mirrors/z3
3
0
Fork 0
mirror of https://github.com/Z3Prover/z3 synced 2025-06-29 01:18:45 +00:00
Code Activity

finish minimization

Browse source 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2016-03-01 00:04:03 -08:00
parent 4a15d756d7
commit 830a99aab4
2 changed files with 151 additions and 173 deletions
Download patch file Download diff file Expand all files Collapse all files

8
src/math/automata/symbolic_automata.h
View file

@ -79,16 +79,18 @@ class symbolic_automata {
return m_rep; return m_rep;
} }
void add(unsigned i) { m_set.insert(i); } void insert(unsigned i) { m_set.insert(i); }
bool contains(unsigned i) const { return m_set.contains(i); } bool contains(unsigned i) const { return m_set.contains(i); }
bool is_empty() const { return m_set.empty(); } bool is_empty() const { return m_set.empty(); }
unsigned size() const { return m_set.num_elems(); } unsigned size() const { return m_set.num_elems(); }
void remove(unsigned i) { m_set.remove(i); m_rep_chosen = false; } void remove(unsigned i) { m_set.remove(i); m_rep_chosen = false; }
void clear() { m_set.reset(); m_rep_chosen = false; } void clear() { m_set.reset(); m_rep_chosen = false; }
uint_set::iterator begin() { return m_set.begin(); } uint_set::iterator begin() const { return m_set.begin(); }
uint_set::iterator end() { return m_set.end(); } uint_set::iterator end() const { return m_set.end(); }
}; };
void add_block(block const& p1, unsigned p0_index, unsigned_vector& blocks, vector<block>& pblocks, unsigned_vector& W);
public: public:
symbolic_automata(M& m, ba_t& ba): m(m), m_ba(ba) {} symbolic_automata(M& m, ba_t& ba): m(m), m_ba(ba) {}
automaton_t* mk_determinstic(automaton_t& a); automaton_t* mk_determinstic(automaton_t& a);

316
src/math/automata/symbolic_automata_def.h
View file

@ -35,7 +35,7 @@ typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_total
moves_t mvs, new_mvs; moves_t mvs, new_mvs;
for (unsigned i = 0; i < dead_state; ++i) { for (unsigned i = 0; i < dead_state; ++i) {
mvs.reset(); mvs.reset();
a.get_moves(i, mvs, true); a.get_moves_from(i, mvs, true);
refs_t vs(m); refs_t vs(m);
for (unsigned j = 0; j < mvs.size(); ++j) { for (unsigned j = 0; j < mvs.size(); ++j) {
@ -54,7 +54,8 @@ typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_total
return a.clone(); return a.clone();
} }
new_mvs.push_back(move_t(m, dead_state, dead_state, m_ba.mk_true())); new_mvs.push_back(move_t(m, dead_state, dead_state, m_ba.mk_true()));
automaton_t::append_moves(0, a, new_mvs);
// TBD private: automaton_t::append_moves(0, a, new_mvs);
return alloc(automaton_t, m, a.init(), a.final_states(), new_mvs); return alloc(automaton_t, m, a.init(), a.final_states(), new_mvs);
} }
@ -78,47 +79,65 @@ typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_minim
} }
template<class T, class M>
void symbolic_automata<T, M>::add_block(block const& p1, unsigned p0_index, unsigned_vector& blocks, vector<block>& pblocks, unsigned_vector& W) {
block& p0 = pblocks[p0_index];
if (p1.size() < p0.size()) {
unsigned p1_index = pblocks.size();
pblocks.push_back(p1);
for (uint_set::iterator it = p1.begin(), end = p1.end(); it != end; ++it) {
p0.remove(*it);
