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add intersection using symbolic automata facility

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2016-02-28 17:05:12 -08:00
parent 4cf72e23e6
commit df2d7e7628
8 changed files with 561 additions and 28 deletions

View file

@ -25,6 +25,8 @@ Notes:
#include"automaton.h"
#include"well_sorted.h"
#include"var_subst.h"
#include"symbolic_automata_def.h"
expr_ref sym_expr::accept(expr* e) {
ast_manager& m = m_t.get_manager();
@ -37,6 +39,7 @@ expr_ref sym_expr::accept(expr* e) {
}
case t_char:
SASSERT(m.get_sort(e) == m.get_sort(m_t));
SASSERT(m.get_sort(e) == m_sort);
result = m.mk_eq(e, m_t);
break;
case t_range: {
@ -67,8 +70,114 @@ struct display_expr1 {
}
};
class sym_expr_boolean_algebra : public boolean_algebra<sym_expr*> {
ast_manager& m;
expr_solver& m_solver;
typedef sym_expr* T;
public:
sym_expr_boolean_algebra(ast_manager& m, expr_solver& s):
m(m), m_solver(s) {}
virtual T mk_false() {
expr_ref fml(m.mk_false(), m);
return sym_expr::mk_pred(fml, m.mk_bool_sort()); // use of Bool sort for bound variable is arbitrary
}
virtual T mk_true() {
expr_ref fml(m.mk_true(), m);
return sym_expr::mk_pred(fml, m.mk_bool_sort());
}
virtual T mk_and(T x, T y) {
if (x->is_char() && y->is_char()) {
if (x->get_char() == y->get_char()) {
return x;
}
if (m.are_distinct(x->get_char(), y->get_char())) {
expr_ref fml(m.mk_false(), m);
return sym_expr::mk_pred(fml, x->sort());
}
}
var_ref v(m.mk_var(0, x->sort()), m);
expr_ref fml1 = x->accept(v);
expr_ref fml2 = y->accept(v);
if (m.is_true(fml1)) return y;
if (m.is_true(fml2)) return x;
expr_ref fml(m.mk_and(fml1, fml2), m);
return sym_expr::mk_pred(fml, x->sort());
}
virtual T mk_or(T x, T y) {
if (x->is_char() && y->is_char() &&
x->get_char() == y->get_char()) {
return x;
}
var_ref v(m.mk_var(0, x->sort()), m);
expr_ref fml1 = x->accept(v);
expr_ref fml2 = y->accept(v);
if (m.is_false(fml1)) return y;
if (m.is_false(fml2)) return x;
expr_ref fml(m.mk_or(fml1, fml2), m);
return sym_expr::mk_pred(fml, x->sort());
}
virtual T mk_and(unsigned sz, T const* ts) {
switch (sz) {
case 0: return mk_true();
case 1: return ts[0];
default: {
T t = ts[0];
for (unsigned i = 1; i < sz; ++i) {
t = mk_and(t, ts[i]);
}
return t;
}
}
}
virtual T mk_or(unsigned sz, T const* ts) {
switch (sz) {
case 0: return mk_false();
case 1: return ts[0];
default: {
T t = ts[0];
for (unsigned i = 1; i < sz; ++i) {
t = mk_or(t, ts[i]);
}
return t;
}
}
}
virtual lbool is_sat(T x) {
if (x->is_char()) {
return l_true;
}
