3761 Mon Sep 17 00:00:00 2001
From: Nikolaj Bjorner <nbjorner@microsoft.com>
Date: Mon, 10 Jun 2013 10:51:56 -0400
Subject: [PATCH] add convex interior generalizer
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
---
src/muz_qe/fixedpoint_params.pyg | 1 +
src/muz_qe/pdr_context.cpp | 3 +
src/muz_qe/pdr_generalizers.cpp | 171 +++++++++++++++++++++++++++++++
src/muz_qe/pdr_generalizers.h | 17 +++
4 files changed, 192 insertions(+)
diff --git a/src/muz_qe/fixedpoint_params.pyg b/src/muz_qe/fixedpoint_params.pyg
index d38c3c9b0..c2996dd8f 100644
--- a/src/muz_qe/fixedpoint_params.pyg
+++ b/src/muz_qe/fixedpoint_params.pyg
@@ -48,6 +48,7 @@ def_module_params('fixedpoint',
('use_multicore_generalizer', BOOL, False, "PDR: extract multiple cores for blocking states"),
('use_inductive_generalizer', BOOL, True, "PDR: generalize lemmas using induction strengthening"),
('use_arith_inductive_generalizer', BOOL, False, "PDR: generalize lemmas using arithmetic heuristics for induction strengthening"),
+ ('use_convex_hull_generalizer', BOOL, False, "PDR: generalize using convex hulls of lemmas"),
('cache_mode', UINT, 0, "PDR: use no (0), symbolic (1) or explicit cache (2) for model search"),
('inductive_reachability_check', BOOL, False, "PDR: assume negation of the cube on the previous level when "
"checking for reachability (not only during cube weakening)"),
diff --git a/src/muz_qe/pdr_context.cpp b/src/muz_qe/pdr_context.cpp
index 76f744325..1c49e0c83 100644
--- a/src/muz_qe/pdr_context.cpp
+++ b/src/muz_qe/pdr_context.cpp
@@ -1572,6 +1572,9 @@ namespace pdr {
}
}
+ if (m_params.use_convex_hull_generalizer()) {
+ m_core_generalizers.push_back(alloc(core_convex_hull_generalizer, *this));
+ }
if (!use_mc && m_params.use_inductive_generalizer()) {
m_core_generalizers.push_back(alloc(core_bool_inductive_generalizer, *this, 0));
}
diff --git a/src/muz_qe/pdr_generalizers.cpp b/src/muz_qe/pdr_generalizers.cpp
index 1b8ea22f9..800a21eaf 100644
--- a/src/muz_qe/pdr_generalizers.cpp
+++ b/src/muz_qe/pdr_generalizers.cpp
@@ -147,6 +147,177 @@ namespace pdr {
}
+ core_convex_hull_generalizer::core_convex_hull_generalizer(context& ctx):
+ core_generalizer(ctx),
+ m(ctx.get_manager()),
+ a(m),
+ m_sigma(m),
+ m_trail(m) {
+ m_sigma.push_back(m.mk_fresh_const("sigma", a.mk_real()));
+ m_sigma.push_back(m.mk_fresh_const("sigma", a.mk_real()));
+ }
+
+ void core_convex_hull_generalizer::operator()(model_node& n, expr_ref_vector& core, bool& uses_level) {
+ manager& pm = n.pt().get_pdr_manager();
+ expr_ref_vector conv1(m), conv2(m), core1(m), core2(m), eqs(m);
+ if (core.empty()) {
+ return;
+ }
+ if (!m_left.contains(n.pt().head())) {
+ expr_ref left(m), right(m);
+ m_left.insert(n.pt().head(), 0);
+ unsigned sz = n.pt().sig_size();
+ for (unsigned i = 0; i < sz; ++i) {
+ func_decl* fn0 = n.pt().sig(i);
+ sort* srt = fn0->get_range();
+ if (a.is_int_real(srt)) {
+ func_decl* fn1 = pm.o2n(fn0, 0);
