public static function postprocessDefinition(&$machine_def)
{
if (!isset($machine_def['bpmn_fragments'])) {
return;
}
$bpmn_fragments = $machine_def['bpmn_fragments'];
unset($machine_def['bpmn_fragments']);
$states = [];
$actions = [];
// Each included BPMN file provided one fragment
foreach ($bpmn_fragments as $fragment_file => $fragment) {
$primary_process_id = $fragment['process_id'];
$state_machine_participant_id = $fragment['state_machine_participant_id'];
$prefix = "bpmn_" . (0xffff & crc32($fragment_file)) . '_';
$diagram = "\tsubgraph cluster_{$prefix} {\n\t\tlabel= \"BPMN:\\n" . basename($fragment_file) . "\"; color=\"#5373B4\";\n\n";
// Calculate neighbour nodes
$next_node = [];
foreach ($fragment['arrows'] as $id => $a) {
if ($a['type'] == 'sequenceFlow') {
$next_node[$a['source']][] = $a['target'];
}
}
// Collect start nodes
$start_nodes = [];
$end_nodes = [];
foreach ($fragment['nodes'] as $id => $n) {
if ($n['type'] == 'startEvent') {
$start_nodes[] = $id;
$fragment['nodes'][$id]['_distance'] = 0;
} else {
// Mark all other nodes as unreachable (but define the distance)
$fragment['nodes'][$id]['_distance'] = null;
}
}
// Calculate distance of each node from nearest start event to detect backward arrows (DFS)
$queue = $start_nodes;
while (!empty($queue)) {
$id = array_pop($queue);
$distance = $fragment['nodes'][$id]['_distance'] + 1;
if (isset($next_node[$id])) {
foreach ($next_node[$id] as $next_id) {
$n = $fragment['nodes'][$next_id];
if (!isset($n['_distance'])) {
$fragment['nodes'][$next_id]['_distance'] = $distance;
$queue[] = $next_id;
}
}
}
}
/*
* State machine synthesis
*/
// Find nodes connected to state machine participant
$state_machine_participant_id = $fragment['state_machine_participant_id'];
$invoking_actions = [];
$receiving_nodes = [];
$starting_nodes = [];
$ending_nodes = [];
foreach ($fragment['arrows'] as $a_id => $a) {
if ($a['target'] == $state_machine_participant_id) {
$invoking_actions[$a['source']] = $a;
//$fragment['nodes'][$a['source']];
}
if ($a['source'] == $state_machine_participant_id) {
$receiving_nodes[$a['target']] = $fragment['nodes'][$a['target']];
}
}
// Find start & end nodes
foreach ($fragment['nodes'] as $n_id => $n) {
if ($n['type'] == 'startEvent') {
$starting_nodes[$n_id] = $n;
} else {
if ($n['type'] == 'endEvent') {
$ending_nodes[$n_id] = $n;
}
}
}
// Find receiving nodes for each invoking node
// (DFS to next task, the receiver cannot be further than that)
$inv_rc_nodes = [];
foreach ($invoking_actions as $in_id => $invoking_action) {
$queue = [$in_id];
$inv_rc_nodes[$in_id] = [];
$in = $fragment['nodes'][$in_id];
$cur_process = $in['process'];
while (!empty($queue)) {
$id = array_pop($queue);
if (isset($next_node[$id])) {
foreach ($next_node[$id] as $next_id) {
$n = $fragment['nodes'][$next_id];
if ($n['process'] != $cur_process || isset($invoking_actions[$next_id])) {
// The receiving node must be within the same process and it must not be invoking node.
continue;
}
if (isset($receiving_nodes[$next_id])) {
$inv_rc_nodes[$in_id][$next_id] = $n;
} else {
if (!isset($seen[$next_id])) {
$queue[] = $next_id;
$seen[$next_id] = true;
}
}
}
}
}
if (empty($inv_rc_nodes[$in_id])) {
$inv_rc_nodes[$in_id][$in_id] = $in;
$receiving_nodes[$in_id] = $in;
}
}
// Find connections to next transition invocations
$sm_next_node = [];
$seen = [];
foreach (array_merge($starting_nodes, $receiving_nodes) as $in_id => $in) {
$queue = [$in_id];
while (!empty($queue)) {
$id = array_pop($queue);
if (isset($next_node[$id])) {
foreach ($next_node[$id] as $next_id) {
if (isset($invoking_actions[$next_id]) || isset($receiving_nodes[$next_id]) || isset($ending_nodes[$next_id])) {
$sm_next_node[$in_id][] = $next_id;
} else {
if (!isset($seen[$next_id])) {
$queue[] = $next_id;
$seen[$next_id] = true;
}
}
}
}
}
}
$action_no = 1;
$eq_states = [];
$eq_start_states = [];
$eq_end_states = [];
// Add initial states
foreach ($starting_nodes as $s_id => $s_n) {
$q = 'Qs_' . $s_id;
$states[$q] = [];
// Connect to initial state (for now)
$eq_start_states[] = $q;
}
// Build isolated fragments of the state machine (blue arrows; invoking--receiving groups)
// Part 1/2: States
foreach ($invoking_actions as $in_id => $in_a) {
$qi = 'Qi_' . $in_id;
$states[$qi] = [];
foreach ($inv_rc_nodes[$in_id] as $rcv_id => $rcv_n) {
$qr = 'Qr_' . $rcv_id;
$states[$qr] = [];
}
}
// Add final states
foreach ($ending_nodes as $e_id => $e_n) {
$q = 'Qe_' . $e_id;
$states[$q] = [];
// Connect to initial state
$eq_end_states[] = $q;
}
// Connect fragments of the state machine (green arrows)
foreach ($sm_next_node as $src => $dst_list) {
$qr = isset($starting_nodes[$src]) ? 'Qs_' . $src : 'Qr_' . $src;
foreach ($dst_list as $dst) {
$qi = isset($ending_nodes[$dst]) ? 'Qe_' . $dst : 'Qi_' . $dst;
$eq_states[$qr][] = $qi;
}
}
// Build replacement table
$uf = new UnionFind();
$uf->add('');
foreach ($states as $s_id => $s) {
$uf->add($s_id);
}
foreach ($starting_nodes as $s_id => $s_n) {
$uf->union('', 'Qs_' . $s_id);
}
foreach ($eq_states as $src => $dst_list) {
foreach ($dst_list as $dst) {
$uf->union($src, $dst);
}
}
foreach ($ending_nodes as $e_id => $e_n) {
$uf->union('', 'Qe_' . $e_id);
}
$state_replace = $uf->findAll();
/*
echo "<pre>";
foreach ($state_replace as $src => $dst) {
if ($src == $dst) {
echo "<span style=\"color:grey\">$src == $dst</span>\n";
} else {
echo "$src == $dst\n";
}
}
echo "</pre>";
// */
// Build isolated fragments of the state machine (blue arrows; invoking--receiving groups)
// Part 2/2: Actions
foreach ($invoking_actions as $in_id => $in_a) {
$qi = 'Qi_' . $in_id;
foreach ($inv_rc_nodes[$in_id] as $rcv_id => $rcv_n) {
$qr = 'Qr_' . $rcv_id;
$inv_a = $invoking_actions[$in_id];
$a = $inv_a['name'] ?: 'A' . $action_no++;
$qir = $state_replace[$qi];
$qrr = $state_replace[$qr];
$actions[$a]['transitions'][$qir]['targets'][] = $qrr;
}
}
// Remove merged states
foreach ($state_replace as $src => $dst) {
if ($src !== $dst) {
unset($states[$src]);
}
}
/*
* Render
*/
// Draw arrows
foreach ($fragment['arrows'] as $id => $a) {
$source = AbstractMachine::exportDotIdentifier($a['source'], $prefix);
$target = AbstractMachine::exportDotIdentifier($a['target'], $prefix);
$backwards = $fragment['nodes'][$a['source']]['_distance'] >= $fragment['nodes'][$a['target']]['_distance'] && $fragment['nodes'][$a['target']]['_distance'];
$diagram .= "\t\t" . $source . ' -> ' . $target . ' [tooltip="' . addcslashes($a['id'], '"') . '"';
$diagram .= ",label=\"" . addcslashes($a['name'], '"') . "\"";
if ($backwards) {
$diagram .= ',constraint=0';
}
switch ($a['type']) {
case 'sequenceFlow':
$diagram .= 'style=solid,color="#666666"';
$w = $backwards ? 3 : 5;
break;
case 'messageFlow':
$diagram .= 'style=dashed,color="#666666",arrowhead=empty,arrowtail=odot';
$w = 0;
break;
default:
$diagram .= 'color=red';
break;
}