if (x->is_range()) {
// TBD check lower is below upper.
}
expr_ref v(m.mk_fresh_const("x", x->sort()), m);
expr_ref fml = x->accept(v);
if (m.is_true(fml)) {
return l_true;
}
if (m.is_false(fml)) {
return l_false;
}
return m_solver.check_sat(fml);
}
virtual T mk_not(T x) {
var_ref v(m.mk_var(0, x->sort()), m);
expr_ref fml(m.mk_not(x->accept(v)), m);
return sym_expr::mk_pred(fml, x->sort());
}
};
re2automaton::re2automaton(ast_manager& m): m(m), u(m), bv(m), m_ba(0), m_sa(0) {}
re2automaton::~re2automaton() {}
void re2automaton::set_solver(expr_solver* solver) {
m_solver = solver;
m_ba = alloc(sym_expr_boolean_algebra, m, *solver);
m_sa = alloc(symbolic_automata_t, sm, *m_ba.get());
}
re2automaton::re2automaton(ast_manager& m): m(m), u(m), bv(m) {}
eautomaton* re2automaton::operator()(expr* e) {
eautomaton* r = re2aut(e);
@ -136,7 +245,7 @@ eautomaton* re2automaton::re2aut(expr* e) {
expr_ref _start(bv.mk_numeral(start, nb), m);
expr_ref _stop(bv.mk_numeral(stop, nb), m);
expr_ref _pred(m.mk_not(m.mk_and(bv.mk_ule(_start, v), bv.mk_ule(v, _stop))), m);
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred));
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred, s));
return a.detach();
}
else if (u.re.is_to_re(e0, e1) && u.str.is_string(e1, s1) && s1.length() == 1) {
@ -145,13 +254,14 @@ eautomaton* re2automaton::re2aut(expr* e) {
expr_ref v(m.mk_var(0, s), m);
expr_ref _ch(bv.mk_numeral(s1[0], nb), m);
expr_ref _pred(m.mk_not(m.mk_eq(v, _ch)), m);
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred));
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred, s));
return a.detach();
}
else if (u.re.is_to_re(e0, e1) && u.str.is_unit(e1, e2)) {
expr_ref v(m.mk_var(0, m.get_sort(e2)), m);
sort* s = m.get_sort(e2);
expr_ref v(m.mk_var(0, s), m);
expr_ref _pred(m.mk_not(m.mk_eq(v, e2)), m);
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred));
a = alloc(eautomaton, sm, sym_expr::mk_pred(_pred, s));
return a.detach();
}
else {
@ -187,14 +297,15 @@ eautomaton* re2automaton::re2aut(expr* e) {
}
else if (u.re.is_full(e)) {
expr_ref tt(m.mk_true(), m);
sym_expr* _true = sym_expr::mk_pred(tt);
sort* seq_s, *char_s;
VERIFY (u.is_re(m.get_sort(e), seq_s));
VERIFY (u.is_seq(seq_s, char_s));
sym_expr* _true = sym_expr::mk_pred(tt, char_s);
return eautomaton::mk_loop(sm, _true);
}
#if 0
else if (u.re.is_intersect(e, e1, e2)) {
// maybe later
else if (u.re.is_intersection(e, e1, e2) && m_sa && (a = re2aut(e1)) && (b = re2aut(e2))) {
return m_sa->mk_product(*a, *b);
}
#endif
return 0;
}