+ left = m.mk_fresh_const(fn1->get_name().str().c_str(), srt);
+ right = m.mk_fresh_const(fn1->get_name().str().c_str(), srt);
+ m_left.insert(fn1, left);
+ m_right.insert(fn1, right);
+ m_trail.push_back(left);
+ m_trail.push_back(right);
+ }
+ }
+ }
+ unsigned sz = n.pt().sig_size();
+ for (unsigned i = 0; i < sz; ++i) {
+ expr* left, *right;
+ func_decl* fn0 = n.pt().sig(i);
+ func_decl* fn1 = pm.o2n(fn0, 0);
+ if (m_left.find(fn1, left) && m_right.find(fn1, right)) {
+ eqs.push_back(m.mk_eq(m.mk_const(fn1), a.mk_add(left, right)));
+ }
+ }
+ if (!mk_convex(core, 0, conv1)) {
+ IF_VERBOSE(0, verbose_stream() << "Non-convex: " << mk_pp(pm.mk_and(core), m) << "\n";);
+ return;
+ }
+ conv1.append(eqs);
+ conv1.push_back(a.mk_gt(m_sigma[0].get(), a.mk_numeral(rational(0), a.mk_real())));
+ conv1.push_back(a.mk_gt(m_sigma[1].get(), a.mk_numeral(rational(0), a.mk_real())));
+ conv1.push_back(m.mk_eq(a.mk_numeral(rational(1), a.mk_real()), a.mk_add(m_sigma[0].get(), m_sigma[1].get())));
+ expr_ref fml = n.pt().get_formulas(n.level(), false);
+ expr_ref_vector fmls(m);
+ datalog::flatten_and(fml, fmls);
+ for (unsigned i = 0; i < fmls.size(); ++i) {
+ fml = m.mk_not(fmls[i].get());
+ core2.reset();
+ datalog::flatten_and(fml, core2);
+ if (!mk_convex(core2, 1, conv2)) {
+ IF_VERBOSE(0, verbose_stream() << "Non-convex: " << mk_pp(pm.mk_and(core2), m) << "\n";);
+ continue;
+ }
+ conv2.append(conv1);
+ expr_ref state = pm.mk_and(conv2);
+ TRACE("pdr", tout << "Check:\n" << mk_pp(state, m) << "\n";
+ tout << "New formula:\n" << mk_pp(pm.mk_and(core), m) << "\n";
+ tout << "Old formula:\n" << mk_pp(fml, m) << "\n";
+
+ );
+ model_node nd(0, state, n.pt(), n.level());
+ if (l_false == n.pt().is_reachable(nd, &conv2, uses_level)) {
+ TRACE("pdr",
+ tout << mk_pp(state, m) << "\n";
+ tout << "Generalized to:\n" << mk_pp(pm.mk_and(conv2), m) << "\n";);
+ IF_VERBOSE(0,
+ verbose_stream() << mk_pp(state, m) << "\n";
+ verbose_stream() << "Generalized to:\n" << mk_pp(pm.mk_and(conv2), m) << "\n";);
+ core.reset();
+ core.append(conv2);
+ }
+ }
+ }
+
+ bool core_convex_hull_generalizer::mk_convex(expr_ref_vector const& core, unsigned index, expr_ref_vector& conv) {
+ conv.reset();
+ for (unsigned i = 0; i < core.size(); ++i) {
+ mk_convex(core[i], index, conv);
+ }
+ return !conv.empty();
+ }
+
+ void core_convex_hull_generalizer::mk_convex(expr* fml, unsigned index, expr_ref_vector& conv) {
+ expr_ref result(m), r1(m), r2(m);
+ expr* e1, *e2;
+ bool is_not = m.is_not(fml, fml);
+ if (a.is_le(fml, e1, e2) && mk_convex(e1, index, false, r1) && mk_convex(e2, index, false, r2)) {
+ result = a.mk_le(r1, r2);
+ }
+ else if (a.is_ge(fml, e1, e2) && mk_convex(e1, index, false, r1) && mk_convex(e2, index, false, r2)) {
+ result = a.mk_ge(r1, r2);
+ }
+ else if (a.is_gt(fml, e1, e2) && mk_convex(e1, index, false, r1) && mk_convex(e2, index, false, r2)) {
+ result = a.mk_gt(r1, r2);
+ }
