bool StateConstraints::isInMaxTrap(const PetriNet& net,
size_t place,
const BitField& places,
const MarkVal* resultMarking) const{
if(!places.test(place))
return false;
/*
0 if M(p_i) = 1
0 if there is (p_i , t) â F such that x_j = 0
for every p_j â tâ˘
1 otherwise
*/
if(resultMarking[place] > 0)
return false;
for(unsigned int t = 0; t < net.numberOfTransitions(); t++){
if(net.inArc(place, t) > 0){
bool exclude = true;
for(unsigned int j = 0; j < net.numberOfPlaces(); j++){
if(net.outArc(t, j) > 0){
exclude &= !places.test(j);
}
}
if(exclude)
return false;
}
}
return true;
}
int StateConstraints::fireVectorSize(const PetriNet& net,
const MarkVal* m0,
const VarVal*) const{
assert(nPlaces == net.numberOfPlaces());
assert(nVars == net.numberOfVariables());
// Create linary problem
lprec* lp;
lp = make_lp(0, net.numberOfTransitions()); // One variable for each entry in the firing vector
assert(lp);
if(!lp) return false;
// Set verbosity
set_verbose(lp, IMPORTANT);
// Set transition names (not strictly needed)
for(size_t i = 0; i < net.numberOfTransitions(); i++)
set_col_name(lp, i+1, const_cast<char*>(net.transitionNames()[i].c_str()));
// Start adding rows
set_add_rowmode(lp, TRUE);
REAL row[net.numberOfTransitions() + 1];
for(size_t p = 0; p < nPlaces; p++){
// Set row zero
memset(row, 0, sizeof(REAL) * net.numberOfTransitions() + 1);
for(size_t t = 0; t < net.numberOfTransitions(); t++){
int d = net.outArc(t, p) - net.inArc(p, t);
row[1+t] = d;
}
if(pcs[p].min == pcs[p].max &&
pcs[p].max != CONSTRAINT_INFTY){
double target = pcs[p].min - m0[p];
add_constraint(lp, row, EQ, target);
}else{
// There's always a min, even zero is interesting
double target = pcs[p].min - m0[p];
add_constraint(lp, row, GE, target);
if(pcs[p].max != CONSTRAINT_INFTY){
double target = pcs[p].max - m0[p];
add_constraint(lp, row, LE, target);
}
}
}
// Finished adding rows
set_add_rowmode(lp, FALSE);
// Create objective
memset(row, 0, sizeof(REAL) * net.numberOfTransitions() + 1);
for(size_t t = 0; t < net.numberOfTransitions(); t++)
row[1+t] = 1; // The sum the components in the firing vector
// Set objective
set_obj_fn(lp, row);
// Minimize the objective
set_minim(lp);
// Set variables as integer variables
for(size_t i = 0; i < net.numberOfTransitions(); i++)
set_int(lp, 1+i, TRUE);
// Attempt to solve the problem
int result = solve(lp);
// Limit on traps to test
size_t traplimit = nPlaces * OVER_APPROX_TRAP_FACTOR;
// Try to add a minimal trap constraint
while((result == OPTIMAL) && traplimit-- < 0){
memset(row, 0, sizeof(REAL) * net.numberOfTransitions() + 1);
// Get the firing vector
get_variables(lp, row);
// Compute the resulting marking
MarkVal rMark[net.numberOfPlaces()];
for(size_t p = 0; p < nPlaces; p++){
rMark[p] = m0[p];
for(size_t t = 0; t < net.numberOfTransitions(); t++)
rMark[p] += (net.outArc(t, p) - net.inArc(p, t)) * (int)row[t];
}
// Find an M-trap
BitField trap(minimalTrap(net, m0, rMark));
//Break if there's no trap
if(trap.none()) break;
// Compute the new equation
for(size_t t = 0; t < net.numberOfTransitions(); t++){
row[1+t] = 0;
for(size_t p = 0; p < nPlaces; p++)
if(trap.test(p))
row[1+t] += net.outArc(t, p) - net.inArc(p, t);
}
// Add a new row with target as greater than equal to 1
set_add_rowmode(lp, TRUE);
add_constraint(lp, row, GE, 1);
set_add_rowmode(lp, FALSE);
// Attempt to solve the again
result = solve(lp);
}
int retval = 0;
if(result != INFEASIBLE){
get_variables(lp, row);
for(size_t t = 0; t < net.numberOfTransitions(); t++)
retval += (int)row[t];
}
// Delete the linear problem
delete_lp(lp);
lp = NULL;
// Return true, if it was infeasible
return retval;
}