SddNode* Prover::branchToSDD(std::vector<SddLiteral> variables, SddManager* m) {
SddNode* alpha = sdd_manager_true(m);
SddNode* tmp;
for (SddLiteral i: variables) {
alpha = sdd_conjoin(tmp = alpha, sdd_manager_literal(i,m),m);
sdd_ref(alpha,m); sdd_deref(tmp,m);
}
sdd_deref(alpha,m);
return alpha;
}
SddNode* S4Prover::refineSdd(std::vector<SddLiteral> literals, SddNode* oldSdd, SddManager* m) {
SddNode* tmp;
SddNode* newSdd = sdd_manager_false(m);
for (SddLiteral lit : literals) {
newSdd = sdd_disjoin(tmp = newSdd, sdd_manager_literal(-lit,m),m);
sdd_ref(newSdd,m); sdd_deref(tmp,m);
}
newSdd = sdd_conjoin(oldSdd,tmp = newSdd,m);
sdd_deref(tmp,m);
return newSdd;
}
/*
# of literals = term*len + nonTerm*len*(len+1)/2
first term*len literals:
Terminal i corresponds to S(i/term,i%term)
next nonTerm*len*(len+1)/2 correspond to non-terminals
literal for T[i][j][k] = (j*(j+1)/2)*nonTerm+i*nonTerm+k + firstNon
*/
SddNode* sddParsings(SddManager*m, int nonTerm, int term, int nonRules[][3], int termRules[][2], int nonRuleCount, int termRuleCount, int start, int len){
SddNode* S[term][len];
int i,j,k,index;
for(j = 0; j < len; j++){
for(i = 0; i < term; i++){
S[i][j] = sdd_manager_literal(j*term+i+1,m);
for(k = 0; k < term; k++){
if (k != i){
S[i][j] = sdd_conjoin(sdd_manager_literal(0-(j*term+k+1),m),S[i][j],m);
}
}
}
}
int firstNon = term*len+1;
SddNode* T[len][len][nonTerm];
//set diagonal according to terminal rules
for (index = 0;index < len; index++){
for(k = 0; k < nonTerm; k++){
T[index][index][k] = sdd_manager_false(m);
}
for(i = 0; i < termRuleCount; i++){
k = termRules[i][0];
int termVal = termRules[i][1];
T[index][index][k] = sdd_disjoin(T[index][index][k],S[termVal][index],m);
}
for(k = 0; k < nonTerm; k++){
T[index][index][k] = sdd_conjoin(T[index][index][k],sdd_manager_literal((index*(index+1)/2)*nonTerm+index*nonTerm+k + firstNon,m),m);
for(j = 0; j < nonTerm; j++){
if (j != k){
T[index][index][k] = sdd_conjoin(T[index][index][k],sdd_manager_literal(0-((index*(index+1)/2)*nonTerm+index*nonTerm+j + firstNon),m),m);
}
}
}
}
return T[0][0][0];
}
//converts a clause/term into an equivalent sdd
//all variables of litset must appear in vtree
SddNode* apply_litset_manual(LitSet* litset, Vtree* vtree, SddManager* manager) {
BoolOp op = litset->op; //conjoin (term) or disjoin (clause)
SddLiteral* literals = litset->literals;
SddNode* node = ONE(manager,op);
for(SddLiteral i=0; i<litset->literal_count; i++) {
SddNode* literal = sdd_manager_literal(literals[i],manager);
node = sdd_apply_in_vtree(node,literal,op,vtree,manager);
}
return node;
}
//converts a clause/term into an equivalent sdd
SddNode* apply_litset_auto(LitSet* litset, SddManager* manager) {
BoolOp op = litset->op; //conjoin (term) or disjoin (clause)
SddLiteral* literals = litset->literals;
SddNode* node = ONE(manager,op); //will not be gc'd
for(SddLiteral i=0; i<litset->literal_count; i++) {
SddNode* literal = sdd_manager_literal(literals[i],manager);
node = sdd_apply(node,literal,op,manager);
}
return node;
}
bool S4Prover::isSatisfiable(SddNode* alpha, SddManager* m, std::unordered_set<SddLiteral> permVars, SddNode* permSdd,
std::unordered_set<SddNode*,SddHasher>& assumedSatSdds , std::unordered_set<SddLiteral>& responsibleVars) {
//Match against cache
if (satCache.count(alpha) == 1) {
return true;
}
//Base cases
if (sdd_node_is_true(alpha)) {
return true;
}
if (sdd_node_is_false(alpha)) {
return false;
}
//Scrape off a single satisfying set, corresponding to a single open tableaux branch.
std::vector<SddLiteral> branch = getOpenBranch(alpha, std::vector<SddLiteral>());
SddNode* branchSdd = branchToSDD(branch,m);
sdd_ref(branchSdd,m);
/*std::cout << "BRANCH\n\n";
for (SddLiteral i : branch) {
if (i < 0) std::cout << "~" << *literalsToAtoms[-i] << "\n\n";
else std::cout << *literalsToAtoms[i] << "\n\n";
}
std::cout << "BRANCH END\n\n";*/
//Extract all modal atoms from the branch.
std::vector<SddLiteral> boxes;
std::vector<SddLiteral> negBoxes;
if (extractModals(branch,boxes,negBoxes) == 0) {
return true;
};
//Checks for new boxed variables
SddNode* tmp;
std::unordered_set<SddLiteral> newPermVars = permVars;
std::vector<SddLiteral> unboxed;
SddNode* postUnboxingBranch = sdd_conjoin(sdd_manager_true(m),branchSdd,m);
sdd_ref(postUnboxingBranch,m);
SddNode* newPermSdd = sdd_conjoin(sdd_manager_true(m),permSdd,m);
sdd_ref(newPermSdd,m);
for (SddLiteral i : boxes) {
if (newPermVars.count(i) == 0) {
unboxed.push_back(i);
newPermVars.insert(i);
postUnboxingBranch = sdd_conjoin(tmp = postUnboxingBranch, compiler::KtoSDD(&literalsToAtoms[i]->getleft(),m),m);
sdd_deref(tmp,m); sdd_ref(postUnboxingBranch,m);
newPermSdd = sdd_conjoin(tmp = newPermSdd, compiler::KtoSDD(&literalsToAtoms[i]->getleft(),m),m);
sdd_deref(tmp,m); sdd_ref(newPermSdd,m);
newPermSdd = sdd_conjoin(tmp = newPermSdd, compiler::KtoSDD(literalsToAtoms[i],m),m);
sdd_deref(tmp,m); sdd_ref(newPermSdd,m);
//If becomes false while unboxing, recurse.
if (sdd_node_is_false(postUnboxingBranch)) {
//Determine minimal set of unboxed variables
std::vector<SddLiteral> minLits;
minLits.push_back(i);
responsibleVars.insert(i);
std::vector<SddLiteral>::iterator endIt = --(unboxed.end());
SddNode* minimalSdd = sdd_conjoin(compiler::KtoSDD(&literalsToAtoms[i]->getleft(),m),branchSdd,m);
sdd_ref(minimalSdd,m);
SddNode* minBoxVarsSdd = sdd_conjoin(compiler::KtoSDD(&literalsToAtoms[i]->getleft(),m),sdd_manager_true(m),m);
sdd_ref(minBoxVarsSdd,m);
while (true) {
sdd_deref(postUnboxingBranch,m);
postUnboxingBranch = sdd_conjoin(minimalSdd, sdd_manager_true(m), m);
sdd_ref(postUnboxingBranch,m);
if (sdd_node_is_false(postUnboxingBranch)) break; //Last one added made it false
for (std::vector<SddLiteral>::iterator v = unboxed.begin();
v != endIt; ++v) {
postUnboxingBranch = sdd_conjoin(tmp = postUnboxingBranch, compiler::KtoSDD(&literalsToAtoms[*v]->getleft(),m),m);
sdd_deref(tmp,m); sdd_ref(postUnboxingBranch,m);
if (sdd_node_is_false(postUnboxingBranch)) {
//Last one added made it false
minimalSdd = sdd_conjoin(tmp = minimalSdd, compiler::KtoSDD(&literalsToAtoms[*v]->getleft(),m),m);
sdd_deref(tmp,m); sdd_ref(minimalSdd,m);
minBoxVarsSdd = sdd_conjoin(tmp = minBoxVarsSdd,compiler::KtoSDD(&literalsToAtoms[*v]->getleft(),m),m);
sdd_deref(tmp,m); sdd_ref(minBoxVarsSdd,m);
minLits.push_back(*v);
responsibleVars.insert(*v);
endIt = v;
break;
}
}
}
// Determine minimal set of branch variables together with unboxed variables
std::vector<SddLiteral>::iterator BendIt = branch.end();
sdd_deref(minimalSdd,m);
minimalSdd = sdd_conjoin(sdd_manager_true(m),minBoxVarsSdd,m);
sdd_ref(minimalSdd,m);
while (true) {
sdd_deref(minBoxVarsSdd,m);
minBoxVarsSdd = sdd_conjoin(minimalSdd, sdd_manager_true(m), m);
sdd_ref(minBoxVarsSdd,m);
if (sdd_node_is_false(minBoxVarsSdd)) break; //Last one added made it false
for (std::vector<SddLiteral>::iterator v = branch.begin();
v != BendIt; ++v) {
minBoxVarsSdd = sdd_conjoin(tmp = minBoxVarsSdd, sdd_manager_literal(*v,m), m);
sdd_deref(tmp,m); sdd_ref(minBoxVarsSdd,m);
if (sdd_node_is_false(minBoxVarsSdd)) {
//Last one added made it false
minimalSdd = sdd_conjoin(tmp = minimalSdd, sdd_manager_literal(*v,m),m);
sdd_deref(tmp,m); sdd_ref(minimalSdd,m);
minLits.push_back(*v);
responsibleVars.insert(*v);
BendIt = v;
break;
}
}
}
sdd_deref(minimalSdd,m); sdd_deref(postUnboxingBranch,m); sdd_deref(minBoxVarsSdd,m);
//std::cout << *literalsToAtoms[minLits[0]] << " and " << *literalsToAtoms[minLits[1]] << "\n";
SddNode* beta = refineSdd(minLits, alpha, m);
sdd_ref(beta,m);
dependentSdds.insert(alpha);
bool isSat = isSatisfiableRefined(beta, m, permVars, permSdd, assumedSatSdds, responsibleVars);
dependentSdds.erase(alpha);
sdd_deref(beta,m); sdd_deref(branchSdd,m); sdd_deref(newPermSdd,m);
return isSat;
}
}
}
// There were new boxes, so recurse.
if (!unboxed.empty()) {
dependentSdds.insert(alpha);
std::unordered_set<SddLiteral> postResponsibleVars;
if (!isSatisfiable(postUnboxingBranch,m,newPermVars,newPermSdd,assumedSatSdds, postResponsibleVars)) {
std::vector<SddLiteral> minLits;
for (SddLiteral v : branch) {
if (postResponsibleVars.count(v) == 1) {
minLits.push_back(v);
responsibleVars.insert(v);
}
}
for (SddLiteral v : unboxed) {
std::unordered_set<SddLiteral> children;
KFormula::computeChildrenBoxS4(&literalsToAtoms[v]->getleft(), children);
if (shareAnElement(postResponsibleVars, children)) {
minLits.push_back(v);
responsibleVars.insert(v);
}
}
SddNode* beta = refineSdd(minLits, alpha, m);
sdd_ref(beta,m);
bool isSat = isSatisfiableRefined(beta, m, permVars, permSdd, assumedSatSdds, responsibleVars);
sdd_deref(beta,m); sdd_deref(branchSdd,m); sdd_deref(newPermSdd,m); sdd_deref(postUnboxingBranch,m);
dependentSdds.erase(alpha);
return isSat;
}
sdd_deref(branchSdd,m); sdd_deref(newPermSdd,m);
dependentSdds.erase(alpha);
return true;
}
// There are no new boxes, so start undiamonding.