+ else if (a.is_lt(fml, e1, e2) && mk_convex(e1, index, false, r1) && mk_convex(e2, index, false, r2)) {
+ result = a.mk_lt(r1, r2);
+ }
+ else if (m.is_eq(fml, e1, e2) && a.is_int_real(e1) && mk_convex(e1, index, false, r1) && mk_convex(e2, index, false, r2)) {
+ result = m.mk_eq(r1, r2);
+ }
+ else {
+ TRACE("pdr", tout << "Did not handle " << mk_pp(fml, m) << "\n";);
+ return;
+ }
+ if (is_not) {
+ result = m.mk_not(result);
+ }
+ conv.push_back(result);
+ }
+
+
+ bool core_convex_hull_generalizer::translate(func_decl* f, unsigned index, expr_ref& result) {
+ expr* tmp;
+ if (index == 0 && m_left.find(f, tmp)) {
+ result = tmp;
+ return true;
+ }
+ if (index == 1 && m_right.find(f, tmp)) {
+ result = tmp;
+ return true;
+ }
+ return false;
+ }
+
+
+ bool core_convex_hull_generalizer::mk_convex(expr* term, unsigned index, bool is_mul, expr_ref& result) {
+ if (!is_app(term)) {
+ return false;
+ }
+ app* app = to_app(term);
+ expr* e1, *e2;
+ expr_ref r1(m), r2(m);
+ if (translate(app->get_decl(), index, result)) {
+ return true;
+ }
+ if (a.is_add(term, e1, e2) && mk_convex(e1, index, is_mul, r1) && mk_convex(e2, index, is_mul, r2)) {
+ result = a.mk_add(r1, r2);
+ return true;
+ }
+ if (a.is_sub(term, e1, e2) && mk_convex(e1, index, is_mul, r1) && mk_convex(e2, index, is_mul, r2)) {
+ result = a.mk_sub(r1, r2);
+ return true;
+ }
+ if (a.is_mul(term, e1, e2) && mk_convex(e1, index, true, r1) && mk_convex(e2, index, true, r2)) {
+ result = a.mk_mul(r1, r2);
+ return true;
+ }
+ if (a.is_numeral(term)) {
+ if (is_mul) {
+ result = term;
+ }
+ else {
+ result = a.mk_mul(m_sigma[index].get(), term);
+ }
+ return true;
+ }
+ IF_VERBOSE(0, verbose_stream() << "Not handled: " << mk_pp(term, m) << "\n";);
+ return false;
+ }
+
+
// ---------------------------------
// core_arith_inductive_generalizer
// NB. this is trying out some ideas for generalization in
diff --git a/src/muz_qe/pdr_generalizers.h b/src/muz_qe/pdr_generalizers.h
index 03bd89c4d..a4be9d1fa 100644
--- a/src/muz_qe/pdr_generalizers.h
+++ b/src/muz_qe/pdr_generalizers.h
@@ -73,6 +73,23 @@ namespace pdr {
virtual void collect_statistics(statistics& st) const;
};
+ class core_convex_hull_generalizer : public core_generalizer {
+ ast_manager& m;
+ arith_util a;
+ expr_ref_vector m_sigma;
+ expr_ref_vector m_trail;
+ obj_map<func_decl, expr*> m_left;
+ obj_map<func_decl, expr*> m_right;
+ bool mk_convex(expr_ref_vector const& core, unsigned index, expr_ref_vector& conv);
+ void mk_convex(expr* fml, unsigned index, expr_ref_vector& conv);
+ bool mk_convex(expr* term, unsigned index, bool is_mul, expr_ref& result);
+ bool translate(func_decl* fn, unsigned index, expr_ref& result);
+ public:
+ core_convex_hull_generalizer(context& ctx);
+ virtual ~core_convex_hull_generalizer() {}
+ virtual void operator()(model_node& n, expr_ref_vector& core, bool& uses_level);
+ };
+
class core_multi_generalizer : public core_generalizer {
core_bool_inductive_generalizer m_gen;
public: