def construct_tree(net, initial_marking):
"""
Construct a restricted coverability marking.
For more information, see the thesis "Verification of WF-nets", 4.3.
:param net:
:param initial_marking:
:return:
"""
initial_marking = helper.convert_marking(net, initial_marking)
firing_dict = helper.split_incidence_matrix(
helper.compute_incidence_matrix(net), net)
req_dict = helper.compute_firing_requirement(net)
look_up_indices = {}
j = 0
coverability_graph = nx.DiGraph()
coverability_graph.add_node(j, marking=initial_marking)
look_up_indices[np.array2string(initial_marking)] = j
j += 1
new_arc = True
while new_arc:
new_arc = False
nodes = list(coverability_graph.nodes).copy()
while len(nodes) > 0:
m = nodes.pop()
if not np.inf in coverability_graph.nodes[m]['marking']:
possible_markings = helper.enabled_markings(
firing_dict, req_dict,
coverability_graph.nodes[m]['marking'])
m2 = None
if len(possible_markings) > 0:
for marking in possible_markings:
# check for m1 + since we want to construct a tree, we do not want that a marking is already in a graph since it is going to have an arc
if np.array2string(marking[0]) not in look_up_indices:
if check_if_transition_unique(
m, coverability_graph, marking[1]):
m2 = marking
new_arc = True
break
if new_arc:
break
if new_arc:
m3 = np.zeros(len(list(net.places)))
for place in list(net.places):
if check_for_smaller_marking(m2, coverability_graph,
list(net.places).index(place), m,
look_up_indices):
m3[list(net.places).index(place)] = np.inf
else:
m3[list(net.places).index(place)] = m2[0][list(
net.places).index(place)]
coverability_graph.add_node(j, marking=m3)
coverability_graph.add_edge(m, j, transition=m2[1])
look_up_indices[np.array2string(m3)] = j
j += 1
return coverability_graph
def compute_non_live_sequences(woflan_object):
"""
We want to compute the sequences of transitions which lead to deadlocks.
To do this, we first compute a reachbility graph (possible, since we know that the Petri Net is bounded) and then we
convert it to a spanning tree. Afterwards, we compute the paths which lead to nodes from which the final marking cannot
be reached. Note: We are searching for the shortest sequence. After the first red node, all successors are also red.
Therefore, we do not have to consider them.
:param woflan_object: Object that contains the necessary information
:return: List of sequence of transitions, each sequence is a list
"""
woflan_object.set_r_g(
reachability_graph(woflan_object.get_net(),
woflan_object.get_initial_marking()))
f_m = convert_marking(woflan_object.get_net(),
woflan_object.get_final_marking())
sucessfull_terminate_state = None
for node in woflan_object.get_r_g().nodes:
if all(np.equal(woflan_object.get_r_g().nodes[node]['marking'], f_m)):
sucessfull_terminate_state = node
break
# red nodes are those from which the final marking is not reachable
red_nodes = []
for node in woflan_object.get_r_g().nodes:
if not nx.has_path(woflan_object.get_r_g(), node,
sucessfull_terminate_state):
red_nodes.append(node)
# Compute directed spanning tree
spanning_tree = nx.algorithms.tree.Edmonds(
woflan_object.get_r_g()).find_optimum()
queue = set()
paths = {}
# root node
queue.add(0)
paths[0] = []
processed_nodes = set()
red_paths = []
while len(queue) > 0:
v = queue.pop()
for node in spanning_tree.neighbors(v):
if node not in paths and node not in processed_nodes:
paths[node] = paths[v].copy()