if ($primary_process_id && $a['process'] == $primary_process_id) {
$diagram .= ',color="#44aa44",penwidth=1.5';
}
$diagram .= ",weight={$w}];\n";
$nodes[$source] = $a['source'];
$nodes[$target] = $a['target'];
}
$diagram .= "\n";
// Draw nodes
foreach ($fragment['nodes'] as $id => $n) {
$graph_id = AbstractMachine::exportDotIdentifier($id, $prefix);
$diagram .= "\t\t" . $graph_id . " [tooltip=\"" . addcslashes($n['id'], '"') . "\"";
switch ($n['type']) {
case 'startEvent':
case 'endEvent':
case 'intermediateCatchEvent':
case 'intermediateThrowEvent':
//$diagram .= ",xlabel=\"".addcslashes($n['name'], '"')."\"";
break;
default:
$diagram .= ",label=\"" . addcslashes($n['name'], '"') . "\"";
break;
}
switch ($n['type']) {
case 'participant':
$diagram .= ',shape=box,style=filled,fillcolor="#ffffff",penwidth=2';
break;
case 'startEvent':
$diagram .= ',shape=circle,width=0.4,height=0.4,label="",root=1';
break;
case 'intermediateCatchEvent':
$diagram .= ',shape=doublecircle,width=0.35,label=""';
break;
case 'intermediateThrowEvent':
$diagram .= ',shape=doublecircle,width=0.35,label=""';
break;
case 'endEvent':
$diagram .= ',shape=circle,width=0.4,height=0.4,penwidth=3,label=""';
break;
case 'exclusiveGateway':
$diagram .= ',shape=diamond,style=filled,height=0.5,width=0.5,label="X"';
break;
case 'parallelGateway':
$diagram .= ',shape=diamond,style=filled,height=0.5,width=0.5,label="+"';
break;
case 'inclusiveGateway':
$diagram .= ',shape=diamond,style=filled,height=0.5,width=0.5,label="O"';
break;
case 'complexGateway':
$diagram .= ',shape=diamond,style=filled,height=0.5,width=0.5,label="*"';
break;
case 'eventBasedGateway':
$diagram .= ',shape=diamond,style=filled,height=0.5,width=0.5,label="E"';
break;
}
// Algorithm-specific nodes
if ($primary_process_id && $n['process'] == $primary_process_id || $state_machine_participant_id && $n['id'] == $state_machine_participant_id) {
$diagram .= ',color="#44aa44",fillcolor="#eeffdd"';
}
if (isset($starting_nodes[$id]) || isset($ending_nodes[$id])) {
$diagram .= ',fillcolor="#ffccaa"';
}
// Receiving/invoking background
if (isset($invoking_actions[$id]) && isset($receiving_nodes[$id])) {
$diagram .= ',fillcolor="#ffff88;0.5:#aaddff",gradientangle=270';
} else {
if (isset($invoking_actions[$id])) {
$diagram .= ',fillcolor="#ffff88"';
} else {
if (isset($receiving_nodes[$id])) {
$diagram .= ',fillcolor="#aaddff"';
}
}
}
$diagram .= "];\n";
}
// Draw groups
foreach ($fragment['groups'] as $id => $g) {
$graph_id = AbstractMachine::exportDotIdentifier($id, $prefix);
$diagram .= "\n\t\tsubgraph cluster_{$graph_id} {\n\t\t\tlabel= \"" . basename($g['name']) . "\"; color=\"#aaaaaa\";\n\n";
foreach ($g['nodes'] as $n_id) {
$graph_n_id = AbstractMachine::exportDotIdentifier($n_id, $prefix);
$diagram .= "\t\t\t" . $graph_n_id . ";\n";
}
$diagram .= "\t\t}\n";
}
//-------------------------------------------
// Draw $sm_next_node
foreach ($sm_next_node as $src => $dst_list) {
foreach ($dst_list as $dst) {
$source = AbstractMachine::exportDotIdentifier($src, $prefix);
$target = AbstractMachine::exportDotIdentifier($dst, $prefix);
$diagram .= "\t\t" . $source . ' -> ' . $target . ' [constraint=0,splines=line,penwidth=5,color="#88dd6688"' . "]\n";
}
}
// Draw $inv_rc_nodes
foreach ($inv_rc_nodes as $src => $dst_list) {
foreach ($dst_list as $dst_node) {
$dst = $dst_node['id'];
$source = AbstractMachine::exportDotIdentifier($src, $prefix);
$target = AbstractMachine::exportDotIdentifier($dst, $prefix);
$diagram .= "\t\t" . $source . ' -> ' . $target . ' [constraint=0,splines=line,penwidth=5,color="#66aaff88"' . "]\n";
}
}
// Draw $eq_states
/*
foreach ($eq_start_states as $q) {
$actions['=']['transitions']['']['targets'][] = $q;
$actions['=']['transitions']['']['color'] = '#88dd66';
}
foreach ($eq_states as $src => $dst_list) {
foreach($dst_list as $dst) {
