/* dfa_patterns_optimize_variations() tries to reduce the size of DFA by
* altering pattern variations (in fact, transformations). The algorithm
* is to change several patterns' variations and if this happens to give
* size reduction, to keep the change, otherwise, revert.
*
* This function contains many heuristically chosen values for variation
* changing probability etc. They have been chosen by observing algorithm
* effectiveness and seem to be very good.
*
* Note that we subtract 1 from the number of nodes to be consistent with
* the standard builder, which doesn't count error state.
*/
int *
dfa_patterns_optimize_variations(dfa_patterns *patterns, int iterations)
{
int k = 0;
int failed_iterations = 0;
int min_nodes_so_far;
int num_nodes_original;
int *best_variations;
double lower_limit = 2.0 / patterns->num_patterns;
double upper_limit = 6.0 / patterns->num_patterns;
double change_probability = 4.0 / patterns->num_patterns;
dfa_pattern *pattern;
best_variations = malloc(patterns->num_patterns * sizeof(*best_variations));
assert(best_variations);
for (pattern = patterns->patterns; pattern; pattern = pattern->next, k++)
best_variations[k] = pattern->current_variation;
dfa_patterns_build_graph(patterns);
num_nodes_original = patterns->graph.num_nodes;
min_nodes_so_far = num_nodes_original;
fprintf(stderr, "Original number of DFA states: %d\n", min_nodes_so_far - 1);
fprintf(stderr, "Trying to optimize in %d iterations\n", iterations);
gg_srand(num_nodes_original + patterns->num_patterns);
while (iterations--) {
int changed_variations = 0;
int k = 0;
/* Randomly change some variations. */
for (pattern = patterns->patterns; pattern; pattern = pattern->next, k++) {
if (gg_drand() < change_probability && pattern->num_variations > 1) {
int new_variation = gg_rand() % (pattern->num_variations - 1);
if (new_variation >= pattern->current_variation)
new_variation++;
pattern->current_variation = new_variation;
changed_variations++;
}
else
pattern->current_variation = best_variations[k];
}
if (changed_variations == 0) {
iterations++;
continue;
}
fprintf(stderr, ".");
dfa_patterns_build_graph(patterns);
if (patterns->graph.num_nodes < min_nodes_so_far) {
/* If the new set of variations produces smaller dfa, save it. */
int k = 0;
for (pattern = patterns->patterns; pattern; pattern = pattern->next, k++)
best_variations[k] = pattern->current_variation;
fprintf(stderr, "\nOptimized: %d => %d states (%d iterations left)\n",
min_nodes_so_far - 1, patterns->graph.num_nodes - 1, iterations);
min_nodes_so_far = patterns->graph.num_nodes;
failed_iterations = 0;
}
else
failed_iterations++;
if (failed_iterations >= 30) {
/* If haven't succeded in 30 last iterations, try to alter variation
* change probability.
*/
double delta = gg_drand() / patterns->num_patterns;
if (change_probability > upper_limit
|| (change_probability >= lower_limit && gg_rand() % 2 == 0))
delta = -delta;
change_probability += delta;
failed_iterations = 0;
}
}
fprintf(stderr, "\nTotal optimization result: %d => %d states\n",
num_nodes_original - 1, min_nodes_so_far - 1);
dfa_graph_clear(&(patterns->graph));
return best_variations;
}
int
main(int argc, char **argv)
{
static bstate states[N];
static bstate out_states[3 * N];
int num_outstates = 0;
int j;
int k;
int x, y;
double sum_p = 0.0;
double sum_squared_p = 0.0;
int num_legal_final_states;
int height;
int width;
int num_iterations = 100;
if (argc < 5) {
fprintf(stderr, "Usage: estimate_legal_stratified <height> <width> <num_samples> <seed>\n");
return 1;
}
height = atoi(argv[1]);
width = atoi(argv[2]);
num_iterations = atoi(argv[3]);
gg_srand(atoi(argv[4]));
setwidth(height);
for (j = 0; j < num_iterations; j++) {
double p = 1.0;
for (k = 0; k < N; k++)
memcpy(states[k], *startstate(), sizeof(bstate));
for (y = 0; y < width; y++)
for (x = 0; x < height; x++) {
num_outstates = 0;
for (k = 0; k < N; k++) {
bstate expanded_states[3];
int num_expanded_states;
int m;
num_expanded_states = expandstate(states[k], x, expanded_states);
for (m = 0; m < num_expanded_states; m++) {
memcpy(out_states[num_outstates++], expanded_states[m], sizeof(bstate));
}
}
p *= (double) num_outstates / (3 * N);
for (k = 0; k < N; k++)
memcpy(states[k], out_states[random_choice(num_outstates)], sizeof(bstate));
}
num_legal_final_states = 0;
