def atom_plus(atom: Atom, q: ConjunctiveQuery) -> Set[AtomValue]:
"""
Computes the plus q set of an atom (Read report for more information)
:param atom: Atom whose plus will be computed
:param q: A ConjunctiveQuery
:return: The plus q set of variables of atom
"""
if q.is_atom_consistent(atom):
return transitive_closure(set(q.get_key_vars(atom)), q.get_all_fd())
else:
return transitive_closure(set(q.get_key_vars(atom)),
q.get_all_fd(atom))
def all_cycles_weak(attack_graph: nx.DiGraph, q: ConjunctiveQuery) -> bool:
"""
Returns True if the given Attack Graph contains no strong cycle
:param attack_graph: An Attack Graph
:param q: A ConjunctiveQuery
:return: True if attack_graph contains no strong cycle, False if not
"""
cycles = nx.algorithms.simple_cycles(attack_graph)
for cycle in cycles:
full_cycle = cycle + [cycle[0]]
for i in range(0, len(cycle)):
atom1 = full_cycle[i]
atom2 = full_cycle[i + 1]
for var in q.get_key_vars(atom2):
if var not in transitive_closure(set(q.get_key_vars(atom1)),
q.get_all_fd()):
return False
return True
def find_bad_internal_fd(
q: ConjunctiveQuery) -> FrozenSet[FunctionalDependency]:
"""
Given a non saturated ConjunctiveQuery, returns the FunctionalDependencies culprit of it's non saturation.
:param q: A ConjunctiveQuery.
:return: A FrozenSet containing the FunctionalDependencies culprit of the non saturation of q.
"""
res = frozenset()
possible_starts = []
possible_ends = []
for fd in q.get_all_fd().set:
if fd.left not in possible_starts:
possible_starts.append(fd.left)
if fd.right not in possible_ends:
possible_ends.append(fd.right)
for left in possible_starts:
for right in possible_ends:
test_fd = FunctionalDependency(left, right)
if fd_is_internal(test_fd, q):
if right not in transitive_closure(set(left),
q.get_consistent_fd()):
res = res.union(frozenset([test_fd]))
return res