def is_action(places, transitions, m0, i, m_ip, tau_it, space_between_fired):
'''
The is_action method used by is_run creates the formula of each instant. Which transition fired ?
:param places (list) :
:param transitions (list) :
:param m0 (marking) : initial marking
:param i (int) : instant in the run
:param m_ip (function) : function to get the number of the boolean variables of the markings, see variablesGenerator.
:param tau_it (function) : function to get the number of the boolean variables of the transitions, see variablesGenerator.
:return:
'''
# only one transition is true at instant i
or_formulas = []
for t in transitions:
or_formulas.append(
And([tau_it([i, transitions.index(t)])], [
tau_it([i, transitions.index(t2)])
for t2 in transitions if t != t2
], []))
formulas = [Or([], [], or_formulas)]
# if transition t fires at instant i, then we have the good marking
for t in transitions:
formulas.append(
Or([], [tau_it([i, transitions.index(t)])],
[is_transition(places, t, i, m_ip, space_between_fired)]))
return And([], [], formulas)
def initialisation_ReducedForAntiAlignment(transitions, silent_transitions, tau_it, lambda_jia, djiid, j, size_of_run,
wait_transition, max_d):
'''
Initialisation of the edit distance reduced for anti-alignmet.
This is the 3 first axioms of the _Encoding Conformance Checking Artefacts in SAT_ paper
:param transitions (list) : list of transitions
:param silent_transitions (list) : list of the silent transitions
:param tau_it (fun) : function that returns the boolean variable number of the firing transition t at an instant i
:param lambda_jia (fun) : function that returns the boolean variable number of the letter of trace j at instant i
:param djiid (fun) : function that returns the boolean variable that says at instant i and i of we have d distance
:param j (int) : jth trace
:param size_of_run (int) : maximal size of a run
:param wait_transition (transition) : to finish words
:param max_d (int): heuristic
:return: formula
'''
def t(transition):
return transitions.index(transition)
positives = []
# diid is true for d = 0
for i_m in range(0, size_of_run + 1):
for i_t in range(0, size_of_run + 1):
positives.append(djiid([j, i_m, i_t, 0]))
# diid is false for 1 1 d and d >0
negatives = [djiid([j, 0, 0, d]) for d in range(1, max_d + 1)]
formulas = []
for d in range(0, max_d):
for i_m in range(0, size_of_run):
# (i_m <> w and i_m <> tau ) <=> (d im+1 0 d+1 => d im 0 d )
condition = [tau_it([i_m + 1, t(wait_transition)])]
for st in silent_transitions:
condition.append(tau_it([i_m + 1, t(st)]))
this_condition = condition
this_condition.append(djiid([j, i_m, 0, d]))
i_t_null_and_i_m_cost = Or(this_condition, [djiid([j, i_m + 1, 0, d + 1])], [])
formulas.append(i_t_null_and_i_m_cost)
# (i_m == w or i_m == tau ) <=> (d im+1 0 d => d im 0 d )
i_t_null_and_i_m_dont_cost = Or([djiid([j, i_m, 0, d])], [djiid([j, i_m + 1, 0, d])], [
And([], condition, [])
])
formulas.append(i_t_null_and_i_m_dont_cost)
for i_t in range(0, size_of_run):
# i_t <> w <=> (d 0 it+1 d+1 => d 0 it d )
i_m_null_and_i_t_cost = Or(
[lambda_jia([j, i_t + 1, t(wait_transition)]), djiid([j, 0, i_t, d])],
[djiid([j, 0, i_t + 1, d + 1])], [])
formulas.append(i_m_null_and_i_t_cost)
# i_t == w <=> (d 0 it+1 d => d 0 it d )
i_m_null_and_i_t_dont_cost = Or([djiid([j, 0, i_t, d])],
[lambda_jia([j, i_t + 1, t(wait_transition)]),
djiid([j, 0, i_t + 1, d])], [])
formulas.append(i_m_null_and_i_t_dont_cost)
return And(positives, negatives, formulas)
def __sup_to_minimize_with_distance_function(self, artefact,
variablesFunction):
list_of_formula = []
if artefact == ANTI_ALIGNMENT:
for d in range(0, self.__max_d + 1):
list_of_d = []
for j in range(0, len(self.__traces)):
# delta_j1nnd and delta_j2nnd and ... delta_jlnnd
list_of_d.append(variablesFunction(j, d))
# not di or ( dji and dji ... dji)
not_di_or_list_of_and = Or(
[], [self.__vars.get(BOOLEAN_VAR_SUP, [d])],
[And(list_of_d, [], [])])
list_of_formula.append(not_di_or_list_of_and)
if artefact == MULTI_ALIGNMENT:
for d in range(0, self.__max_d + 1):
list_of_d = []
for j in range(0, len(self.__traces)):
# not delta_j1nnd or not delta_j2nnd or ... not delta_jlnnd
list_of_d.append(variablesFunction(j, d))
# di or ( dji or dji ... dji)
not_di_or_list_of_and = Or(
[self.__vars.get(BOOLEAN_VAR_SUP, [d])], [],
[And([], list_of_d, [])])
list_of_formula.append(not_di_or_list_of_and)
return list_of_formula
def bodyHammingDistance(transitions, silent_transitions, vars, nbTraces, size_of_run):
'''
Exact formula of hamming distance.