# we can use directly 0 here, since we are working on a spanning tree and there should be no more edges to a node
paths[node].append(woflan_object.get_r_g().get_edge_data(
v, node)[0]['transition'])
if node not in red_nodes:
queue.add(node)
else:
red_paths.append(paths[node])
processed_nodes.add(v)
return red_paths
def apply(net, initial_marking, original_net=None):
"""
Method that computes a reachability graph as networkx object
:param net: Petri Net
:param initial_marking: Initial Marking of the Petri Net
:param original_net: Petri Net without short-circuited transition
:return: Networkx Graph that represents the reachability graph of the Petri Net
"""
initial_marking = helper.convert_marking(net, initial_marking,
original_net)
firing_dict = helper.split_incidence_matrix(
helper.compute_incidence_matrix(net), net)
req_dict = helper.compute_firing_requirement(net)
look_up_indices = {}
j = 0
reachability_graph = nx.MultiDiGraph()
reachability_graph.add_node(j, marking=initial_marking)
working_set = set()
working_set.add(j)
look_up_indices[np.array2string(initial_marking)] = j
j += 1
while len(working_set) > 0:
m = working_set.pop()
possible_markings = helper.enabled_markings(
firing_dict, req_dict, reachability_graph.nodes[m]['marking'])
for marking in possible_markings:
if np.array2string(marking[0]) not in look_up_indices:
look_up_indices[np.array2string(marking[0])] = j
reachability_graph.add_node(j, marking=marking[0])
working_set.add(j)
reachability_graph.add_edge(m, j, transition=marking[1])
j += 1
else:
reachability_graph.add_edge(m,
look_up_indices[np.array2string(
marking[0])],
transition=marking[1])
return reachability_graph
def compute_unbounded_sequences(woflan_object):
"""
We compute the sequences which lead to an infinite amount of tokens. To do this, we compute a restricted coverability tree.
The tree works similar to the graph, despite we consider tree characteristics during the construction.
:param woflan_object: Woflan object that contains all needed information.
:return: List of unbounded sequences, each sequence is a list of transitions
"""
def check_for_markings_larger_than_final_marking(graph, f_m):
markings = []
for node in graph.nodes:
if all(np.greater_equal(graph.nodes[node]['marking'], f_m)):
markings.append(node)
return markings
woflan_object.set_restricted_coverability_tree(
restricted_coverability_tree(woflan_object.get_net(),
woflan_object.get_initial_marking()))
f_m = convert_marking(woflan_object.get_net(),
woflan_object.get_final_marking())
infinite_markings = []
for node in woflan_object.get_restricted_coverability_tree().nodes:
if np.inf in woflan_object.get_restricted_coverability_tree(
).nodes[node]['marking']:
infinite_markings.append(node)
larger_markings = check_for_markings_larger_than_final_marking(
woflan_object.get_restricted_coverability_tree(), f_m)
green_markings = []
for node in woflan_object.get_restricted_coverability_tree().nodes:
add_to_green = True
for marking in infinite_markings:
if nx.has_path(woflan_object.get_restricted_coverability_tree(),
node, marking):
add_to_green = False
for marking in larger_markings:
if nx.has_path(woflan_object.get_restricted_coverability_tree(),
node, marking):
add_to_green = False
if add_to_green:
green_markings.append(node)
red_markings = []
for node in woflan_object.get_restricted_coverability_tree().nodes:
add_to_red = True
for node_green in green_markings:
if nx.has_path(woflan_object.get_restricted_coverability_tree(),
node, node_green):
add_to_red = False
break
if add_to_red:
red_markings.append(node)
