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https://github.com/Z3Prover/z3
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re-adding saturation for inequalities
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
e6e5621366
commit
d8f0926620
6 changed files with 343 additions and 238 deletions
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@ -1,4 +1,4 @@
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/*++
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/*++
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Copyright (c) 2021 Microsoft Corporation
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Module Name:
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@ -10,6 +10,15 @@ Author:
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Nikolaj Bjorner (nbjorner) 2021-03-19
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Jakob Rath 2021-04-6
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TODO:
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- currently saturation just removes premise or premises and adds new clauses
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- this needs to be fixed as follows:
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- per calculus it really adds a propagation to the stack
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- then it adds the propagated literal to the core and removes the premise that needed to be simplified from core.
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TODO:
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- remove level information from created constraints.
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-
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--*/
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#include "math/polysat/saturation.h"
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#include "math/polysat/solver.h"
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@ -73,4 +82,293 @@ namespace polysat {
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return false;
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}
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bool inf_saturate::perform(pvar v, conflict_core& core) {
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for (auto c1 : core) {
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auto c = c1.as_inequality();
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if (try_ugt_x(v, core, c))
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return true;
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if (try_ugt_y(v, core, c))
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return true;
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if (try_ugt_z(v, core, c))
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return true;
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if (try_y_l_ax_and_x_l_z(v, core, c))
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return true;
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}
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return false;
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}
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/**
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* Implement the inferences
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* [x] zx > yx ==> Ω*(x,y) \/ z > y
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* [x] yx <= zx ==> Ω*(x,y) \/ y <= z
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*/
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bool inf_saturate::try_ugt_x(pvar v, conflict_core& core, inequality const& c) {
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LOG_H3("Try zx > yx where x := v" << v);
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if (c.lhs.degree(v) != 1)
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return false;
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if (c.rhs.degree(v) != 1)
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return false;
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pdd const x = s().var(v);
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pdd y = x;
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if (!c.lhs.factor(v, 1, y))
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return false;
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pdd z = x;
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if (!c.rhs.factor(v, 1, z))
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return false;
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unsigned const lvl = c.src->level();
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// Omega^*(x, y)
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if (!push_omega_mul(core, lvl, x, y))
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return false;
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push_l(core, lvl, c.is_strict, y, z);
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// TODO
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// requires signed constraint: core.remove(*c.src);
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return true;
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}
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void inf_saturate::push_l(conflict_core& core, unsigned lvl, bool is_strict, pdd const& lhs, pdd const& rhs) {
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if (is_strict)
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core.insert(s().m_constraints.ult(lvl, lhs, rhs));
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else
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core.insert(s().m_constraints.ule(lvl, lhs, rhs));
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}
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/// Add Ω*(x, y) to the conflict state.
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///
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/// @param[in] p bit width
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bool inf_saturate::push_omega_mul(conflict_core& core, unsigned level, pdd const& x, pdd const& y) {
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LOG_H3("Omega^*(x, y)");
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LOG("x = " << x);
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LOG("y = " << y);
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auto& pddm = x.manager();
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unsigned p = pddm.power_of_2();
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unsigned min_k = 0;
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unsigned max_k = p - 1;
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unsigned k = p / 2;
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rational x_val;
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if (s().try_eval(x, x_val)) {
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unsigned x_bits = x_val.bitsize();
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LOG("eval x: " << x << " := " << x_val << " (x_bits: " << x_bits << ")");
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SASSERT(x_val < rational::power_of_two(x_bits));
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min_k = x_bits;
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}
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rational y_val;
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if (s().try_eval(y, y_val)) {
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unsigned y_bits = y_val.bitsize();
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LOG("eval y: " << y << " := " << y_val << " (y_bits: " << y_bits << ")");
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SASSERT(y_val < rational::power_of_two(y_bits));
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max_k = p - y_bits;
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}
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if (min_k > max_k) {
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// In this case, we cannot choose k such that both literals are false.
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// This means x*y overflows in the current model and the chosen rule is not applicable.
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// (or maybe we are in the case where we need the msb-encoding for overflow).
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return false;
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}
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SASSERT(min_k <= max_k); // if this assertion fails, we cannot choose k s.t. both literals are false
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// TODO: could also choose other value for k (but between the bounds)
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if (min_k == 0)
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k = max_k;
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else
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k = min_k;
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LOG("k = " << k << "; min_k = " << min_k << "; max_k = " << max_k << "; p = " << p);
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SASSERT(min_k <= k && k <= max_k);
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// x >= 2^k
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auto c1 = s().m_constraints.ule(level, pddm.mk_val(rational::power_of_two(k)), x);
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// y > 2^{p-k}
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auto c2 = s().m_constraints.ult(level, pddm.mk_val(rational::power_of_two(p - k)), y);
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core.insert(~c1);
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core.insert(~c2);
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return true;
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}
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/*
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* Match [v] .. <= v
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*/
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bool inf_saturate::is_l_v(pvar v, inequality const& i) {
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return i.rhs == s().var(v);
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}
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/*
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* Match [v] v <= ...
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*/
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bool inf_saturate::is_g_v(pvar v, inequality const& i) {
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return i.lhs == s().var(v);
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}
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/*
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* Match [x] y <= a*x
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*/
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bool inf_saturate::is_y_l_ax(pvar x, inequality const& d, pdd& a, pdd& y) {
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y = d.lhs;
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return d.rhs.degree(x) == 1 && d.rhs.factor(x, 1, a);
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}
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/**
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* Match [v] v*x <= z*x
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*/
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bool inf_saturate::is_Xy_l_XZ(pvar v, inequality const& c, pdd& x, pdd& z) {
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if (c.lhs.degree(v) != 1)
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return false;
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if (!c.lhs.factor(v, 1, x))
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return false;
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// TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
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// so for now we just allow the form 'value*variable'.
