TimeType MonaAutomataDotWalker::_constructAutomaton(ASTForm* form) {
DFA *monaAutomaton = nullptr;
try {
DFA *temp = nullptr;
size_t monaStates = 0, minimizedStates = 0;
toMonaAutomaton(form, monaAutomaton, false);
assert(monaAutomaton != nullptr);
monaStates = monaAutomaton->ns;
temp = dfaCopy(monaAutomaton);
dfaUnrestrict(temp);
monaAutomaton = dfaMinimize(temp);
minimizedStates = monaAutomaton->ns;
// Clean up
dfaFree(monaAutomaton);
monaAutomaton = nullptr;
/*dfaFree(temp);
temp = nullptr;*/
return std::make_pair(minimizedStates, monaStates);
} catch (std::exception &e) {
if(monaAutomaton != nullptr) {
dfaFree(monaAutomaton);
}
return std::make_pair(0, 0);
}
}
DFA *dfa_Prefix(DFA *M, int c1, int c2, int var, int* indices) //Output M' so that L(M')={w| w'\in \Sigma*, ww' \in L(M), c_1 <= |w|<=c_2 }
{
int i, sink;
DFA *M1 = dfaSigmaC1toC2(c1, c2, var, indices);
DFA *M2 = dfaCopy(M);
//dfaPrintVerbose(M2);
sink = find_sink(M);
for(i=0; i<M2->ns; i++){
if(i!= sink) M2->f[i]=1;
}
//dfaPrintVerbose(M2);
DFA *result = dfa_intersect(M2, M1);
//dfaPrintVerbose(result);
dfaFree(M1);
dfaFree(M2);
return dfaMinimize(result);
}//end of prefix
// Constructs a DFA for the inequation coeffs*variables+constant<0
// in two's complement arithmetic
DFA *build_DFA_ineq_2sc(int vars, int *coeffs, int constant, int *indices) {
int min, max, states, next_index, next_label, result, target, count;
long i;
unsigned long j, transitions;
struct map_ent *map;
char *statuces;
DFA *inequality, *temp;
//int write1, overbits, label1, label2, co;
int write1, label1, label2, co;
preprocess(vars, coeffs, &constant, 1);
//initialization
min = 0;
max = 0;
for (i = 0; i < vars; i++)
if (coeffs[i] > 0)
max += coeffs[i];
else
min += coeffs[i];
if (constant > max)
max = constant;
else if (constant < min)
min = constant;
states = max - min + 1;
//overbits= ceil(log(states)/log(2));
states *= 2;
//This array maps state labels (carries) to state indices
map = (struct map_ent *) malloc(states * sizeof(struct map_ent)) - min;
for (i = min; i < max + 1; i++) {
map[i].s = 0;
map[i].sr = 0;
map[i].i = -1;
map[i].ir = -1;
}
map[constant].sr = 1; //the first state to be expanded
next_index = 0; //the next available state index
next_label = constant; //the next available state label
map[constant].i = -1;
map[constant].ir = 0;
count = 0;
transitions = 1 << vars; //number of transitions from each state
//Begin building
dfaSetup(states, vars, indices);
while (next_label < max + 1) { //there is a state to expand (excuding sink)
if (map[next_label].i == count)
map[next_label].s = 2;
else
map[next_label].sr = 2;
dfaAllocExceptions(transitions);
for (j = 0; j < transitions; j++) {
co = count_ones(j, vars, coeffs);
result = next_label + co;
if (result >= 0)
target = result / 2;
else
target = (result - 1) / 2;
write1 = result & 1;
label1 = next_label;
label2 = target;
while (label1 != label2) {
label1 = label2;
result = label1 + co;
if (result >= 0)
label2 = result / 2;
else
label2 = (result - 1) / 2;
write1 = result & 1;
}
if (write1) {
if (map[target].s == 0) {
map[target].s = 1;
next_index++;
map[target].i = next_index;
}
dfaStoreException(map[target].i, bintostr(j, vars));
} else {
if (map[target].sr == 0) {
map[target].sr = 1;
next_index++;
map[target].ir = next_index;
}
dfaStoreException(map[target].ir, bintostr(j, vars));
}
}
dfaStoreState(count);
count++;
for (next_label = min; (next_label <= max) && (map[next_label].i
!= count) && (map[next_label].ir != count); next_label++)
;
//find next state to expand
}
for (i = count; i < states; i++) {
dfaAllocExceptions(0);
dfaStoreState(i);
}
//define accepting and rejecting states
statuces = (char *) malloc(states + 1);
for (i = 0; i < states; i++)
statuces[i] = '-';
for (next_label = min; next_label <= max; next_label++)
if (map[next_label].s == 2)
statuces[map[next_label].i] = '+';
statuces[states] = '\0';
temp = dfaBuild(statuces);
temp->ns -= states - count;
inequality = dfaMinimize(temp);
return inequality;
}
//Constructs a DFA for the inequation coeffs*variables+constant<0
DFA *build_DFA_ineq_new(int vars, int *coeffs, int constant, int *indices) {
int min, max, states, next_index, next_label, result, target, count;
long i, transitions;
unsigned long j;
struct map_ent *map;
char *statuces;
DFA *inequality, *temp;
preprocess(vars, coeffs, &constant, 1);
//initialization
min = 0;
max = 0;
for (i = 0; i < vars; i++)
if (coeffs[i] > 0)
max += coeffs[i];
else
min += coeffs[i];
if (constant > max)
max = constant;
else if (constant < min)
min = constant;
states = max - min + 1;
//This array maps state labels (carries) to state indices
map = (struct map_ent *) malloc(states * sizeof(struct map_ent)) - min;
for (i = min; i < max + 1; i++) {
map[i].s = 0;
map[i].i = -1;
}
map[constant].s = 1; //the first state to be expanded
next_index = 0; //the next available state index
next_label = constant; //the next available state label
map[constant].i = 0;
count = 0;
transitions = 1 << vars; //number of transitions from each state
//Begin building
dfaSetup(states + 1, vars, indices);
dfaAllocExceptions(0);
dfaStoreState(1);
//count++;
while (next_label < max + 1) { //there is a state to expand
map[next_label].s = 2;
dfaAllocExceptions(transitions);
for (j = 0; j < transitions; j++) {
result = next_label + count_ones(j, vars, coeffs);
if (result >= 0)
target = result / 2;
else
target = (result - 1) / 2;
if (map[target].s == 0) {
map[target].s = 1;
next_index++;
map[target].i = next_index;
}
dfaStoreException(map[target].i + 1, bintostr(j, vars));
}
dfaStoreState(count);
count++;
for (next_label = min; (next_label <= max) && (map[next_label].i
!= count); next_label++)
;
//find next state to expand
}
for (i = count; i <= states; i++) {
dfaAllocExceptions(0);
dfaStoreState(i);
}
//define accepting and rejecting states
statuces = (char *) malloc(states + 2);
for (i = 0; i <= count; i++)
statuces[i] = '-';
for (; i <= states; i++)
statuces[i] = '0';
for (i = min; i < 0; i++)
if (map[i].s == 2)
statuces[map[i].i + 1] = '+';
statuces[states + 1] = '\0';
temp = dfaBuild(statuces);
temp->ns -= states - count;
inequality = dfaMinimize(temp);
return inequality;
}
// Constructs a DFA for the equation coeffs*variables+constant=0
// in two's complement arithmetic
DFA *build_DFA_eq_2sc(int vars, int *coeffs, int constant, int *indices) {
int min, max, states, next_index, next_label, result, target, count;
long i;
unsigned long j, transitions;
struct map_ent *map;
char *statuces;
DFA *equality, *temp;
if (preprocess(vars, coeffs, &constant, 0))
return dfaFalse();
//initialization
min = 0;
max = 0;
for (i = 0; i < vars; i++)
if (coeffs[i] > 0)
max += coeffs[i];
else
min += coeffs[i];
if (constant > max)
max = constant;
else if (constant < min)
min = constant;
states = 2 * max - 2 * min + 3;
//This array maps state labels (carries) to state indices