View file

@ -25,6 +25,7 @@ Notes:
#include"params.h"
#include"lbool.h"
#include"automaton.h"
#include"symbolic_automata.h"
class sym_expr {
enum ty {
@ -33,21 +34,24 @@ class sym_expr {
t_range
};
ty m_ty;
sort* m_sort;
expr_ref m_t;
expr_ref m_s;
unsigned m_ref;
sym_expr(ty ty, expr_ref& t, expr_ref& s) : m_ty(ty), m_t(t), m_s(s), m_ref(0) {}
sym_expr(ty ty, expr_ref& t, expr_ref& s, sort* srt) : m_ty(ty), m_sort(srt), m_t(t), m_s(s), m_ref(0) {}
public:
expr_ref accept(expr* e);
static sym_expr* mk_char(expr_ref& t) { return alloc(sym_expr, t_char, t, t); }
static sym_expr* mk_char(expr_ref& t) { return alloc(sym_expr, t_char, t, t, t.get_manager().get_sort(t)); }
static sym_expr* mk_char(ast_manager& m, expr* t) { expr_ref tr(t, m); return mk_char(tr); }
static sym_expr* mk_pred(expr_ref& t) { return alloc(sym_expr, t_pred, t, t); }
static sym_expr* mk_range(expr_ref& lo, expr_ref& hi) { return alloc(sym_expr, t_range, lo, hi); }
static sym_expr* mk_pred(expr_ref& t, sort* s) { return alloc(sym_expr, t_pred, t, t, s); }
static sym_expr* mk_range(expr_ref& lo, expr_ref& hi) { return alloc(sym_expr, t_range, lo, hi, lo.get_manager().get_sort(hi)); }
void inc_ref() { ++m_ref; }
void dec_ref() { --m_ref; if (m_ref == 0) dealloc(this); }
std::ostream& display(std::ostream& out) const;
bool is_char() const { return m_ty == t_char; }
bool is_pred() const { return !is_char(); }
bool is_range() const { return m_ty == t_range; }
sort* sort() const { return m_sort; }
expr* get_char() const { SASSERT(is_char()); return m_t; }
};
@ -58,17 +62,31 @@ public:
void dec_ref(sym_expr* s) { if (s) s->dec_ref(); }
};
class expr_solver {
public:
virtual ~expr_solver() {}
virtual lbool check_sat(expr* e) = 0;
};
typedef automaton<sym_expr, sym_expr_manager> eautomaton;
class re2automaton {
typedef boolean_algebra<sym_expr*> boolean_algebra_t;
typedef symbolic_automata<sym_expr, sym_expr_manager> symbolic_automata_t;
ast_manager& m;
sym_expr_manager sm;
seq_util u;
bv_util bv;
scoped_ptr<expr_solver> m_solver;
scoped_ptr<boolean_algebra_t> m_ba;
scoped_ptr<symbolic_automata_t> m_sa;
eautomaton* re2aut(expr* e);
eautomaton* seq2aut(expr* e);
public:
public:
re2automaton(ast_manager& m);
~re2automaton();
eautomaton* operator()(expr* e);
void set_solver(expr_solver* solver);
};
/**

View file

@ -178,15 +178,19 @@ public:
return alloc(automaton, a.m, a.init(), final, mvs);
}
automaton* clone() const {
return clone(*this);
}
// create the sum of disjoint automata
static automaton* mk_union(automaton const& a, automaton const& b) {
SASSERT(&a.m == &b.m);
M& m = a.m;
if (a.is_empty()) {
return clone(b);
return b.clone();
}
if (b.is_empty()) {
return clone(a);
return a.clone();
}
moves mvs;
unsigned_vector final;
@ -213,7 +217,7 @@ public:
mvs.push_back(move(m, 0, a.init() + offset));
}
if (a.is_empty()) {
return clone(a);
return a.clone();
}
mvs.push_back(move(m, init, a.final_state() + offset));
@ -227,16 +231,16 @@ public:
SASSERT(&a.m == &b.m);
M& m = a.m;
if (a.is_empty()) {
return clone(a);
return a.clone();
}
if (b.is_empty()) {
return clone(b);
return b.clone();
}
if (a.is_epsilon()) {
return clone(b);
return b.clone();
}
if (b.is_epsilon()) {
return clone(a);
return a.clone();
}
moves mvs;
@ -458,6 +462,7 @@ public:
}
unsigned init() const { return m_init; }
unsigned_vector const& final_states() const { return m_final_states; }
unsigned in_degree(unsigned state) const { return m_delta_inv[state].size(); }
unsigned out_degree(unsigned state) const { return m_delta[state].size(); }
move const& get_move_from(unsigned state) const { SASSERT(m_delta[state].size() == 1); return m_delta[state][0]; }

View file

@ -0,0 +1,46 @@
/*++
Copyright (c) 2015 Microsoft Corporation
Module Name:
boolean_algebra.h
Abstract:
Boolean Algebra, a la Margus Veanes Automata library.
Author:
Nikolaj Bjorner (nbjorner) 2016-2-27
Revision History:
--*/
#ifndef BOOLEAN_ALGEBRA_H_
#define BOOLEAN_ALGEBRA_H_
#include "util.h"
template<class T>
class positive_boolean_algebra {
public:
virtual T mk_false() = 0;
virtual T mk_true() = 0;
virtual T mk_and(T x, T y) = 0;
virtual T mk_or(T x, T y) = 0;
virtual T mk_and(unsigned sz, T const* ts) = 0;
virtual T mk_or(unsigned sz, T const* ts) = 0;
virtual lbool is_sat(T x) = 0;
};
template<class T>
class boolean_algebra : public positive_boolean_algebra<T> {
public:
virtual T mk_not(T x) = 0;
//virtual lbool are_equivalent(T x, T y) = 0;
//virtual T simplify(T x) = 0;
};
#endif

