def do_iteration(self) -> bool:
"""
Do one iteration.
:return: False if the current iteration failed, else True.
"""
logger.info(f"Iteration {self.iteration}")
done = self._reset_and_check_if_done()
if done:
return True
(
chosen_candidate_node,
biggest_multiset,
) = self.compute_multisets_and_get_biggest()
if sum(biggest_multiset.values()) == 0:
logger.info("Biggest multiset has cardinality 0, done")
return True
non_distinct_vertices = self._compute_non_distinct_vertices(
chosen_candidate_node)
self._add_new_state_or_edge(chosen_candidate_node,
non_distinct_vertices)
# end of iteration
self.iteration += 1
done = self.iteration >= self.iteration_upper_bound
return done
def _compute_N(params: PalmerParams, m0: int):
"""Compute N."""
eps = params.epsilon
delta = params.delta_1
n = params.n
s = params.alphabet_size
N1 = 8 * (n ** 2) * (s ** 2) / (eps ** 2) * (log((2 ** (n * s)) * n * s / delta))
N2 = 4 * m0 * n * s / eps
N = ceil(max(N1, N2))
logger.info(f"N1 = {N1}, N2 = {N2}. Chosen: {N}")
return N
def learn_pdfa(**kwargs) -> PDFA:
"""
PAC-learn a PDFA.
This is a wrapper function to the 'Learner' class, defined below.
:param kwargs: the keyword arguments of the algorithm (see the BalleParams class).
:return: the learnt PDFA.
"""
params = BalleParams(**kwargs)
logger.info(f"Parameters: {pprint.pformat(str(params))}")
automaton = Learner(params).learn()
return automaton
def _sample_and_update(self):
"""Do the sampling."""
logger.info("Generating the sample.")
if self.params.sample_generator:
generator = self.params.sample_generator
samples = generator.sample(n=self.params.nb_samples)
samples = list(map(lambda x: tuple(x), samples))
else:
samples = self.params.dataset
self.average_trace_length = sum(map(len, samples)) / len(samples)
logger.info(f"Average trace length: {self.average_trace_length}.")
logger.info("Populate root multiset.")
self.main_multiset.update(samples)
def learn_pdfa(**kwargs):
"""
PAC-learn a PDFA.
:param kwargs: the keyword arguments of the algorithm (see the PalmerParams class).
:return: the learnt PDFA.
"""
params = PalmerParams(**kwargs)
logger.info(f"Parameters: {pprint.pformat(str(params))}")
vertices, transitions = learn_subgraph(params)
logger.info(f"Number of vertices: {len(vertices)}.")
logger.info(f"Transitions: {pprint.pformat(transitions)}.")
pdfa = learn_probabilities((vertices, transitions), params)
return pdfa
def learn_probabilities(graph: Tuple[Set[int], Dict[int, Dict[int, int]]],
params: PalmerParams) -> PDFA:
"""
Learn the probabilities of the PDFA.
:param graph: the learned subgraph of the true PDFA.
:param params: the parameters of the algorithms.
:return: the PDFA.
"""
logger.info("Start learning probabilities.")
vertices, transitions = graph
initial_state = 0
N = _sample_size(params)
logger.info(f"Sample size: {N}.")
N = min(N, params.n2_max_debug if params.n2_max_debug else N)
logger.info(f"Using N = {N}.")
generator = params.sample_generator
sample = generator.sample(N)
n_observations: Counter = Counter()
for word in sample:
current_state = initial_state
for character in word:
# update statistics
n_observations.update([(current_state, character)])
# compute next state
next_state: Optional[int] = transitions.get(current_state,
{}).get(character)
if next_state is None:
break # pragma: no cover
current_state = next_state
gammas: Dict[int, Dict[int, float]] = {}
# compute number of times q is visited
q_visits: Counter = Counter()
for (q, _), counts in n_observations.items():
q_visits[q] += counts
# compute mean
for (q, sigma), counts in n_observations.items():
gammas.setdefault(q, {})[sigma] = counts / q_visits[q]
# rescale probabilities
for _, out_probabilities in gammas.items():
characters, probabilities = zip(*list(out_probabilities.items()))
probability_sum = math.fsum(probabilities)
new_probabilities = [p / probability_sum for p in probabilities]
out_probabilities.update(dict(zip(characters, new_probabilities)))
# compute transition function for the PDFA
transition_dict: TransitionFunctionDict = {}
for q, out_transitions in transitions.items():
transition_dict.setdefault(q, {})
for sigma, q_prime in out_transitions.items():
prob = gammas.get(q, {}).get(sigma, 0.0)
transition_dict[q][sigma] = (q_prime, prob)
logger.info(f"Computed vertices: {pprint.pformat(vertices)}")
logger.info(
f"Computed transition dictionary: {pprint.pformat(transition_dict)}")
return PDFA(len(vertices), params.alphabet_size, transition_dict)
def learn_subgraph( # noqa: ignore
params: PalmerParams,
) -> Tuple[Set[int], Dict[int, Dict[Character, int]]]:
"""
Learn a subgraph of the true PDFA.