blocks[*it] = p1_index;
}
if (W.contains(p0_index)) {
W.push_back(p1_index);
}
else if (p0.size() <= p1.size()) {
W.push_back(p0_index);
}
else {
W.push_back(p1_index);
}
}
}
template<class T, class M> template<class T, class M>
typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_minimize_total(automaton_t& a) { typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_minimize_total(automaton_t& a) {
vector<block> pblocks; vector<block> pblocks;
unsigned_vector blocks; unsigned_vector blocks;
pblocks.push_back(block(fa->final_states())); // 0 |-> final states unsigned_vector non_final;
// pblocks.push_back(block(fa->non_final_states()); // 1 |-> non-final states for (unsigned i = 0; i < a.num_states(); ++i) {
for (unsigned i = 0; i < fa->num_states(); ++i) { if (!a.is_final_state(i)) {
if (fa->is_final_state(i)) { non_final.push_back(i);
blocks.push_back(0);
}
else {
blocks.push_back(1); blocks.push_back(1);
} }
else {
blocks.push_back(0);
}
} }
vector<block> W; pblocks.push_back(block(a.final_states())); // 0 |-> final states
if (final_block.size() > non_final_block.size()) { pblocks.push_back(block(non_final)); // 1 |-> non-final states
W.push_back(1);
} unsigned_vector W;
else { W.push_back(pblocks[0].size() > pblocks[1].size() ? 1 : 0);
W.push_back(0);
}
#if 0
refs_t trail(m); refs_t trail(m);
u_map<T*> gamma; u_map<T*> gamma;
moves_t mvs; moves_t mvs;
while (!W.empty()) { while (!W.empty()) {
block R(pblocks[W.back()]); block R(pblocks[W.back()]);
W.pop_back(); W.pop_back();
block Rcopy(R);
gamma.reset(); gamma.reset();
uint_set::iterator it = Rcopy.begin(), end = Rcopy.end(); uint_set::iterator it = R.begin(), end = R.end();
for (; it != end; ++it) { for (; it != end; ++it) {
unsigned q = *it; unsigned dst = *it;
mvs.reset(); mvs.reset();
fa->get_moves_to(q, mvs); a.get_moves_to(dst, mvs);
for (unsigned i = 0; i < mvs.size(); ++i) { for (unsigned i = 0; i < mvs.size(); ++i) {
unsigned src = mvs[i].src(); unsigned src = mvs[i].src();
if (pblocks[src].size() > 1) { if (pblocks[src].size() > 1) {
T* t = mvs[i](); T* t = mvs[i].t();
T* t1;
if (gamma.find(src, t1)) { if (gamma.find(src, t1)) {
t = m_ba.mk_or(t, t1); t = m_ba.mk_or(t, t1);
trail.push_back(t); trail.push_back(t);
@ -127,177 +146,131 @@ typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_minim
} }
} }
} }
uint_set relevant; uint_set relevant1;
u_map<T*>::iterator gend = gamma.end(); u_map<T*>::iterator gend = gamma.end();
for (u_map<T*>::iterator it = gamma.begin(); it != gend; ++it) { for (u_map<T*>::iterator git = gamma.begin(); git != gend; ++git) {
relevant.insert(blocks[it->m_key]); unsigned p0A_index = blocks[git->m_key];
} if (relevant1.contains(p0A_index)) {
uint_set::iterator uit = relevant.begin(), uend = relevant.end(); continue;
for (; uit != uend; ++uit) { }
unsigned p0_index = *uit; relevant1.insert(p0A_index);
block& p0 = pblocks[p0_index]; block& p0A = pblocks[p0A_index];
block p1; block p1;
for (u_map<T*>::iterator it = gamma.begin(); it != gend; ++it) { for (u_map<T*>::iterator it = gamma.begin(); it != gend; ++it) {
if (p0.contains(*it)) p1.push_back(*it); if (p0A.contains(it->m_key)) p1.insert(it->m_key);
} }
if (p1.size() < p0.size()) {
