1. Arlen Cox
  2. z3

Source

z3 / src / tactic / smtlogics / qflia_tactic.cpp

/*++
Copyright (c) 2012 Microsoft Corporation

Module Name:

    qflia_tactic.cpp

Abstract:

    Tactic for QF_LIA

Author:

    Leonardo (leonardo) 2012-02-26

Notes:

--*/
#include"tactical.h"
#include"simplify_tactic.h"
#include"propagate_values_tactic.h"
#include"propagate_ineqs_tactic.h"
#include"normalize_bounds_tactic.h"
#include"solve_eqs_tactic.h"
#include"elim_uncnstr_tactic.h"
#include"smt_tactic.h"
// include"mip_tactic.h"
#include"add_bounds_tactic.h"
#include"pb2bv_tactic.h"
#include"lia2pb_tactic.h"
#include"ctx_simplify_tactic.h"
#include"bit_blaster_tactic.h"
#include"max_bv_sharing_tactic.h"
#include"aig_tactic.h"
#include"sat_tactic.h"
#include"bound_manager.h"
#include"probe_arith.h"

struct quasi_pb_probe : public probe {
    virtual result operator()(goal const & g) {
        bool found_non_01 = false;
        bound_manager bm(g.m());
        bm(g);
        rational l, u; bool st;
        bound_manager::iterator it  = bm.begin();
        bound_manager::iterator end = bm.end();
        for (; it != end; ++it) {
            expr * t = *it;
            if (bm.has_lower(t, l, st) && bm.has_upper(t, u, st) && (l.is_zero() || l.is_one()) && (u.is_zero() || u.is_one()))
                continue;
            if (found_non_01)
                return false;
            found_non_01 = true;
        }
        return true;
    }
};

probe * mk_quasi_pb_probe() {
    return mk_and(mk_not(mk_is_unbounded_probe()),
                  alloc(quasi_pb_probe));
}

// Create SMT solver that does not use cuts
static tactic * mk_no_cut_smt_tactic(unsigned rs) {
    params_ref solver_p;
    solver_p.set_uint(":arith-branch-cut-ratio", 10000000);
    solver_p.set_uint(":random-seed", rs);
    return using_params(mk_smt_tactic_using(false), solver_p);
}

// Create SMT solver that does not use cuts
static tactic * mk_no_cut_no_relevancy_smt_tactic(unsigned rs) {
    params_ref solver_p;
    solver_p.set_uint(":arith-branch-cut-ratio", 10000000);
    solver_p.set_uint(":random-seed", rs);
    solver_p.set_uint(":relevancy", 0);
    return using_params(mk_smt_tactic_using(false), solver_p);
}

static tactic * mk_bv2sat_tactic(ast_manager & m) {
    params_ref solver_p;
    // The cardinality constraint encoding generates a lot of shared if-then-else's that can be flattened.
    // Several of them are simplified to and/or. If we flat them, we increase a lot the memory consumption.
    solver_p.set_bool(":flat", false); 
    solver_p.set_bool(":som", false); 
    // dynamic psm seems to work well.
    solver_p.set_sym(":gc-strategy", symbol("dyn-psm"));
    
    return using_params(and_then(mk_simplify_tactic(m),
                                 mk_propagate_values_tactic(m),
                                 mk_solve_eqs_tactic(m),
                                 mk_max_bv_sharing_tactic(m),
                                 mk_bit_blaster_tactic(m),
                                 mk_aig_tactic(),
                                 mk_sat_tactic(m)),
                        solver_p);
}

#define SMALL_SIZE 80000

static tactic * mk_pb_tactic(ast_manager & m) {
    params_ref pb2bv_p;
    pb2bv_p.set_bool(":ite-extra", true);    
    pb2bv_p.set_uint(":pb2bv-all-clauses-limit", 8);
    
    return and_then(fail_if_not(mk_is_pb_probe()),
                    fail_if(mk_produce_proofs_probe()),
                    fail_if(mk_produce_unsat_cores_probe()),
                    or_else(and_then(fail_if(mk_ge(mk_num_exprs_probe(), mk_const_probe(SMALL_SIZE))),
                                     fail_if_not(mk_is_ilp_probe()),
                                     // try_for(mk_mip_tactic(m), 8000),
                                     mk_fail_if_undecided_tactic()),
                            and_then(using_params(mk_pb2bv_tactic(m), pb2bv_p),
                                     fail_if_not(mk_is_qfbv_probe()),
                                     mk_bv2sat_tactic(m))));
}


static tactic * mk_lia2sat_tactic(ast_manager & m) {
    params_ref pb2bv_p;
    pb2bv_p.set_bool(":ite-extra", true);    
    pb2bv_p.set_uint(":pb2bv-all-clauses-limit", 8);
    
    return and_then(fail_if(mk_is_unbounded_probe()),
                    fail_if(mk_produce_proofs_probe()),
                    fail_if(mk_produce_unsat_cores_probe()),
                    mk_propagate_ineqs_tactic(m),
                    mk_normalize_bounds_tactic(m),
                    mk_lia2pb_tactic(m),
                    using_params(mk_pb2bv_tactic(m), pb2bv_p),
                    fail_if_not(mk_is_qfbv_probe()),                    
                    mk_bv2sat_tactic(m));
}