:param transitions (list) : the transitions
:param silent_transitions (list) : the silent transitions
:param variables (variablesGenerator) : to creates the variables numbers
:param nbTraces (int) : number of traces
:param size_of_run (int) : maximal size of run
:return: formula
'''
formulas = []
for j in range(0, nbTraces):
for i in range(1, size_of_run + 1):
for t in range(0, len(transitions)):
if transitions[t] not in silent_transitions:
create_diff = Or([],
[],
[
And([vars.get(BOOLEAN_VAR_FIRING_TRANSITION_PN, [i, t])], [], [
Or([vars.get(BOOLEAN_VAR_TRACES_ACTIONS, [j, i, t]),
vars.get(BOOLEAN_VAR_HAMMING_DISTANCE, [j, i])], [], [])
]),
And([], [vars.get(BOOLEAN_VAR_FIRING_TRANSITION_PN, [i, t]),
vars.get(BOOLEAN_VAR_TRACES_ACTIONS, [j, i, t]),
vars.get(BOOLEAN_VAR_HAMMING_DISTANCE, [j, i])], [])
])
else:
create_diff = Or([], [vars.get(BOOLEAN_VAR_FIRING_TRANSITION_PN, [i, t]),
vars.get(BOOLEAN_VAR_HAMMING_DISTANCE, [j, i])], [])
formulas.append(create_diff)
return formulas
def __getDiffTracesCentroids(self, chi_jia, diffl_ji, diffm_ji,
lambda_jia):
'''
This function that defines the difference between the traces and its centroid and calls
__maxDiffTracesCentroids().
:param chi_jia (function)
:param diff_ji (function)
:param lambda_jia (function)
:return: list of formula
'''
formulas = []
for j in range(0, len(self.__traces)):
aDiffPerInstant = []
for i in range(1, self.__size_of_run + 1):
# for each instant, a transition is true and there is or not a diff
for t in range(0, len(self.__transitions)):
# if silent transition : diffjit is false
if self.__transitions[t] in self.__silent_transititons:
indexOfWaitModel = self.__transitions.index(
self.__wait_transition_model)
indexOfWaitTrace = self.__transitions.index(
self.__wait_transition_trace)
diffjit = Or([
diffl_ji([j, i]),
lambda_jia([j, i, indexOfWaitModel]),
lambda_jia([j, i, indexOfWaitTrace])
], [chi_jia([j, i, t])], [])
# chi_jia => lambda_jia or diff_ji
elif self.__transitions[t] == self.__wait_transition_model:
diffjit = Or([diffl_ji([j, i]),
lambda_jia([j, i, t])],
[chi_jia([j, i, t])], [])
elif self.__transitions[t] == self.__wait_transition_trace:
diffjit = Or([diffm_ji([j, i])], [chi_jia([j, i, t])],
[])
else:
indexOfWaitTrace = self.__transitions.index(
self.__wait_transition_trace)
diffjit = Or([], [], [
Or([lambda_jia([j, i, t])], [chi_jia([j, i, t])], [
And([diffl_ji([j, i]),
diffm_ji([j, i])], [], [])
]),
And([
diffm_ji([j, i]),
lambda_jia([j, i, indexOfWaitTrace]),
chi_jia([j, i, t])
], [], [])
])
aDiffPerInstant.append(diffjit)
diffPerJ = And([], [], aDiffPerInstant)
formulas.append(diffPerJ)
# then there is maximal number of diff :
self.__maxDiffTracesCentroids(formulas)
return formulas
def __createSATformula(self, pn, m0, mf, max_d, max_t, traces_xes,
nbTraces):
'''
This function creates and solve the SAT formula of the clustering problem.