unsigned p1_index = pblocks.size(); add_block(p1, p0A_index, blocks, pblocks, W);
pblocks.push_back(p1);
for (uint_set::iterator it = p1.begin(), end = p1.end(); it != end; ++it) {
p0.remove(*it);
blocks[*it] = p1_index;
}
if (W.contains(p0_index)) {
W.push_back(p1_index);
}
else if (p0.size() <= p1.size()) {
W.push_back(p0_index);
}
else {
W.push_back(p1_index);
}
}
bool iterate = true; bool iterate = true;
while (iterate) { while (iterate) {
iterate = false; iterate = false;
uint_set relevant; uint_set relevant2;
for (u_map<T*>::iterator it = gamma.begin(); it != gend; ++it) { for (u_map<T*>::iterator it = gamma.begin(); it != gend; ++it) {
if (pblocks[blocks[it->m_key]].size() > 1) { unsigned p0B_index = blocks[it->m_key];
relevant.insert(blocks[it->m_key]); if (pblocks[p0B_index].size() <= 1 || relevant2.contains(p0B_index)) {
continue;
} }
} relevant2.insert(p0B_index);
uint_set::iterator it = relevant.begin(), end = relevant.end(); block const& p0B = pblocks[p0B_index];
for (; it != end; ++it) { uint_set::iterator bi = p0B.begin(), be = p0B.end();
block const& p = pblocks[*it];
uint_set::iterator bi = p.begin(), be = p.end();
block p1; block p1;
p1.insert(*bi); p1.insert(*bi);
// psi = gamma[*bi]; // name of key or block? bool split_found = false;
ref_t psi(gamma[*bi], m);
++bi; ++bi;
for (; bi != be; ++bi) { for (; bi != be; ++bi) {
unsigned q = *bi;
ref_t phi(gamma[q], m);
if (split_found) {
ref_t phi_and_psi(m_ba.mk_and(phi, psi), m);
switch (m_ba.is_sat(phi_and_psi)) {
case l_true:
p1.insert(q);
break;
case l_undef:
return 0;
default:
break;
}
}
else {
ref_t psi_min_phi(m_ba.mk_and(psi, m_ba.mk_not(phi)), m);
lbool is_sat = m_ba.is_sat(psi_min_phi);
if (is_sat == l_undef) {
return 0;
}
if (is_sat == l_true) {
psi = psi_min_phi;
split_found = true;
continue;
}
// psi is a subset of phi
ref_t phi_min_psi(m_ba.mk_and(phi, m_ba.mk_not(psi)), m);
is_sat = m_ba.is_sat(phi_min_psi);
if (is_sat == l_undef) {
return 0;
}
else if (is_sat == l_false) {
p1.insert(q); // psi and phi are equivalent
}
else {
p1.clear();
p1.insert(q);
psi = phi_min_psi;
split_found = true;
}
}
} }
if (p1.size() < p0B.size() && p0B.size() > 2) iterate = true;
add_block(p1, p0B_index, blocks, pblocks, W);
} }
} }
} }
} }
#endif
#if 0 unsigned new_init = pblocks[blocks[a.init()]].get_representative();
Func<T, T, T> MkDiff = (x, y) => solver.MkAnd(x, solver.MkNot(y));
while (!W.IsEmpty) // set moves
{ map<unsigned_pair, T*, pair_hash<unsigned_hash, unsigned_hash>, default_eq<unsigned_pair> > conds;
//keep using Bcopy until no more changes occur svector<unsigned_pair> keys;
//effectively, this replaces the loop over characters moves_t new_moves;
bool iterate = true;
//in each relevant block all states lead to B due to the initial splitting
//only relevant blocks are potentially split for (unsigned i = 0; i < a.num_states(); ++i) {
foreach (var P in relevant2) unsigned src = pblocks[blocks[i]].get_representative();
{ automaton_t::moves const& mvs = a.get_moves_from(i);
var PE = P.GetEnumerator(); for (unsigned j = 0; j < mvs.size(); ++j) {
PE.MoveNext(); unsigned dst = pblocks[blocks[mvs[j].dst()]].get_representative();