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@ -0,0 +1,104 @@
/*++
Copyright (c) 2015 Microsoft Corporation
Module Name:
symbolic_automata.h
Abstract:
Symbolic Automata over Boolean Algebras, a la Margus Veanes Automata library.
Author:
Nikolaj Bjorner (nbjorner) 2016-02-27.
Revision History:
--*/
#ifndef SYMBOLIC_AUTOMATA_H_
#define SYMBOLIC_AUTOMATA_H_
#include "automaton.h"
#include "boolean_algebra.h"
template<class T, class M = default_value_manager<T> >
class symbolic_automata {
typedef automaton<T, M> automaton_t;
typedef boolean_algebra<T*> ba_t;
typedef typename automaton_t::move move_t;
typedef vector<move_t> moves_t;
typedef obj_ref<T, M> ref_t;
typedef ref_vector<T, M> refs_t;
M& m;
ba_t& m_ba;
class block {
uint_set m_set;
unsigned m_rep;
bool m_rep_chosen;
public:
block(): m_rep(0), m_rep_chosen(false) {}
block(uint_set const& s):
m_set(s),
m_rep(0),
m_rep_chosen(false) {
}
block(unsigned_vector const& vs) {
for (unsigned i = 0; i < vs.size(); ++i) {
m_set.insert(vs[i]);
}
m_rep_chosen = false;
m_rep = 0;
}
block& operator=(block const& b) {
m_set = b.m_set;
m_rep = 0;
m_rep_chosen = false;
return *this;
}
unsigned get_representative() {
if (!m_rep_chosen) {
uint_set::iterator it = m_set.begin();
if (m_set.end() != it) {
m_rep = *it;
}
m_rep_chosen = true;
}
return m_rep;
}
void add(unsigned i) { m_set.insert(i); }
bool contains(unsigned i) const { return m_set.contains(i); }
bool is_empty() const { return m_set.empty(); }
unsigned size() const { return m_set.num_elems(); }
void remove(unsigned i) { m_set.remove(i); m_rep_chosen = false; }
void clear() { m_set.reset(); m_rep_chosen = false; }
uint_set::iterator begin() { return m_set.begin(); }
uint_set::iterator end() { return m_set.end(); }
};
public:
symbolic_automata(M& m, ba_t& ba): m(m), m_ba(ba) {}
automaton_t* mk_determinstic(automaton_t& a);
automaton_t* mk_complement(automaton_t& a);
automaton_t* remove_epsilons(automaton_t& a);
automaton_t* mk_total(automaton_t& a);
automaton_t* mk_minimize(automaton_t& a);
automaton_t* mk_product(automaton_t& a, automaton_t& b);
};
#endif