:param pn (Petrinet)
:param m0 (Marking)
:param mf (Marking)
:param max_d (int)
:param max_t (int)
:param traces_xes (Log)
'''
# this object creates variable numbers of the SAT formula
self.__vars = VariablesGenerator()
# formula version of data event log
log_to_PN_w_formula, self.__traces = log_to_Petri_with_w(
traces_xes,
self.__transitions,
self.__vars,
self.__size_of_run,
self.__wait_transition_trace,
self.__wait_transition_model,
label_l=BOOLEAN_VAR_TRACES_ACTIONS,
max_nbTraces=nbTraces)
# creates the boolean variables for the next formulas
self.__createBooleanVariables()
# formula of centroids
centroidsFormulasList = self.__createCentroids(m0, mf)
# formula that describes maximal distance
diffTracesCentroids = self.__getDiffTracesCentroids(
self.__vars.getFunction(BOOLEAN_VAR_CHI_TRANSITIONS),
self.__vars.getFunction(BOOLEAN_VAR_DIFF_l),
self.__vars.getFunction(BOOLEAN_VAR_DIFF_m),
self.__vars.getFunction(BOOLEAN_VAR_TRACES_ACTIONS))
# formula that create BOOLEAN_VAR_COMMON_T variables
listOfCommonTransitions = self.__commonTransitions(
self.__vars.getFunction(BOOLEAN_VAR_COMMON_T),
self.__vars.getFunction(BOOLEAN_VAR_K_CONTAINS_T))
# formula that describes that a trace belongs to at most one cluster
aClusterMax = self.__tracesInAClusterOnly(
self.__vars.getFunction(BOOLEAN_VAR_J_CLUSTERISED),
self.__vars.getFunction(BOOLEAN_VAR_J_IN_K))
# concat the formula
full_formula = And([], [], log_to_PN_w_formula +
centroidsFormulasList + diffTracesCentroids +
listOfCommonTransitions + aClusterMax)
# formula to cnf
cnf = full_formula.operatorToCnf(self.__vars.iterator)
# CNF is completed with minimisation and solved
self.__createWCNFWithMinimization(cnf)
def maxDistance2(vars, diff1, diff2, max_d, size_of_run):
list_to_size_of_run = list(range(1, size_of_run * 2 + 1))
max_distance = max_d
# IDEA : there are at least max_distance number of false variables
combinaisons_of_instants = list(
itertools.combinations(list_to_size_of_run, max_distance))
distFalseVariables = []
for instants in combinaisons_of_instants:
list_distances = []
for i in instants:
if i <= size_of_run:
list_distances.append(diff1([i]))
else:
list_distances.append(diff2([i - size_of_run]))
list_distances2 = []
for i in range(1, size_of_run * 2 + 1):
if i not in instants:
if i <= size_of_run:
list_distances2.append(diff1([i]))
else:
list_distances2.append(diff2([i - size_of_run]))
distFalseVariables.append(
Or([], list_distances, [And([], list_distances2, [])]))
return Or([], [], distFalseVariables)
def is_run_centroid(j, size_of_run, m0, mf, m_jip, tau_jip, c_kt,
chi_jk, nb_clusters, transitions, places):
'''
Initialization of centroids. There is a run per trace. This run represents alignment of the trace to the
model. If trace is clusterised then transition of it run are containing in the centroid of its cluster.