# Make the path as short as possible. If we reach a red state, we stop and do not go further in the "red zone".
queue = set()
queue.add(0)
paths = {}
paths[0] = []
paths_to_red = []
while len(queue) > 0:
v = queue.pop()
successors = woflan_object.get_restricted_coverability_tree(
).successors(v)
for suc in successors:
paths[suc] = paths[v].copy()
paths[suc].append(
woflan_object.get_restricted_coverability_tree().get_edge_data(
v, suc)['transition'])
if suc in red_markings:
paths_to_red.append(paths[suc])
else:
queue.add(suc)
return paths_to_red
def minimal_coverability_tree(net, initial_marking, original_net=None):
"""
This method computes the minimal coverability tree. It is part of a method to obtain a minial coverability graph
:param net: Petri Net
:param initial_marking: Initial Marking of the Petri Net
:param original_net: Petri Net without short-circuited transition
:return: Minimal coverability tree
"""
def check_if_marking_already_in_processed_nodes(n, processed_nodes):
for node in processed_nodes:
if np.array_equal(G.nodes[node]['marking'], G.nodes[n]['marking']):
return True
return False
def is_m_smaller_than_other(m, processed_nodes):
for node in processed_nodes:
if all(np.less_equal(m, G.nodes[node]['marking'])):
return True
return False
def is_m_greater_than_other(m, processed_nodes):
for node in processed_nodes:
if all(np.greater_equal(m, G.nodes[node]['marking'])):
return True
return False
def get_first_smaller_marking_on_path(n, m2):
path = nx.shortest_path(G, source=0, target=n)
for node in path:
if all(np.less_equal(G.nodes[node]['marking'], m2)):
return node
return None
def remove_subtree(tree, n):
bfs_tree = nx.bfs_tree(tree, n)
for edge in bfs_tree.edges:
tree.remove_edge(edge[0], edge[1])
for node in bfs_tree.nodes:
if node != n:
tree.remove_node(node)
return tree
G = nx.MultiDiGraph()
incidence_matrix = helper.compute_incidence_matrix(net)
firing_dict = helper.split_incidence_matrix(incidence_matrix, net)
req_dict = helper.compute_firing_requirement(net)
initial_mark = helper.convert_marking(net, initial_marking, original_net)
j = 0
unprocessed_nodes = set()
G.add_node(j, marking=initial_mark)
unprocessed_nodes.add(j)
j += 1
processed_nodes = set()
while len(unprocessed_nodes) > 0:
n = unprocessed_nodes.pop()
if check_if_marking_already_in_processed_nodes(n, processed_nodes):
processed_nodes.add(n)
elif is_m_smaller_than_other(G.nodes[n]['marking'], processed_nodes):
G.remove_edge(next(G.predecessors(n)), n)
G.remove_node(n)
elif is_m_greater_than_other(G.nodes[n]['marking'], processed_nodes):
m2 = G.nodes[n]['marking'].copy()
ancestor_bool = False
for ancestor in nx.ancestors(G, n):
if is_m_greater_than_other(G.nodes[n]['marking'], [ancestor]):
i = 0
while i < len(G.nodes[n]['marking']):
if G.nodes[ancestor]['marking'][i] < G.nodes[n][
'marking'][i]:
m2[i] = np.inf
i += 1
n1 = None
for ancestor in nx.ancestors(G, n):
if all(np.less_equal(G.nodes[ancestor]['marking'], m2)):
n1 = get_first_smaller_marking_on_path(n, m2)
break
if n1 != None:
ancestor_bool = True
G.nodes[n1]['marking'] = m2.copy()
subtree = nx.bfs_tree(G, n1)
for node in subtree:
if node in processed_nodes:
processed_nodes.remove(node)
if node in unprocessed_nodes:
unprocessed_nodes.remove(node)
G = remove_subtree(G, n1)
unprocessed_nodes.add(n1)
processed_nodes_copy = copy(processed_nodes)
for node in processed_nodes_copy:
if node in G.nodes:
if all(np.less_equal(G.nodes[node]['marking'], m2)):
subtree = nx.bfs_tree(G, node)
for node in subtree:
if node in processed_nodes:
processed_nodes.remove(node)
if node in unprocessed_nodes:
unprocessed_nodes.remove(node)
remove_subtree(G, node)
G.remove_node(node)
if not ancestor_bool:
unprocessed_nodes.add(n)
else:
for el in helper.enabled_markings(firing_dict, req_dict,
G.nodes[n]['marking']):
G.add_node(j, marking=el[0])
G.add_edge(n, j, transition=el[1])
unprocessed_nodes.add(j)
j += 1
processed_nodes.add(n)
return (G, firing_dict, req_dict)