sdd_deref(branchSdd,m);
if (negBoxes.empty()) {
return true;
}
dependentSdds.insert(alpha);
SddNode* nextWorld;
for (SddLiteral i : negBoxes) {
nextWorld = sdd_conjoin(permSdd, sdd_negate(compiler::KtoSDD(&literalsToAtoms[-i]->getleft(),m),m),m);
sdd_ref(nextWorld,m);
if (sdd_node_is_false(nextWorld)) {
sdd_deref(nextWorld,m);
nextWorld = sdd_conjoin(sdd_manager_true(m), sdd_negate(compiler::KtoSDD(&literalsToAtoms[-i]->getleft(),m),m),m);
sdd_ref(nextWorld,m);
responsibleVars.insert(i);
std::vector<SddLiteral> minLits;
minLits.push_back(i);
// Determine a minimal unsatisfiable subset.
std::unordered_set<SddLiteral>::iterator endIt = permVars.end();
SddNode* minimalSdd = sdd_conjoin(nextWorld, sdd_manager_true(m),m);
sdd_ref(minimalSdd,m);
while (true) {
sdd_deref(nextWorld,m);
nextWorld = sdd_conjoin(minimalSdd, sdd_manager_true(m), m);
sdd_ref(nextWorld,m);
if (sdd_node_is_false(nextWorld)) break;
for (std::unordered_set<SddLiteral>::iterator v = permVars.begin();
v != endIt; ++v) {
nextWorld = sdd_conjoin(tmp = nextWorld,compiler::KtoSDD(&literalsToAtoms[*v]->getleft(),m) ,m);
sdd_deref(tmp, m); sdd_ref(nextWorld,m);
nextWorld = sdd_conjoin(tmp = nextWorld,sdd_manager_literal(*v,m) ,m);
sdd_deref(tmp, m); sdd_ref(nextWorld,m);
if (sdd_node_is_false(nextWorld)) {
minimalSdd = sdd_conjoin(tmp = minimalSdd,compiler::KtoSDD(&literalsToAtoms[*v]->getleft(),m) ,m);
sdd_deref(tmp, m); sdd_ref(minimalSdd,m);
minimalSdd = sdd_conjoin(tmp = minimalSdd,sdd_manager_literal(*v,m) ,m);
sdd_deref(tmp, m); sdd_ref(minimalSdd,m);
minLits.push_back(*v);
responsibleVars.insert(*v);
endIt = v;
break;
}
}
}
SddNode* beta = refineSdd(minLits, alpha, m);
sdd_ref(beta,m);
bool isSat = isSatisfiableRefined(beta, m, permVars, permSdd, assumedSatSdds, responsibleVars);
sdd_deref(beta,m); sdd_deref(nextWorld,m); sdd_deref(minimalSdd,m);
dependentSdds.erase(alpha);
return isSat;
}
if (dependentSdds.count(nextWorld) == 1) {
//Loop detected
assumedSatSdds.insert(nextWorld);
continue;
}
std::unordered_set<SddNode*,SddHasher> postModalAssumedSatSdds = assumedSatSdds;
std::unordered_set<SddLiteral> postResponsibleVars;
if (!isSatisfiable(nextWorld,m,permVars,permSdd,postModalAssumedSatSdds, postResponsibleVars)) {
std::vector<SddLiteral> minLits;
bool newPostModalJumpResVarsAdded = true;
while (newPostModalJumpResVarsAdded) {
newPostModalJumpResVarsAdded = false;
for (std::unordered_set<SddLiteral>::iterator v = permVars.begin();
v != permVars.end(); ++v) {
if (responsibleVars.count(*v) != 0) {
continue;
}
std::unordered_set<SddLiteral> children = getChildren(*v);
children.insert(*v);
if (shareAnElement(postResponsibleVars, children)) {
minLits.push_back(*v);
responsibleVars.insert(*v);
// Add in other children to postModalJumpResVars
postResponsibleVars.insert(children.begin(),
children.end());
newPostModalJumpResVarsAdded = true;
}
}
if (responsibleVars.count(i) != 0) {
// Don't bother, we've already accounted for this dia var.