:param j (int) : index of trace
:param size_of_run (int) : maximal size of the run, prefix
:param m0 (Marking) : initial marking
:param m_jip (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_CHI_MARKINGS variables
:param tau_jip (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_CHI_TRANSITIONS
variables
:param c_kt (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_K_CONTAINS_T variables
:param chi_jk (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_J_IN_K variables
:param nb_clusters (int) : number of cluster
:param transitions (list) : list of Transitions
:param places (list) : list of Places
:return:
'''
positives = [m_jip([j, 0, places.index(m)]) for m in m0]
for m in mf:
positives.append(m_jip([j, size_of_run, places.index(m)]))
negatives = [
m_jip([j, 0, places.index(m)]) for m in places if m not in m0
]
formulas = [
is_action_centroid(j, places, transitions, i, m_jip, tau_jip,
c_kt, chi_jk, nb_clusters)
for i in range(1, size_of_run + 1)
]
run_of_pn = And(positives, negatives, formulas)
return run_of_pn
def is_run_for_j(j, size_of_run, places, pn_transitions, trace_transitions,
m0, mf, m_ip, tau_it, reach_final):
'''
The is_run_for_j method creates run of centroid of trace j, i. e., alignment.
:param j (int) : index of trace
:param size_of_run (int): maximal size of the run
:param places (list) : list of Places
:param pn_transitions (list) : transitions of the model 'cause needed...
:param trace_transitions (list) : transitions of the trace
:param m0 (marking) : initial marking of trace
:param mf (Marking) : final marking of trace
:param m_ip (function) : marking boolean variables of the trace
:param tau_it (function) : transitions boolean variables of the trace, @see variablesGenerator.
:param reach_final (bool) : true or false to reach final marking
:return:
'''
positives = [m_ip([j, 0, places.index(m)]) for m in m0]
if reach_final:
[
positives.append(m_ip([j, size_of_run,
places.index(m)])) for m in mf
]
negatives = [
m_ip([j, 0, places.index(m)]) for m in places if m not in m0
]
formulas = [
is_action_for_j(j, places, pn_transitions, trace_transitions, i,
m_ip, tau_it) for i in range(1, size_of_run + 1)
]
run_of_pn = And(positives, negatives, formulas)
return run_of_pn
def is_run(size_of_run, places, transitions, m0, mf, m_ip, tau_it, reach_final,
space_between_fired):
'''
The is_run method allows one to create the boolean paths of the petri net.
:param size_of_run (int): maximal size of the run
:param places (list) :
:param transitions (list) :
:param m0 (marking) : initial marking
:param m_ip (marking) : final marking
:param tau_it (function) : function to get the number of the boolean variables, see variablesGenerator.
:param reach_final (bool) : true or false to reach final marking
:return:
'''
positives = [m_ip([0, places.index(m)]) for m in m0]
if reach_final:
positives += [m_ip([size_of_run, places.index(m)]) for m in mf]
negatives = [m_ip([0, places.index(m)]) for m in places if m not in m0]
formulas = [
is_action(places, transitions, m0, i, m_ip, tau_it,
space_between_fired)
for i in range(space_between_fired, size_of_run +
1, space_between_fired)
]
run_of_pn = And(positives, negatives, formulas)
return run_of_pn
def for_hamming_distance_aux_supd_anti(variables,lenTraces,max_d,size_of_run):
list_of_formula=[]
list_to_size_of_run= list(range(1,size_of_run+1))
not_d_or_and_diff=[]
for j in range (0, lenTraces):
for d in range(1,min(max_d + 1,size_of_run+1)):
combinaisons_of_instants=list(itertools.combinations(list_to_size_of_run,d))
and_sub_instants=[]
for sub_list_of_instants in combinaisons_of_instants:
instants_to_combine=[]
for instant in list(sub_list_of_instants):
instants_to_combine.append(variables.get(BOOLEAN_VAR_HAMMING_DISTANCE, [j, instant]))
and_sub_instants.append(And(instants_to_combine,[],[]))
not_d_or_and_diff.append(Or([], [variables.get(BOOLEAN_VAR_HAMMING_SUP_AUX, [j, d])], and_sub_instants))
list_of_formula.append(And([],[],not_d_or_and_diff))
return list_of_formula
def __maxDiffTracesCentroids(self, formulas):
'''
This function uses self.__max_d that determines the maximal distance of the trace to its centroid.
Idea of the threshold : there are at least N diff variables false per trace.
