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 sequential_proof_rec(fd: FunctionalDependency, acc: Set[AtomValue],
q: ConjunctiveQuery, current_sp: List[Atom],
current_res: List[SequentialProof]) -> None:
"""
Recursive function used to compute sequential proofs for a given FD X -> z
:param fd: A FD of the form X -> z
:param acc: A set of Variables containing the variables implied by X with the current sequential proof
:param q: A ConjunctiveQuery
:param current_sp: Current sequential proof
:param current_res: List that will contain all the sequential proofs for X -> z
"""
if fd.right in acc:
sequential_proof = SequentialProof(fd, current_sp)
to_remove = []
for sp in current_res:
if sequential_proof.is_subset_of(sp):
to_remove.append(sp)
elif sp.is_subset_of(sequential_proof):
return None
for sp in to_remove:
current_res.remove(sp)
current_res.append(sequential_proof)
else:
for atom in [atom for atom in q.get_atoms() if atom not in current_sp]:
if set(q.get_key_vars(atom)).issubset(acc):
sequential_proof_rec(fd, acc.union(set(atom.variables())), q,
current_sp + [atom], current_res)
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 gen_m_graph(q: ConjunctiveQuery) -> nx.DiGraph:
"""
Computes the M-graph of a given ConjunctiveQuery q.
:param q: A ConjunctiveQuery
:return: Generated M-Graph
"""
atoms = q.get_atoms()
g = nx.DiGraph()
for atom1 in atoms:
g.add_node(atom1)
closure = transitive_closure(set(atom1.variables()),
q.get_consistent_fd())
for atom2 in [atom for atom in atoms if atom != atom1]:
if set(q.get_key_vars(atom2)).issubset(closure):
g.add_edge(atom1, atom2)
return g