map = (struct map_ent *) malloc(states * sizeof(struct map_ent)) - min;
for (i = min; i < max + 1; i++) {
map[i].s = 0;
map[i].sr = 0;
map[i].i = -1;
map[i].ir = -1;
}
map[constant].sr = 1; //the first state to be expanded
next_index = 0; //the next available state index
next_label = constant; //the next available state label
map[constant].i = -1;
map[constant].ir = 0;
count = 0;
transitions = 1 << vars; //number of transitions from each state
//Begin building
dfaSetup(states, vars, indices);
while (next_label < max + 1) { //there is a state to expand (excuding sink)
if (map[next_label].i == count)
map[next_label].s = 2;
else
map[next_label].sr = 2;
dfaAllocExceptions(transitions / 2);
for (j = 0; j < transitions; j++) {
result = next_label + count_ones(j, vars, coeffs);
if (!(result & 1)) {
target = result / 2;
if (target == next_label) {
if (map[target].s == 0) {
map[target].s = 1;
next_index++;
map[target].i = next_index;
}
dfaStoreException(map[target].i, bintostr(j, vars));
} else {
if (map[target].sr == 0) {
map[target].sr = 1;
next_index++;
map[target].ir = next_index;
}
dfaStoreException(map[target].ir, bintostr(j, vars));
}
}
}
dfaStoreState(states - 1);
count++;
for (next_label = min; (next_label <= max) && (map[next_label].i
!= count) && (map[next_label].ir != count); next_label++)
;
//find next state to expand
}
for (; count < states; count++) {
dfaAllocExceptions(0);
dfaStoreState(states - 1);
}
//define accepting and rejecting states
statuces = (char *) malloc(states + 1);
for (i = 0; i < states; i++)
statuces[i] = '-';
for (next_label = min; next_label <= max; next_label++)
if (map[next_label].s == 2)
statuces[map[next_label].i] = '+';
statuces[states] = '\0';
temp = dfaBuild(statuces);
equality = dfaMinimize(temp);
dfaFree(temp);
return equality;
}
DFA *dfaSigmaC1toC2(int c1, int c2, int var, int* indices){
int i, n;
char *statuces;
DFA *result=NULL;
if(c2<=-1){ //accept everything after c1 steps
n=c1+1;
statuces=(char *)malloc((n+1)*sizeof(char));
dfaSetup(n,var,indices);
//the 0 to c1-1 states(unaccepted)
for( i=0; i<c1; i++){
dfaAllocExceptions(0);
dfaStoreState(i+1);
statuces[i]='-';
}
//the c1 state
dfaAllocExceptions(0);
dfaStoreState(i);
statuces[i]='+'; //i==c1
statuces[n]='\0'; //n==c1+1
}else if(c1<=-1){
n=c2+2; //add one sink state
statuces=(char *)malloc((n+1)*sizeof(char));
dfaSetup(n,var,indices);
//the 0 to c2 states(accepted)
for( i=0; i<=c2; i++){
dfaAllocExceptions(0);
dfaStoreState(i+1);
statuces[i]='+';
}
//the c1 state
dfaAllocExceptions(0);
dfaStoreState(i);
statuces[i]='-'; //i==c2
statuces[n]='\0'; //n==c1+1
}else {
assert(c2>=c1);
n=c2+2; //add one sink state
statuces=(char *)malloc((n+1)*sizeof(char));
dfaSetup(n,var,indices);
//the 0 to c2 states(accepted)
for( i=0; i<=c2; i++){
dfaAllocExceptions(0);
dfaStoreState(i+1);
if(i>=c1) statuces[i]='+';
else statuces[i]='-';
}
//the c1 state
dfaAllocExceptions(0);
dfaStoreState(i);
statuces[i]='-'; //i==c2
statuces[n]='\0'; //n==c1+1
}
result=dfaBuild(statuces);
//dfaPrintVerbose(result);
free(statuces);
if(c1==0) result->f[result->s]=1;
DFA *tmp = dfaMinimize(result);
dfaFree(result);
return tmp;
}
DFA *dfa_Suffix(DFA *M, int c1, int c2, int var, int *oldindices)
{
DFA *result = NULL;
DFA *tmpM = NULL;
int aux=0;
struct int_list_type *states=NULL;
struct int_type *tmpState=NULL;
int maxCount = 0;
int *indices = oldindices; //indices is updated if you need to add auxiliary bits
paths state_paths, pp;