:param formulas (list of formula to fill)
:return: void
'''
# this function uses combinations of itertools to get all the combinations : this is better than parameter
# at_most of pysat library
list_to_size_of_run = list(range(1, (self.__size_of_run * 2) + 1))
max_distance = (self.__size_of_run * 2) - self.__max_d
# IDEA : there are at least max_distance number of false variables
combinaisons_of_instants = list(
itertools.combinations(list_to_size_of_run, max_distance))
for j in range(0, len(self.__traces)):
distFalseVariables = []
for instants in combinaisons_of_instants:
list_distances = []
for i in instants:
if i <= self.__size_of_run:
list_distances.append(
self.__vars.get(BOOLEAN_VAR_DIFF_l, [j, i]))
else:
list_distances.append(
self.__vars.get(BOOLEAN_VAR_DIFF_m,
[j, (i - self.__size_of_run)]))
distFalseVariables.append(And([], list_distances, []))
formulas.append(Or([], [], distFalseVariables))
def is_action_for_j(j, trace_places, pn_transitions, trace_transitions, i,
m_ip, tau_it):
'''
The is_action method used by is_run creates the formula of each instant. Which transition fired ?
:param places (list) :
:param pn_transitions (list) : we need all the alphabet to refuse transitions that aren't in trace
:param trace_transitions (list) : transitions of the trace
:param i (int) : instant in the run
:param m_ip (function) : function to get the number of the boolean variables of the markings, see variablesGenerator.
:param tau_it (function) : function to get the number of the boolean variables of the transitions, see variablesGenerator.
:return:
'''
# only one transition is true at instant i
# lazy comment : this verifies that alphabet is complet : all action not executed has to be taken into account
or_formulas = []
formulas = []
label_transitions = [t.label for t in pn_transitions]
copie_transitions = [t for t in pn_transitions]
transitions_already_done = []
for t in trace_transitions:
if t not in transitions_already_done:
other_transitions_with_same_label = []
for t2 in trace_transitions:
if t2.label == t.label:
other_transitions_with_same_label.append(t2)
transitions_already_done.append(t2)
if t.label in label_transitions:
index_of_t = label_transitions.index(t.label)
else:
index_of_t = None # should never happen
copie_transitions.remove(
pn_transitions[(label_transitions.index(t.label))])
or_formulas.append(And([tau_it([j, i, index_of_t])], [], []))
implication = []
for t2 in other_transitions_with_same_label:
implication.append(
is_transition_for_j(j, trace_places, t2, i, m_ip))
formulas.append(
Or([], [tau_it([j, i, index_of_t])], implication))
formulas.append(Or([], [], or_formulas))
formulas.append(
And([], [
tau_it([j, i, pn_transitions.index(r)])
for r in copie_transitions
], []))
return And([], [], formulas)
def __createWncf(self, initialisationFormulas, distanceFormula,
artefactForMinimization):
'''
This method creates the wncf formulas with the weighted variables depending on the distance and artefact.
:param initialisationFormulas: @see __artefactsInitialisation
:param distanceFormula: @see __compute_distance
:param artefactForMinimization: MULTI_ALIGNMENT or ANTI_ALIGNMENT or EXACT_ALIGNMENT
:return:
'''
formulas = initialisationFormulas + distanceFormula + self.__sup_to_minimize(
artefactForMinimization)
full_formula = And([], [], formulas)
cnf = full_formula.operatorToCnf(self.__vars.iterator)
wcnf = WCNF()
wcnf.extend(cnf)
wcnf = self.__createWeights(wcnf, artefactForMinimization)
self.__formula_time = time.time()
return wcnf
def is_action_centroid(j, places, transitions, i, m_jip, tau_jip, c_kt,
chi_jk, nb_clusters):
'''
@see pnToFormula.py, is_action_centroid says if transition is fired.