:param params: the parameters of the algorithms.
:return: the graph
"""
# unpack parameters
generator = params.sample_generator
mu = params.mu
# initialize variables
initial_state = 0
vertices = {initial_state}
transitions: Dict[int, Dict[Character, int]] = {}
alphabet = set(range(params.alphabet_size))
vertex2multiset: Dict[int, Counter] = {}
m0 = _compute_m0(params)
N = _compute_N(params, m0)
logger.info(f"m0 = {m0}")
logger.info(f"N = {N}")
m0 = min(m0, params.m0_max_debug if params.m0_max_debug else m0)
N = min(N, params.n1_max_debug if params.n1_max_debug else N)
logger.info(f"using m0 = {m0}, N = {N}")
samples = generator.sample(n=N)
logger.info("Sampling done.")
logger.info(f"Number of samples: {len(samples)}.")
logger.info(f"Avg. length of samples: {sum(map(len, samples))/len(samples)}.")
# multiset for initial state is the entire sample
vertex2multiset[initial_state] = _compute_first_multiset(samples)
done = False
iteration = 0
while not done:
logger.info(f"Iteration {iteration}")
candidate_nodes_by_transitions: Dict[Tuple[State, Character], int] = {}
candidate_nodes_to_transitions: Dict[int, Tuple[State, Character]] = {}
multisets: Dict[int, Counter] = {}
for v in vertices:
for c in alphabet:
if transitions.get(v, {}).get(c) is None: # if transition undefined
transition = (v, c)
new_candidate = len(vertices) + len(candidate_nodes_to_transitions)
candidate_nodes_to_transitions[new_candidate] = transition
candidate_nodes_by_transitions[transition] = new_candidate
multisets[new_candidate] = Counter()
for s in samples:
# s is always non-empty
for i in range(len(s)):
r, sigma, t = s[:i], s[i], s[i + 1 :]
q = extended_transition_fun(transitions, r)
if q is None:
continue
transition = (q, sigma)
if transition in candidate_nodes_by_transitions:
candidate_node = candidate_nodes_by_transitions[transition]
multisets[candidate_node].update([tuple(t)])
chosen_candidate_node, biggest_multiset = max(
multisets.items(), key=lambda x: sum(x[1].values())
)
cardinality = sum(biggest_multiset.values())
if cardinality >= m0:
# check if there is a similar vertex
similar_vertex: Optional[int] = None
for v in vertices:
vertex_multiset = vertex2multiset[v]
norm = l_infty_norm(biggest_multiset, vertex_multiset)
if norm <= mu / 2.0:
similar_vertex = v
break
if similar_vertex is not None:
transition = candidate_nodes_to_transitions[chosen_candidate_node]
u, sigma = transition
transitions.setdefault(u, {})[sigma] = similar_vertex
else:
new_node = len(vertices)
vertices.add(new_node)
vertex2multiset[new_node] = biggest_multiset
transition = candidate_nodes_to_transitions.pop(chosen_candidate_node)
_tmp = candidate_nodes_by_transitions.pop(transition)
assert chosen_candidate_node == _tmp
u, sigma = transition
transitions.setdefault(u, {})[sigma] = new_node
if cardinality < m0:
done = True
iteration += 1
# complete subgraph
final_node = FINAL_STATE
for vertex in vertices:
transitions.setdefault(vertex, {})[FINAL_SYMBOL] = final_node
logger.info(f"Vertices: {pprint.pformat(vertices)}")
logger.info(f"Transitions: {pprint.pformat(transitions)}")
logger.info(f"Computed final node: {final_node} (no outgoing transitions)")
return vertices, transitions