// Try to find a model for an unbounded ILP problem.
// Fails if the problem is no ILP.
static tactic * mk_ilp_model_finder_tactic(ast_manager & m) {
    params_ref add_bounds_p1;
    add_bounds_p1.set_rat(":add-bound-lower", rational(-16));
    add_bounds_p1.set_rat(":add-bound-upper", rational(15));
    params_ref add_bounds_p2;
    add_bounds_p2.set_rat(":add-bound-lower", rational(-32));
    add_bounds_p2.set_rat(":add-bound-upper", rational(31));

    return and_then(fail_if_not(mk_and(mk_is_ilp_probe(), mk_is_unbounded_probe())),
                    fail_if(mk_produce_proofs_probe()),
                    fail_if(mk_produce_unsat_cores_probe()),
                    mk_propagate_ineqs_tactic(m),
                    or_else(// try_for(mk_mip_tactic(m), 5000),
                            try_for(mk_no_cut_smt_tactic(100), 2000),
                            and_then(using_params(mk_add_bounds_tactic(m), add_bounds_p1),
                                     try_for(mk_lia2sat_tactic(m), 5000)),
                            try_for(mk_no_cut_smt_tactic(200), 5000),
                            and_then(using_params(mk_add_bounds_tactic(m), add_bounds_p2),
                                     try_for(mk_lia2sat_tactic(m), 10000))
                            // , mk_mip_tactic(m)
                            ),
                    mk_fail_if_undecided_tactic());
}

static tactic * mk_bounded_tactic(ast_manager & m) {
    return and_then(fail_if(mk_is_unbounded_probe()),
                    or_else(try_for(mk_no_cut_smt_tactic(100), 5000),
                            try_for(mk_no_cut_no_relevancy_smt_tactic(200), 5000),
                            try_for(mk_no_cut_smt_tactic(300), 15000)
                            ),
                    mk_fail_if_undecided_tactic());
}

tactic * mk_qflia_tactic(ast_manager & m, params_ref const & p) {
    params_ref main_p;
    main_p.set_bool(":elim-and", true);
    main_p.set_bool(":som", true);
    // main_p.set_bool(":push-ite-arith", true);
    
    params_ref pull_ite_p;
    pull_ite_p.set_bool(":pull-cheap-ite", true);
    pull_ite_p.set_bool(":push-ite-arith", false);
    pull_ite_p.set_bool(":local-ctx", true);
    pull_ite_p.set_uint(":local-ctx-limit", 10000000);

    params_ref ctx_simp_p;
    ctx_simp_p.set_uint(":max-depth", 30);
    ctx_simp_p.set_uint(":max-steps", 5000000);

    params_ref lhs_p;
    lhs_p.set_bool(":arith-lhs", true);

    tactic * preamble_st = and_then(and_then(mk_simplify_tactic(m),
                                             mk_propagate_values_tactic(m),
                                             using_params(mk_ctx_simplify_tactic(m), ctx_simp_p),
                                             using_params(mk_simplify_tactic(m), pull_ite_p)),
                                    mk_solve_eqs_tactic(m),
                                    mk_elim_uncnstr_tactic(m),
                                    using_params(mk_simplify_tactic(m), lhs_p) 
                                    );

    params_ref quasi_pb_p;
    quasi_pb_p.set_uint(":lia2pb-max-bits", 64);
    
    params_ref no_cut_p;
    no_cut_p.set_uint(":arith-branch-cut-ratio", 10000000);
    
    
    tactic * st = using_params(and_then(preamble_st,
                                        or_else(mk_ilp_model_finder_tactic(m),
                                                mk_pb_tactic(m),
                                                and_then(fail_if_not(mk_quasi_pb_probe()), 
                                                         using_params(mk_lia2sat_tactic(m), quasi_pb_p),
                                                         mk_fail_if_undecided_tactic()),
                                                mk_bounded_tactic(m),
                                                mk_smt_tactic())),
                               main_p);
    
    st->updt_params(p);
    return st;
}