:param j (int) : index of trace
:param places (list) : places of the petri net, indexes are important
:param transitions (list) : transitions of the petri net, indexes are important
:param i (int) : instant in the run of the centroid
:param m_jip (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_CHI_MARKINGS variables
:param tau_jip (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_CHI_TRANSITIONS
variables
:param c_kt (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_K_CONTAINS_T variables
:param chi_jk (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_J_IN_K variables
:param nb_clusters (int) : number of cluster
:return:
'''
# a transition fires and only one
aTransitionPerInstant = [
And([tau_jip([j, i, t])], [
tau_jip([j, i, t2])
for t2 in range(len(transitions)) if t != t2
], []) for t in range(len(transitions))
]
formulas = [Or([], [], aTransitionPerInstant)]
# runs is_transition for the fired transition
indexOfTraceWait = transitions.index(self.__wait_transition_trace)
for t in range(len(transitions)):
# WAIT_TRANSITION_TRACE is forbidden for centroid
if t == indexOfTraceWait:
formulas.append(And([], [tau_jip([j, i, t])], []))
else:
formulas.append(
Or([], [tau_jip([j, i, t])], [
And([], [], [
is_transition_centroid(
j, places, transitions[t], i, m_jip),
in_cluster_of_j(t, c_kt, j, chi_jk,
nb_clusters)
])
]))
return And([], [], formulas)
def distanceNets(vars, size_of_run, tau1, tau2, pn1_transitions,
pn2_transitions, w1, w2):
formula = []
vars.add(BOOLEAN_VAR_DIFF1, [(1, size_of_run + 1)])
vars.add(BOOLEAN_VAR_DIFF2, [(1, size_of_run + 1)])
for i in range(1, size_of_run + 1):
for t1 in pn1_transitions:
'''
listOfSameLabels=[tau2([i,pn2_transitions.index(t2)]) for t2 in pn2_transitions if t2.label==t1.label]
listOfSameLabels.append(vars.getFunction(BOOLEAN_VAR_DIFF)([i]))
formula.append(Or(listOfSameLabels,[tau1([i,pn1_transitions.index(t1)]) ],[]))
'''
if t1 != w1:
listOfSameLabels = [
tau2([i, pn2_transitions.index(t2)])
for t2 in pn2_transitions if t2.label == t1.label
]
listOfSameLabels.append(tau2([i, pn2_transitions.index(w2)]))
formula.append(
Or(listOfSameLabels,
[tau1([i, pn1_transitions.index(t1)])], [
And([
vars.getFunction(BOOLEAN_VAR_DIFF1)([i]),
vars.getFunction(BOOLEAN_VAR_DIFF2)([i])
], [], [])
]))
formula.append(
Or([vars.getFunction(BOOLEAN_VAR_DIFF1)([i])], [
tau2([i, pn2_transitions.index(w2)]),
tau1([i, pn1_transitions.index(t1)])
], []))
else:
formula.append(
Or([
vars.getFunction(BOOLEAN_VAR_DIFF2)([i]),
tau2([i, pn2_transitions.index(w2)])
], [tau1([i, pn1_transitions.index(t1)])], []))
return And([], [], formula)
def __tracesInAClusterOnly(self, inC_j, chi_jk):
'''
Verifies that j is in a unique cluster or any
:param inC_j (function)
:param chi_jk (function)
'''
formulas = []
for j in range(0, len(self.__traces)):
inCorNot = []
for k1 in range(0, self.__nb_clusters):
# if in k1 then not in other k
inCorNot.append(
And([inC_j([j]), chi_jk([j, k1])], [
chi_jk([j, k])
for k in range(0, self.__nb_clusters) if k != k1
], []))
# if in any k, then not inC
allKNot = [chi_jk([j, k]) for k in range(0, self.__nb_clusters)]
allKNot.append(inC_j([j]))
inCorNot.append(And([], allKNot, []))
formulas.append(Or([], [], inCorNot))
return formulas
def force_wait_transition(vars, w1, pn1_transitions, adapted_size_of_run,
space_between_fired):
pos = []
neg = []
for i in range(0, adapted_size_of_run + 1):
if i % space_between_fired != 0:
for t in pn1_transitions:
if t != w1:
neg.append(
vars.get(BOOLEAN_VAR_FIRING_TRANSITION_PN_1,
[i, pn1_transitions.index(t)]))
else:
pos.append(
vars.get(BOOLEAN_VAR_FIRING_TRANSITION_PN_1,
[i, pn1_transitions.index(t)]))
return And(pos, neg, [])
def in_cluster_of_j(tr, c_kt, j, chi_jk, nb_clusters):
'''
Subfunction of __createCentroids. in_cluster_of_j function affects a transition to the cluster of the trace.
:param tr (Transition)
:param c_kt (function) : @see variablesGenerator.py, function c_kt(k,t) gets BOOLEAN_VAR_K_CONTAINS_T
variables
:param j (int) : index of the current trace
:param chi_jk (function) : @see variablesGenerator.py, function chi_jk gets BOOLEAN_VAR_J_IN_K variables
:param nb_clusters (int) : number of cluster
:return:
'''
# BOOLEAN_VAR_J_IN_K => BOOLEAN_VAR_K_CONTAINS_T
return And([], [], [
Or([c_kt([k, tr])], [chi_jk([j, k])], [])
for k in range(0, nb_clusters)
])
def log_to_SAT(traces_xes,
transitions,
variablesGenerator,
size_of_run,
wait_transition,
label_l=BOOLEAN_VAR_TRACES_ACTIONS,
max_nbTraces=None):
'''
This method returns the formulas of the Log.
