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 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 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)