} else if (shareAnElement(postResponsibleVars, getChildren(i))) {
// Note, <>phi stored as []~phi, thus the nith.
minLits.push_back(i);
responsibleVars.insert(i);
// Add in other children to postModalJumpResVars
postResponsibleVars.insert(getChildren(i).begin(),
getChildren(i).end());
newPostModalJumpResVarsAdded = true;
}
}
SddNode* beta = refineSdd(minLits, alpha, m);
sdd_ref(beta,m);
bool isSat = isSatisfiableRefined(beta, m, permVars, permSdd, assumedSatSdds, responsibleVars);
sdd_deref(beta,m); sdd_deref(nextWorld,m);
dependentSdds.erase(alpha);
return isSat;
}
assumedSatSdds.insert(postModalAssumedSatSdds.begin(),postModalAssumedSatSdds.end());
}
satCache.insert(alpha);
dependentSdds.erase(alpha);
return true;
}
int main(int argc, char** argv) {
// set up vtree and manager
SddLiteral var_count = 5;
int auto_gc_and_minimize = 0;
SddManager* m = sdd_manager_create(var_count,auto_gc_and_minimize);
SddLiteral A = 1, B = 2, C = 3, faulty1 = 4, faulty2 = 5;
SddNode* delta = sdd_manager_true(m);
SddNode* alpha;
////////// CONSTRUCT KNOWLEDGE BASE //////////
// ~faulty1 => ( A <=> ~B )
alpha = sdd_equiv(sdd_manager_literal(A,m),sdd_manager_literal(-B,m),m);
alpha = sdd_imply(sdd_manager_literal(-faulty1,m),alpha,m);
delta = sdd_conjoin(delta,alpha,m);
// faulty1 => ( ( A <=> B ) v ~B )
alpha = sdd_equiv(sdd_manager_literal(A,m),sdd_manager_literal(B,m),m);
alpha = sdd_disjoin(alpha,sdd_manager_literal(-B,m),m);
alpha = sdd_imply(sdd_manager_literal(faulty1,m),alpha,m);
delta = sdd_conjoin(delta,alpha,m);
// ~faulty2 => ( B <=> ~C )
alpha = sdd_equiv(sdd_manager_literal(B,m),sdd_manager_literal(-C,m),m);
alpha = sdd_imply(sdd_manager_literal(-faulty2,m),alpha,m);
delta = sdd_conjoin(delta,alpha,m);
// faulty2 => ( ( B <=> C ) v ~C )
alpha = sdd_equiv(sdd_manager_literal(B,m),sdd_manager_literal(C,m),m);
alpha = sdd_disjoin(alpha,sdd_manager_literal(-C,m),m);
alpha = sdd_imply(sdd_manager_literal(faulty2,m),alpha,m);
delta = sdd_conjoin(delta,alpha,m);
////////// PERFORM QUERY //////////
int* variables;
SddLiteral health_vars = 2, health_vars_count, missing_health_vars;
// make observations
delta = sdd_condition(A,delta,m);
delta = sdd_condition(-C,delta,m);
// check if observations are normal
SddNode* gamma;
gamma = sdd_condition(-faulty1,delta,m);
gamma = sdd_condition(-faulty2,gamma,m);
int is_abnormal = gamma == sdd_manager_false(m); // sdd_node_is_false(gamma,m);
printf("observations normal? : %s\n", is_abnormal ? "abnormal":"normal");
// project onto faults
SddNode* diagnosis = sdd_exists(B,delta,m);
// diagnosis no longer depends on variables A,B or C
// count the number of diagnoses
SddModelCount count = sdd_model_count(diagnosis,m);
// adjust for missing faults
variables = sdd_variables(diagnosis,m);
health_vars_count = variables[faulty1] + variables[faulty2];
missing_health_vars = health_vars - health_vars_count;
count <<= missing_health_vars; // multiply by 2^missing_health_vars
free(variables);
// find minimum cardinality diagnoses
SddNode* min_diagnosis = sdd_minimize_cardinality(diagnosis,m);
variables = sdd_variables(min_diagnosis,m);