:param traces_xes:
:param transitions (list)
:param variablesGenerator (variablesGenerator) : to add the new boolean variables
:param size_of_run (int) : to complete smaller words with "wait" transitions
:param wait_transition (transition) : the "wait" transition
:param label_l (string) : name of the boolean variables of the log
:return:
'''
traces_multiples = project_traces(traces_xes)
#traces=list(np.unique(traces_multiples))
traces = traces_multiples
traces = traces[:max_nbTraces] if max_nbTraces != None else traces
variablesGenerator.add(label_l, [(0, len(traces)), (1, size_of_run + 1),
(0, len(transitions))])
lambda_jia = variablesGenerator.getFunction(label_l)
positives = []
negatives = []
for j in range(0, len(traces)):
for i in range(1, size_of_run + 1):
if len(traces[j]) < (i):
positives.append(
lambda_jia([j, i, transitions.index(wait_transition)]))
for a in transitions:
if a != wait_transition:
negatives.append(
lambda_jia([j, i, transitions.index(a)]))
else:
for a in transitions:
if str(a) == traces[j][i - 1]:
letterFound = True
positives.append(
lambda_jia([j, i, transitions.index(a)]))
else:
negatives.append(
lambda_jia([j, i, transitions.index(a)]))
return And(positives, negatives, []), traces
def numberOfWaitInRun(vars, size_of_run, tau1, pn1_transitions, w1, we):
list_to_size_of_run = list(range(1, size_of_run * 2 + 1))
minw1 = int((size_of_run) / 2)
# IDEA : there are at least max_distance number of w1 variables to false
combinaisons_of_instants = list(
itertools.combinations(list_to_size_of_run, minw1))
w1ToTrue = []
for instants in combinaisons_of_instants:
listOfW1ToTrue = []
for i in instants:
if i <= int(size_of_run):
listOfW1ToTrue.append(tau1([i, pn1_transitions.index(w1)]))
else:
listOfW1ToTrue.append(
tau1([i - int(size_of_run),
pn1_transitions.index(we)]))
w1ToTrue.append(And(listOfW1ToTrue, [], []))
return Or([], [], w1ToTrue)
def is_transition(places, transition, i, m_ip, space_between_fired):
'''
The is_transition method used by is_action creates the formula of a firing transition. Which marking is needed ?
:param places (list) :
:param transitions (list) :
:param i (int) : instant in the run
:param m_ip (function) : function to get the number of the boolean variables of the markings, see variablesGenerator.
:return:
'''
formulas = []
prePlaces = [a.source for a in transition.in_arcs]
postPlaces = [a.target for a in transition.out_arcs]
for p in places:
if p in prePlaces and p in postPlaces:
formulas.append(
And([
m_ip([i, places.index(p)]),
m_ip([i - space_between_fired,
places.index(p)])
], [], []))
elif p in prePlaces and p not in postPlaces:
formulas.append(
And([m_ip([i - space_between_fired,
places.index(p)])], [m_ip([i, places.index(p)])],
[]))
elif p not in prePlaces and p in postPlaces:
formulas.append(
And([m_ip([i, places.index(p)])],
[m_ip([i - space_between_fired,
places.index(p)])], []))
elif p not in prePlaces and p not in postPlaces:
formulas.append(
Or([], [], [
And([
m_ip([i, places.index(p)]),
m_ip([i - space_between_fired,
places.index(p)])
], [], []),
And([], [
m_ip([i, places.index(p)]),
m_ip([i - space_between_fired,
places.index(p)])
], [])
]))
return And([], [], formulas)
def is_transition_centroid(j, places, tr, i, m_ip):
'''
This function verifies marking to fire transition of a centroid.