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// (extension to arbitrary monomials for 'x' should be fairly easy too)
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if (!x.is_unary())
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return false;
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unsigned x_var = x.var();
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rational x_coeff = x.hi().val();
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pdd xz = x;
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if (!c.rhs.try_div(x_coeff, xz))
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return false;
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if (!xz.factor(x_var, 1, z))
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return false;
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LOG("zx > yx: " << show_deref(c.src));
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return true;
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}
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/**
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* Match [z] yx <= zx
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*/
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bool inf_saturate::is_YX_l_zX(pvar z, inequality const& c, pdd& x, pdd& y) {
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if (c.rhs.degree(z) != 1)
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return false;
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if (!c.rhs.factor(z, 1, x))
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return false;
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// TODO: in principle, 'x' could be any polynomial. However, we need to divide the lhs by x, and we don't have general polynomial division yet.
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// so for now we just allow the form 'value*variable'.
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// (extension to arbitrary monomials for 'x' should be fairly easy too)
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if (!x.is_unary())
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return false;
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unsigned x_var = x.var();
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rational x_coeff = x.hi().val();
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pdd xy = x;
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return c.lhs.try_div(x_coeff, xy) && xy.factor(x_var, 1, y);
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}
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/// [y] z' <= y /\ zx > yx ==> Ω*(x,y) \/ zx > z'x
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/// [y] z' <= y /\ yx <= zx ==> Ω*(x,y) \/ z'x <= zx
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bool inf_saturate::try_ugt_y(pvar v, conflict_core& core, inequality const& le_y, inequality const& yx_l_zx, pdd const& x, pdd const& z) {
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LOG_H3("Try z' <= y && zx > yx where y := v" << v);
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pdd const y = s().var(v);
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SASSERT(is_l_v(v, le_y));
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// SASSERT(is_yx_l_zx(v, yx_l_zx, x, z));
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unsigned const lvl = std::max(yx_l_zx.src->level(), le_y.src->level());
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pdd const& z_prime = le_y.lhs;
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// Omega^*(x, y)
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if (!push_omega_mul(core, lvl, x, y))
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return false;
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// z'x <= zx
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push_l(core, lvl, yx_l_zx.is_strict || le_y.is_strict, z_prime * x, z * x);
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// TODO core.remove(*le_y.src);
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// core.remove(*yx_l_zs.src);
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return true;
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}
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bool inf_saturate::try_ugt_y(pvar v, conflict_core& core, inequality const& c) {
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if (!is_l_v(v, c))
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return false;
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pdd x = s().var(v);
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pdd z = x;
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for (auto dd : core) {
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auto d = dd.as_inequality();
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if (is_Xy_l_XZ(v, d, x, z) && try_ugt_y(v, core, c, d, x, z))
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return true;
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}
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return false;
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}
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/// [x] y <= ax /\ x <= z (non-overflow case)
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/// ==> Ω*(a, z) \/ y <= az
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bool inf_saturate::try_y_l_ax_and_x_l_z(pvar x, conflict_core& core, inequality const& c) {
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if (!is_g_v(x, c))
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return false;
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pdd y = s().var(x);
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pdd a = y;
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for (auto dd : core) {
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auto d = dd.as_inequality();
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if (is_y_l_ax(x, d, a, y) && try_y_l_ax_and_x_l_z(x, core, c, d, a, y))
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return true;
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}
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return false;
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}
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bool inf_saturate::try_y_l_ax_and_x_l_z(pvar x, conflict_core& core, inequality const& x_l_z, inequality const& y_l_ax, pdd const& a, pdd const& y) {
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SASSERT(is_g_v(x, x_l_z));
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// SASSERT(is_y_l_ax(x, y_l_ax, a, y));
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LOG_H3("Try y <= ax && x <= z where x := v" << x);
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pdd z = x_l_z.rhs;
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unsigned const lvl = std::max(x_l_z.src->level(), y_l_ax.src->level());
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if (!push_omega_mul(core, lvl, a, z))
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return false;
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push_l(core, lvl, x_l_z.is_strict || y_l_ax.is_strict, y, a * z);
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// core.remove(*x_l_z.src);
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// core.remove(*y_l_ax.src);
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//
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// TBD justify all propagations into the core with the corresponding lemma
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//
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return true;
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}
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/// [z] z <= y' /\ zx > yx ==> Ω*(x,y') \/ y'x > yx
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/// [z] z <= y' /\ yx <= zx ==> Ω*(x,y') \/ yx <= y'x
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bool inf_saturate::try_ugt_z(pvar z, conflict_core& core, inequality const& c) {
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if (!is_g_v(z, c))
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return false;
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pdd y = s().var(z);
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pdd x = y;
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for (auto dd : core) {
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auto d = dd.as_inequality();
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if (is_YX_l_zX(z, d, x, y) && try_ugt_z(z, core, c, d, x, y))
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return true;
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}
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return false;
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}
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bool inf_saturate::try_ugt_z(pvar z, conflict_core& core, inequality const& c, inequality const& d, pdd const& x, pdd const& y) {
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LOG_H3("Try z <= y' && zx > yx where z := v" << z);
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SASSERT(is_g_v(z, c));
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// SASSERT(is_YX_l_zX(x, d, x, y));
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unsigned const lvl = std::max(c.src->level(), d.src->level());
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pdd const& y_prime = c.rhs;
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// Omega^*(x, y')
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if (!push_omega_mul(core, lvl, x, y_prime))
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return false;
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// yx <= y'x
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push_l(core, lvl, c.is_strict || d.is_strict, y * x, y_prime * x);
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return true;
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}
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}
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