unsigned_pair st(src, dst);
var P1 = new Block(); T* t = 0;
bool splitFound = false; if (conds.find(st, t)) {
t = m_ba.mk_or(t, mvs[j].t());
var psi = Gamma[PE.Current]; trail.push_back(t);
P1.Add(PE.Current); //C has at least 2 elements conds.insert(st, t);
#region compute C1 as the new sub-block of C
while (PE.MoveNext())
{
var q = PE.Current;
var phi = Gamma[q];
if (splitFound)
{
var psi_and_phi = solver.MkAnd(psi, phi);
if (solver.IsSatisfiable(psi_and_phi))
P1.Add(q);
}
else
{
var psi_min_phi = MkDiff(psi, phi);
if (solver.IsSatisfiable(psi_min_phi))
{
psi = psi_min_phi;
splitFound = true;
}
else // [[psi]] is subset of [[phi]]
{
var phi_min_psi = MkDiff(phi, psi);
if (!solver.IsSatisfiable(phi_min_psi))
P1.Add(q); //psi and phi are equivalent
else
{
//there is some a: q --a--> B and p --a--> compl(B) for all p in C1
P1.Clear();
P1.Add(q);
psi = phi_min_psi;
splitFound = true;
}
}
}
}
#endregion
#region split P
if (P1.Count < P.Count)
{
iterate = (iterate || (P.Count > 2)); //otherwise C was split into singletons
foreach (var p in P1)
{
P.Remove(p);
Blocks[p] = P1;
}
if (W.Contains(P))
W.Push(P1);
else if (P.Count <= P1.Count)
W.Push(P);
else
W.Push(P1);
}
#endregion
}
}
} }
else {
Dictionary<Pair<int, int>, HashSet<T>> condMap = new Dictionary<Pair<int, int>, HashSet<T>>(); conds.insert(st, mvs[j].t());
foreach (var move in GetMoves()) keys.push_back(st);
{
int s = Blocks[move.SourceState].GetRepresentative();
int t = Blocks[move.TargetState].GetRepresentative();
var st = new Pair<int, int>(s, t);
HashSet<T> condSet;
if (!condMap.TryGetValue(st, out condSet))
{
condSet = new HashSet<T>();
condSet.Add(move.Label);
condMap[st] = condSet;
}
else
condSet.Add(move.Label);
} }
int newInitState = Blocks[fa.InitialState].GetRepresentative(); }
var newMoves = new List<Move<T>>(); }
var newFinals = new HashSet<int>(); for (unsigned i = 0; i < keys.size(); ++i) {
foreach (var entry in condMap) unsigned_pair st = keys[i];
newMoves.Add(Move<T>.Create(entry.Key.First, entry.Key.Second, solver.MkOr(entry.Value))); new_moves.push_back(move_t(m, st.first, st.second, conds[st]));
foreach (var f in GetFinalStates()) }
newFinals.Add(Blocks[f].GetRepresentative()); // set final states.
unsigned_vector new_final;
uint_set new_final_set;
for (unsigned i = 0; i < a.final_states().size(); ++i) {
unsigned f = pblocks[blocks[a.final_states()[i]]].get_representative();
if (!new_final_set.contains(f)) {
new_final_set.insert(f);
new_final.push_back(f);
}
}
var res = Create(newInitState, newFinals, newMoves); return alloc(automaton_t, m, new_init, new_final, new_moves);
res.isDeterministic = true;
res.isEpsilonFree = true;
//res.EliminateDeadStates();
return res;
#endif
return 0;
} }
template<class T, class M> template<class T, class M>
@ -312,6 +285,9 @@ typename symbolic_automata<T, M>::automaton_t* symbolic_automata<T, M>::mk_produ
if (a.is_final_state(a.init()) && b.is_final_state(b.init())) { if (a.is_final_state(a.init()) && b.is_final_state(b.init())) {
final.push_back(0); final.push_back(0);
} }
if (false) {
mk_minimize(a);
}
unsigned n = 1; unsigned n = 1;
moves_t mvsA, mvsB; moves_t mvsA, mvsB;
while (!todo.empty()) { while (!todo.empty()) {