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@ -0,0 +1,227 @@
/*++
Copyright (c) 2015 Microsoft Corporation
Module Name:
symbolic_automata_def.h
Abstract:
Symbolic Automata over Boolean Algebras, a la Margus Veanes Automata library.
Author:
Nikolaj Bjorner (nbjorner) 2016-02-27.
Revision History:
--*/
#ifndef SYMBOLIC_AUTOMATA_DEF_H_
#define SYMBOLIC_AUTOMATA_DEF_H_
#include "symbolic_automata.h"
#include "hashtable.h"
typedef std::pair<unsigned, unsigned> unsigned_pair;
template<class T, class M>
typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_total(automaton_t& a) {
unsigned dead_state = a.num_states();
moves_t mvs;
for (unsigned i = 0; i < dead_state; ++i) {
mvs.reset();
a.get_moves(i, mvs, true);
refs_t vs(m);
for (unsigned j = 0; j < mvs.size(); ++j) {
mv.push_back(mvs[j]());
}
ref_t cond(m_ba.mk_not(m_ba.mk_or(vs.size(), vs.c_ptr())), m);
lbool is_sat = m_ba.is_sat(cond);
if (is_sat == l_undef) {
return 0;
}
if (is_sat == l_true) {
new_mvs.push_back(move_t(m, i, dead_state, cond));
}
}
if (new_mvs.empty()) {
return a.clone();
}
new_mvs.push_back(move_t(m, dead_state, dead_state, m_ba.mk_true()));
automaton_t::append_moves(0, a, new_mvs);
return alloc(automaton_t, m, a.init(), a.final_states(), new_mvs);
}
template<class T, class M>
typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_minimize(automaton_t& a) {
if (a.is_empty()) {
return a.clone();
}
if (a.is_epsilon()) {
return a.clone();
}
// SASSERT(a.is_deterministic());
scoped_ptr<automaton_t> fa = mk_total(a);
if (!fa) {
return 0;
}
block final_block(fa->final_states());
block non_final_block(fa->non_final_states());
vector<block> blocks;
for (unsigned i = 0; i < fa->num_states(); ++i) {
if (fa->is_final_state(i)) {
blocks.push_back(final_block);
}
else {
blocks.push_back(non_final_block);
}
}
vector<block> W;
if (final_block.size() > non_final_block.size()) {
W.push_back(non_final_block);
}
else {
W.push_back(final_block);
}
#if 0
refs_t trail(m);
u_map<T*> gamma;
moves_t mvs;
while (!W.empty()) {
block R(W.back());
W.pop_back();
block Rcopy(R);
gamma.reset();
uint_set::iterator it = Rcopy.begin(), end = Rcopy.end();
for (; it != end; ++it) {
unsigned q = *it;
mvs.reset();
fa->get_moves_to(q, mvs);
for (unsigned i = 0; i < mvs.size(); ++i) {
unsigned src = mvs[i].src();
if (blocks[src].size() > 1) {
T* t = mvs[i]();
if (gamma.find(src, t1)) {
t = m_ba.mk_or(t, t1);
trail.push_back(t);
}
gamma.insert(src, t);
}
}
}
hashtable<block*> relevant;
u_map<T*>::iterator end = gamma.end();
for (u_map<T*>::iterator it = gamma.begin(); it != end; ++it) {
relevant.insert(blocks[it->m_key]);
}
}
#endif
return 0;
}
template<class T, class M>
typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_product(automaton_t& a, automaton_t& b) {
map<unsigned_pair, unsigned, pair_hash<unsigned_hash, unsigned_hash>, default_eq<unsigned_pair> > state_ids;
unsigned_pair init_pair(a.init(), b.init());
svector<unsigned_pair> todo;
todo.push_back(init_pair);
state_ids.insert(init_pair, 0);
moves_t mvs;
unsigned_vector final;
if (a.is_final_state(a.init()) && b.is_final_state(b.init())) {
final.push_back(0);
}
unsigned n = 1;
moves_t mvsA, mvsB;
while (!todo.empty()) {
unsigned_pair curr_pair = todo.back();
todo.pop_back();
unsigned src = state_ids[curr_pair];
mvsA.reset(); mvsB.reset();
a.get_moves_from(curr_pair.first, mvsA, true);
b.get_moves_from(curr_pair.second, mvsB, true);
for (unsigned i = 0; i < mvsA.size(); ++i) {
for (unsigned j = 0; j < mvsB.size(); ++j) {
ref_t ab(m_ba.mk_and(mvsA[i].t(), mvsB[j].t()), m);
lbool is_sat = m_ba.is_sat(ab);
if (is_sat == l_false) {
continue;
}
else if (is_sat == l_undef) {
return 0;
}
unsigned_pair tgt_pair(mvsA[i].dst(), mvsB[j].dst());
unsigned tgt;
if (!state_ids.find(tgt_pair, tgt)) {
tgt = n++;
state_ids.insert(tgt_pair, tgt);
todo.push_back(tgt_pair);
if (a.is_final_state(tgt_pair.first) && b.is_final_state(tgt_pair.second)) {
final.push_back(tgt);
}
}
mvs.push_back(move_t(m, src, tgt, ab));
}
}
}
if (final.empty()) {
return alloc(automaton_t, m);
}
vector<moves_t> inv(n, moves_t());
for (unsigned i = 0; i < mvs.size(); ++i) {
move_t const& mv = mvs[i];
inv[mv.dst()].push_back(move_t(m, mv.dst(), mv.src(), mv.t()));
}
svector<bool> back_reachable(n, false);
for (unsigned i = 0; i < final.size(); ++i) {
back_reachable[final[i]] = true;
}
unsigned_vector stack(final);
while (!stack.empty()) {
unsigned state = stack.back();
stack.pop_back();
moves_t const& mv = inv[state];
for (unsigned i = 0; i < mv.size(); ++i) {
state = mv[i].dst();
if (!back_reachable[state]) {
back_reachable[state] = true;
stack.push_back(state);
}
}
}
moves_t mvs1;
for (unsigned i = 0; i < mvs.size(); ++i) {
move_t const& mv = mvs[i];
if (back_reachable[mv.dst()]) {
mvs1.push_back(mv);
}
}
if (mvs1.empty()) {
return alloc(automaton_t, m);
}
else {
return alloc(automaton_t, m, 0, final, mvs1);
}
}
#endif