$actions['=']['transitions'][$src]['targets'][] = $dst;
$actions['=']['transitions'][$src]['color'] = '#88dd66';
}
}
foreach ($eq_end_states as $q) {
$actions['=']['transitions'][$q]['targets'][] = '';
$actions['=']['transitions'][$q]['color'] = '#88dd66';
}
// */
//-------------------------------------------
// Walk from each task to next tasks, collecting state machine actions
$paths = [];
foreach ($fragment['nodes'] as $n_id => $n) {
// If node is task and it is from the primary process
if (($n['type'] == 'task' || $n['type'] == 'startEvent' || $n['type'] == 'endEvent') && $n['process'] == $primary_process_id) {
// Add task to paths, so we know about all tasks
if (!isset($paths[$n_id])) {
$paths[$n_id] = [];
}
// Find all next tasks (DFS limited to non-task nodes)
$queue = [$n_id];
$visited = [$n_id => true];
while (!empty($queue)) {
$id = array_pop($queue);
if (isset($next_node[$id])) {
foreach ($next_node[$id] as $next_id) {
$next_n = $fragment['nodes'][$next_id];
if ($next_n['process'] == $primary_process_id) {
if ($next_n['type'] == 'task' || $next_n['type'] == 'endEvent') {
$paths[$n_id][] = $next_id;
} else {
if (empty($visited[$next_id])) {
$visited[$next_id] = true;
$queue[] = $next_id;
}
}
}
}
}
}
}
}
// To invoke an action, we have to be in a state, so lets add a state in front of each action
$preceding_states = [];
foreach ($paths as $src => $dst_list) {
$n = $fragment['nodes'][$src];
if ($n['type'] == 'task') {
$preceding_states[$src] = 'before_' . $n['name'];
}
if ($n['type'] == 'endEvent') {
$preceding_states[$src] = '';
}
}
// But if there is path between start event and action,
// then action's preceding state is the start event.
foreach ($paths as $src => $dst_list) {
$n = $fragment['nodes'][$src];
if ($n['type'] == 'startEvent') {
foreach ($dst_list as $dst) {
$preceding_states[$dst] = '';
}
}
}
// Register preceding states
foreach ($preceding_states as $s) {
if ($s != '') {
$states[$s] = [];
}
}
// So the actions start in the newly assigned states...
foreach ($paths as $src => $dst_list) {
if (!isset($preceding_states[$src])) {
continue;
}
$src_state = $preceding_states[$src];
$src_n = $fragment['nodes'][$src];
$action_name = $src_n['name'];
foreach ($dst_list as $dst) {
$dst_state = $preceding_states[$dst];
$actions[$action_name]['transitions'][$src_state]['targets'][] = $dst_state;
}
}
//var_dump($actions);
// Draw found paths
$diagram .= "\tsubgraph cluster_" . $prefix . "_sm {\n\t\tlabel= \"Action paths\"; color=\"#44aa44\"; fillcolor=\"#ffffee\"; style=filled;\n\n";
foreach ($paths as $src => $dst_list) {
// Draw the action
$n = $fragment['nodes'][$src];
$graph_src = AbstractMachine::exportDotIdentifier($src, $prefix . '_action');
$diagram .= $graph_src . "[label=\"" . addcslashes($n['name'], '"') . "\"];\n";
// Draw all follow-up actions
foreach ($dst_list as $dst) {
$source = AbstractMachine::exportDotIdentifier($src, $prefix . '_action');
$target = AbstractMachine::exportDotIdentifier($dst, $prefix . '_action');
$diagram .= "\t\t" . $source . ' -> ' . $target . ";\n";
}
}
$diagram .= "\t}\n";
//echo "<pre>", $diagram, "</pre>";
$diagram .= "\t}\n";
// Add BPMN diagram to state diagram
$machine_def['state_diagram_extras'][] = $diagram;
}
// Update the definition
$machine_def = array_replace_recursive(['states' => $states, 'actions' => $actions], $machine_def);
}
private $id;
public function __construct($numberOfElements)
{
for ($i = 0; $i < $numberOfElements; $i++) {
$this->id[$i] = $i;
}
}
private function root($id)
{
while ($id != $this->id[$id]) {
$id = $this->id[$id];
}
return $id;
}
public function connected($a, $b)
{
return $this->root($a) == $this->root($b);
}
public function union($a, $b)
{
$a = $this->root($a);
$b = $this->root($b);
$this->id[$a] = $b;
}
}
$uf = new UnionFind(10);
$uf->union(0, 1);
$uf->union(2, 3);
$uf->union(5, 1);
$resp = $uf->connected(0, 5);
var_dump($resp);