trace_descr tp;
int i, j, z, k;
char *exeps;
int *to_states;
long max_exeps;
char *statuces;
int len=var;
int sink;
char *auxbit=NULL;
// char *apath =bintostr(a, var);
states = reachable_states_bounded_steps(M, c1, c2);
maxCount = states->count;
if(maxCount>0){ //Need auxiliary bits when there exist some outgoing edges
aux = get_hsig(maxCount);
if(_FANG_DFA_DEBUG) printf("\n There are %d reachable states, need to add %d auxiliary bits\n", maxCount, aux);
auxbit = (char *) malloc(aux*sizeof(char));
len = var+aux; // extra aux bits
indices = allocateArbitraryIndex(len);
}
max_exeps=1<<len; //maybe exponential
sink=find_sink(M);
assert(sink >-1);
//pairs[i] is the list of all reachable states by \sharp1 \bar \sharp0 from i
dfaSetup(M->ns+1, len, indices); //add one new initial state
exeps=(char *)malloc(max_exeps*(len+1)*sizeof(char)); //plus 1 for \0 end of the string
to_states=(int *)malloc(max_exeps*sizeof(int));
statuces=(char *)malloc((M->ns+2)*sizeof(char));
//printf("Before Replace Char\n");
//dfaPrintVerbose(M);
k=0;
//setup for the initial state
tmpState = states->head;
for (z=1; z<=states->count; z++) {
state_paths = pp = make_paths(M->bddm, M->q[tmpState->value]);
while (pp) {
if(pp->to!=sink){
to_states[k]=pp->to+1; //insert itself as the initial state
for (j = 0; j < var; j++) {
//the following for loop can be avoided if the indices are in order
for (tp = pp->trace; tp && (tp->index != indices[j]); tp =tp->next);
if (tp) {
if (tp->value) exeps[k*(len+1)+j]='1';
else exeps[k*(len+1)+j]='0';
}else{
exeps[k*(len+1)+j]='X';
}
}
set_bitvalue(auxbit, aux, z); // aux = 3, z=4, auxbit 001
for (j = var; j < len; j++) { //set to xxxxxxxx100
exeps[k*(len+1)+j]=auxbit[len-j-1];
}
exeps[k*(len+1)+len]='\0';
k++;
}
pp = pp->next;
}//end while
kill_paths(state_paths);
tmpState = tmpState->next;
} //end for
dfaAllocExceptions(k);
for(k--;k>=0;k--)
dfaStoreException(to_states[k],exeps+k*(len+1));
dfaStoreState(sink+1);
if(check_accept(M, states)) statuces[0]='+';
else statuces[0]='0';
//for the rest of states (shift one state)
for (i = 0; i < M->ns; i++) {
state_paths = pp = make_paths(M->bddm, M->q[i]);
k=0;
while (pp) {
if(pp->to!=sink){
for (tp = pp->trace; tp && (tp->index != indices[var]); tp =tp->next); //find the bar value
if (!tp || !(tp->value)) {
to_states[k]=pp->to+1;
for (j = 0; j < var; j++) {
//the following for loop can be avoided if the indices are in order
for (tp = pp->trace; tp && (tp->index != indices[j]); tp =tp->next);
if (tp) {
if (tp->value) exeps[k*(len+1)+j]='1';
else exeps[k*(len+1)+j]='0';
}
else
exeps[k*(len+1)+j]='X';
}
for (j = var; j < len; j++) {
exeps[k*(len+1)+j]='0';
}
exeps[k*(len+1)+len]='\0';
k++;
}
}
pp = pp->next;
}//end while
dfaAllocExceptions(k);
for(k--;k>=0;k--)
dfaStoreException(to_states[k],exeps+k*(len+1));
dfaStoreState(sink+1);
if(M->f[i]==1)
statuces[i+1]='+';
else if(M->f[i]==-1)
statuces[i+1]='-';
else
statuces[i+1]='0';
kill_paths(state_paths);
}
statuces[M->ns+1]='\0';
result=dfaBuild(statuces);
// dfaPrintVerbose(result);
for(i=0; i<aux; i++){
j=len-i-1;
tmpM =dfaProject(result, (unsigned) j);
dfaFree(result);
result = dfaMinimize(tmpM);
dfaFree(tmpM);
// printf("\n After projecting away %d bits", j);
// dfaPrintVerbose(result);
}
free(exeps);
//printf("FREE ToState\n");
free(to_states);
//printf("FREE STATUCES\n");
free(statuces);
if(maxCount>0) free(auxbit);
free_ilt(states);
return dfaMinimize(result);
}