View file

@ -25,6 +25,7 @@ Revision History:
#include "theory_seq.h"
#include "ast_trail.h"
#include "theory_arith.h"
#include "smt_kernel.h"
using namespace smt;
@ -36,6 +37,21 @@ struct display_expr {
}
};
class seq_expr_solver : public expr_solver {
kernel m_kernel;
public:
seq_expr_solver(ast_manager& m, smt_params& fp):
m_kernel(m, fp)
{}
virtual lbool check_sat(expr* e) {
m_kernel.push();
m_kernel.assert_expr(e);
lbool r = m_kernel.check();
m_kernel.pop(1);
return r;
}
};
void theory_seq::solution_map::update(expr* e, expr* r, dependency* d) {
@ -199,26 +215,31 @@ theory_seq::theory_seq(ast_manager& m):
m_new_solution(false),
m_new_propagation(false),
m_mk_aut(m) {
m_prefix = "seq.prefix.suffix";
m_suffix = "seq.suffix.prefix";
m_accept = "aut.accept";
m_reject = "aut.reject";
m_prefix = "seq.p.suffix";
m_suffix = "seq.s.prefix";
m_accept = "aut.accept";
m_reject = "aut.reject";
m_tail = "seq.tail";
m_nth = "seq.nth";
m_seq_first = "seq.first";
m_seq_last = "seq.last";
m_indexof_left = "seq.indexof.left";
m_indexof_right = "seq.indexof.right";
m_indexof_left = "seq.idx.left";
m_indexof_right = "seq.idx.right";
m_aut_step = "aut.step";
m_pre = "seq.pre"; // (seq.pre s l): prefix of string s of length l
m_post = "seq.post"; // (seq.post s l): suffix of string s of length l
m_eq = "seq.eq";
}
theory_seq::~theory_seq() {
m_trail_stack.reset();
}
void theory_seq::init(context* ctx) {
theory::init(ctx);
m_mk_aut.set_solver(alloc(seq_expr_solver, m, get_context().get_fparams()));
}
final_check_status theory_seq::final_check_eh() {
TRACE("seq", display(tout << "level: " << get_context().get_scope_level() << "\n"););

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@ -332,6 +332,7 @@ namespace smt {
obj_hashtable<expr> m_fixed; // string variables that are fixed length.
virtual void init(context* ctx);
virtual final_check_status final_check_eh();
virtual bool internalize_atom(app* atom, bool) { return internalize_term(atom); }
virtual bool internalize_term(app*);