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add power axioms to arith_solver

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This commit is contained in:
Nikolaj Bjorner 2025-04-23 10:48:29 -07:00
parent d73d104ded
commit 579ba8bd70
3 changed files with 32 additions and 0 deletions
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25
src/sat/smt/arith_axioms.cpp
View file

@ -65,6 +65,31 @@ namespace arith {
add_clause(eq, eq_internalize(t, a.mk_numeral(rational(1), a.is_int(t)))); add_clause(eq, eq_internalize(t, a.mk_numeral(rational(1), a.is_int(t))));
} }
// t = n^p
void solver::mk_power_axiom(expr* p, expr* x, expr* y) {
if (a.is_zero(y)) {
mk_power0_axioms(to_app(p), to_app(x));
return;
}
rational r;
// r > 0 => r^y > 0
if (a.is_extended_numeral(x, r) && r > 0) {
expr_ref zero(a.mk_real(0), m);
add_clause(~mk_literal(a.mk_le(p, zero)));
}
if (a.is_extended_numeral(y, r) && r > 0) {
// r is m/n then x >= 0 => x^m = p^n
if (denominator(r) > 1) {
expr_ref x_ge_0(a.mk_ge(x, a.mk_real(0)), m);
expr_ref x(m);
if (numerator(r) > 1)
x = a.mk_power(x, a.mk_real(numerator(r)));
expr_ref x_eq_pn(a.mk_eq(x, a.mk_power(p, a.mk_real(denominator(r)))), m);
add_clause(~mk_literal(x_ge_0), mk_literal(x_eq_pn));
}
}
}
// is_int(x) <=> to_real(to_int(x)) = x // is_int(x) <=> to_real(to_int(x)) = x
void solver::mk_is_int_axiom(expr* n) { void solver::mk_is_int_axiom(expr* n) {
expr* x = nullptr; expr* x = nullptr;

6
src/sat/smt/arith_internalize.cpp
View file

@ -262,6 +262,12 @@ namespace arith {
st.to_ensure_var().push_back(n1); st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2); st.to_ensure_var().push_back(n2);
} }
else if (a.is_power(n, n1, n2)) {
found_unsupported(n);
mk_power_axiom(n, n1, n2);
st.to_ensure_var().push_back(n1);
st.to_ensure_var().push_back(n2);
}
else if (a.is_band(n) || a.is_shl(n) || a.is_ashr(n) || a.is_lshr(n)) { else if (a.is_band(n) || a.is_shl(n) || a.is_ashr(n) || a.is_lshr(n)) {
m_bv_terms.push_back(to_app(n)); m_bv_terms.push_back(to_app(n));
ctx.push(push_back_vector(m_bv_terms)); ctx.push(push_back_vector(m_bv_terms));

1
src/sat/smt/arith_solver.h
View file

@ -312,6 +312,7 @@ namespace arith {
void mk_is_int_axiom(expr* n); void mk_is_int_axiom(expr* n);
void mk_idiv_mod_axioms(expr* p, expr* q); void mk_idiv_mod_axioms(expr* p, expr* q);
void mk_rem_axiom(expr* dividend, expr* divisor); void mk_rem_axiom(expr* dividend, expr* divisor);
void mk_power_axiom(expr* t, expr* n, expr* p);
void mk_bound_axioms(api_bound& b); void mk_bound_axioms(api_bound& b);
void mk_bound_axiom(api_bound& b1, api_bound& b2); void mk_bound_axiom(api_bound& b1, api_bound& b2);
void mk_power0_axioms(app* t, app* n); void mk_power0_axioms(app* t, app* n);