for (k = 0; k < num_outstates; k++)
num_legal_final_states += finalstate(out_states[k]);
p *= (double) num_legal_final_states / num_outstates;
sum_p += p;
sum_squared_p += p * p;
if ((j + 1) % 10 == 0) {
double std = sqrt(sum_squared_p - sum_p * sum_p / (j + 1)) / j;
printf("%d %10.8lg %lg %lg\n", j + 1, sum_p / (j + 1),
std, std * sqrt(j));
}
}
printf("Estimated legal probability: %10.8lg\n", sum_p / num_iterations);
printf("Standard deviation: %lg\n",
sqrt(sum_squared_p - sum_p * sum_p / num_iterations) / num_iterations);
printf("Standard deviation per sample: %lg\n",
sqrt((sum_squared_p - sum_p * sum_p / num_iterations) / num_iterations));
return 0;
}
int main(int argc, char **argv)
{
int visited_states[NUMBER_OF_STATES];
int k;
int j;
const int N = 100;
long double size;
gg_srand(6);
for (k = 0; k < NUMBER_OF_STATES; k++) {
visited_states[k] = 0;
sum_weights[k] = 0.0;
}
for (i = 0; i < N; i++) {
for (k = 0; k < NUMBER_OF_STATES; k++)
Q[k].node = -1;
Q[NUMBER_OF_STATES - 1].node = 0;
Q[NUMBER_OF_STATES - 1].parent_stratum = -1;
Q[NUMBER_OF_STATES - 1].weight = 1.0;
for (k = NUMBER_OF_STATES - 1; k >= 0; k++) {
int r;
int state = Q[k].node;
if (state == -1)
continue;
sum_weights[k] += Q[k].weight;
for (r = k; r > 0; r = Q[r].parent_stratum) {
visited_states[Q[r].node] = 1;
}
for (s = 0; s < 2 * NUMBER_OF_POINTS; s++) {
int next_state = transformations[state][s];
if (next_state >= 0
&& !visited_states[next_state]) {
int next_stratum = compute_stratum(next_state, visited_states);
if (Q[next_stratum].node == -1) {
Q[next_stratum].node = next_state;
Q[next_stratum].parent_stratum = k;
Q[next_stratum].weight = Q[k].weight;
}
else {
Q[next_stratum].weight += Q[k].weight;
if (gg_drand() * Q[next_stratum] < Q[k].weight) {
Q[next_stratum].node = next_state;
Q[next_stratum].parent_stratum = k;
}
}
}
}
for (r = k; r > 0; r = Q[r].parent_stratum) {
visited_states[Q[r].node] = 0;
}
}
}
size = 0.0;
for (k = NUMBER_OF_STATES - 1; k >= 0; k++) {
size += Q[k].weight;
printf("%d %Lg %Lg\n", k, Q[k].weight / N, size / N);
}
printf("Estimated size: %Lg\n%Lf\n", size / N, size / N);
return 0;
}
int main(int argc, char **argv)
{
int k;
int j;
long double size = 0.0;
long double sum_size = 0.0;
long double sum_squared_size = 0.0;
int width;
int height;
struct queue_item *Qin = Q1;
struct queue_item *Qout = Q2;
struct queue_item *tmp;
int x, y;
int num_iterations = 10000;
if (argc < 5) {
fprintf(stderr, "Usage: estimate_legal_stratified <height> <width> <num_samples> <seed>\n");
return 1;
}
height = atoi(argv[1]);
width = atoi(argv[2]);
num_iterations = atoi(argv[3]);
gg_srand(atoi(argv[4]));
setwidth(height);
for (j = 0; j < num_iterations; j++) {
for (k = 0; k < MAX_NUMBER_OF_STRATA; k++)
Qin[k].weight = -1.0;
memcpy(Qin[0].node, *startstate(), sizeof(bstate));
Qin[0].weight = 1.0;
for (y = 0; y < width; y++)
for (x = 0; x < height; x++) {
for (k = 0; k <= height; k++)
Qout[k].weight = -1.0;
for (k = 0; k <= height; k++) {
bstate expanded_states[3];
int num_expanded_states;
int m;
if (Qin[k].weight == -1.0)
continue;
num_expanded_states = expandstate(Qin[k].node, x, expanded_states);
for (m = 0; m < num_expanded_states; m++) {
int next_stratum = stratify(expanded_states[m]);
if (Qout[next_stratum].weight == -1.0) {
memcpy(Qout[next_stratum].node, expanded_states[m], sizeof(bstate));
Qout[next_stratum].weight = Qin[k].weight / 3.0;
}
else {
Qout[next_stratum].weight += Qin[k].weight / 3.0;
if (gg_drand() * Qout[next_stratum].weight < Qin[k].weight / 3.0)
memcpy(Qout[next_stratum].node, expanded_states[m], sizeof(bstate));
}
}
}
tmp = Qin;
Qin = Qout;
Qout = tmp;
}
size = 0;
for (k = 0; k <= height; k++)
if (Qin[k].weight != -1.0 && finalstate(Qin[k].node))
size += Qin[k].weight;
sum_size += size;
sum_squared_size += size * size;
if ((j + 1) % 1000 == 0) {
double std = sqrt(sum_squared_size - sum_size * sum_size / (j + 1)) / j;
printf("%d %10.8Lg %lg %lg\n", j + 1, sum_size / (j + 1),
std, std * sqrt(j));
}
}
printf("Estimated legal probability: %10.8Lg\n", sum_size / num_iterations);
printf("Standard deviation: %lg\n",
sqrt(sum_squared_size - sum_size * sum_size / num_iterations) / num_iterations);
printf("Standard deviation per sample: %lg\n",
sqrt((sum_squared_size - sum_size * sum_size / num_iterations) / num_iterations));
return 0;
}