// adjust for missing faults
if ( variables[faulty1] == 0 )
min_diagnosis = sdd_conjoin(min_diagnosis,sdd_manager_literal(-faulty1,m),m);
if ( variables[faulty2] == 0 )
min_diagnosis = sdd_conjoin(min_diagnosis,sdd_manager_literal(-faulty2,m),m) ;
free(variables);
// count the number of minimum cardinality diagnoses, and minimum cardinality
SddModelCount min_count = sdd_model_count(min_diagnosis,m);
SddLiteral min_card = sdd_minimum_cardinality(min_diagnosis);
printf("sdd model count : %"PRImcS"\n",count);
printf("sdd model count (min) : %"PRImcS"\n",min_count);
printf("sdd cardinality : %"PRIlitS"\n",min_card);
////////// SAVE SDDS //////////
printf("saving sdd and dot ...\n");
sdd_save("output/circuit-kb.sdd",delta);
sdd_save("output/diagnosis.sdd",diagnosis);
sdd_save("output/diagnosis-min.sdd",min_diagnosis);
sdd_save_as_dot("output/circuit-kb.dot",delta);
sdd_save_as_dot("output/diagnosis.dot",diagnosis);
sdd_save_as_dot("output/diagnosis-min.dot",min_diagnosis);
////////// CLEAN UP //////////
sdd_manager_free(m);
return 0;
}
int main(int argc, char** argv) {
// set up vtree and manager
SddLiteral var_count = 4;
const char* type = "right";
Vtree* vtree = sdd_vtree_new(var_count,type);
SddManager* manager = sdd_manager_new(vtree);
// construct the term X_1 ^ X_2 ^ X_3 ^ X_4
SddNode* alpha = sdd_manager_literal(1,manager);
alpha = sdd_conjoin(alpha,sdd_manager_literal(2,manager),manager);
alpha = sdd_conjoin(alpha,sdd_manager_literal(3,manager),manager);
alpha = sdd_conjoin(alpha,sdd_manager_literal(4,manager),manager);
// construct the term ~X_1 ^ X_2 ^ X_3 ^ X_4
SddNode* beta = sdd_manager_literal(-1,manager);
beta = sdd_conjoin(beta,sdd_manager_literal(2,manager),manager);
beta = sdd_conjoin(beta,sdd_manager_literal(3,manager),manager);
beta = sdd_conjoin(beta,sdd_manager_literal(4,manager),manager);
// construct the term ~X_1 ^ ~X_2 ^ X_3 ^ X_4
SddNode* gamma = sdd_manager_literal(-1,manager);
gamma = sdd_conjoin(gamma,sdd_manager_literal(-2,manager),manager);
gamma = sdd_conjoin(gamma,sdd_manager_literal(3,manager),manager);
gamma = sdd_conjoin(gamma,sdd_manager_literal(4,manager),manager);
printf("== before referencing:\n");
printf(" live sdd size = %zu\n", sdd_manager_live_size(manager));
printf(" dead sdd size = %zu\n", sdd_manager_dead_size(manager));
// ref SDDs so that they are not garbage collected
sdd_ref(alpha,manager);
sdd_ref(beta,manager);
sdd_ref(gamma,manager);
printf("== after referencing:\n");
printf(" live sdd size = %zu\n", sdd_manager_live_size(manager));
printf(" dead sdd size = %zu\n", sdd_manager_dead_size(manager));
// garbage collect
sdd_manager_garbage_collect(manager);
printf("== after garbage collection:\n");
printf(" live sdd size = %zu\n", sdd_manager_live_size(manager));
printf(" dead sdd size = %zu\n", sdd_manager_dead_size(manager));
sdd_deref(alpha,manager);
sdd_deref(beta,manager);
sdd_deref(gamma,manager);
printf("saving vtree & shared sdd ...\n");
sdd_vtree_save_as_dot("output/shared-vtree.dot",vtree);
sdd_shared_save_as_dot("output/shared.dot",manager);
sdd_vtree_free(vtree);
sdd_manager_free(manager);
return 0;
}