:param j (int) : index of centroid
:param places (list) : list of places
:param tr (Transition) : transition that wants to fire
:param i (int) : instant of firing
:param m_ip (function) : @see @variablesGenerator.py function to get BOOLEAN_VAR_CHI_MARKINGS variables
'''
formulas = []
prePlaces = [a.source for a in tr.in_arcs]
postPlaces = [a.target for a in tr.out_arcs]
# token game
for p in places:
if p in prePlaces and p in postPlaces:
formulas.append(
And([
m_ip([j, i, places.index(p)]),
m_ip([j, i - 1, places.index(p)])
], [], []))
elif p in prePlaces and p not in postPlaces:
formulas.append(
And([m_ip([j, i - 1, places.index(p)])],
[m_ip([j, i, places.index(p)])], []))
elif p not in prePlaces and p in postPlaces:
formulas.append(
And([m_ip([j, i, places.index(p)])],
[m_ip([j, i - 1, places.index(p)])], []))
elif p not in prePlaces and p not in postPlaces:
formulas.append(
Or([], [], [
And([
m_ip([j, i, places.index(p)]),
m_ip([j, i - 1, places.index(p)])
], [], []),
And([], [
m_ip([j, i, places.index(p)]),
m_ip([j, i - 1, places.index(p)])
], [])
]))
return And([], [], formulas)
def recursionEditDistance_reducedForMultiAlignment(transitions, silent_transitions, tau_it, lambda_jia, djiid, j,
size_of_run,
wait_transition, max_d):
'''
Initialisation of the edit distance reduced for multi-alignment.
This is the 2 lasts axioms of the _Encoding Conformance Checking Artefacts in SAT_ paper
:param transitions (list) : list of transitions
:param silent_transitions (list) : list of the silent transitions
:param tau_it (fun) : function that returns the boolean variable number of the firing transition t at an instant i
:param lambda_jia (fun) : function that returns the boolean variable number of the letter of trace j at instant i
:param djiid (fun) : function that returns the boolean variable that says at instant i and i of we have d distance
:param j (int) : jth trace
:param size_of_run (int) : maximal size of a run
:param wait_transition (transition) : to finish words
:param max_d (int): heuristic
:return: formula
'''
def t(transition):
return transitions.index(transition)
formulas = []
for i_m in range(0, size_of_run):
for i_t in range(0, size_of_run):
for d in range(0, max_d):
# letters are equals i_t+1 == i_m+1 => (d i_t i_m d => d i_t+1 i_m+1 d)
letters_are_equals = Or([djiid([j, i_m + 1, i_t + 1, d+1])], [djiid([j, i_m, i_t, d+1])],
[And([], [],
[Or([], [tau_it([i_m + 1, t]), lambda_jia([j, i_t + 1, t])], []) for t in
range(0, len(transitions))]
)])
formulas.append(letters_are_equals)
# letters are diff : i_t+1 == i_m+1 => (d i_t i_m d => d i_t+1 i_m+1 d)
condition = [tau_it([i_m + 1, t(wait_transition)]), lambda_jia([j, i_t + 1, t(wait_transition)])]
for st in silent_transitions:
condition.append(tau_it([i_m + 1, t(st)]))
condition.append(djiid([j, i_m + 1, i_t + 1, d + 1]))
letters_are_diff = Or(condition,
[djiid([j, i_m + 1, i_t, d]), djiid([j, i_m, i_t + 1, d])],
[And([tau_it([i_m + 1, t]), lambda_jia([j, i_t + 1, t])], [], []) for
t in range(0, len(transitions))])
formulas.append(letters_are_diff)
# ( u_t == w and u_m <> w) => ( d i_m i_t d => d i_m+1 i_t d
finish_run_of_model = Or([tau_it([i_m + 1, t(wait_transition)]), djiid([j, i_m + 1, i_t + 1, d])],
[lambda_jia([j, i_t + 1, t(wait_transition)]), djiid([j, i_m + 1, i_t, d])],
[])
formulas.append(finish_run_of_model)
# ( u_m == w and u_t <> w) => ( d i_m i_t d => d i_m i_t+1 d
condition=[tau_it([i_m + 1, t(wait_transition)])]
for st in silent_transitions:
condition.append(tau_it([i_m + 1, t(st)]))
finish_run_of_trace = Or(
[lambda_jia([j, i_t + 1, t(wait_transition)]), djiid([j, i_m + 1, i_t + 1, d])],
[ djiid([j, i_m, i_t + 1, d])], [
And([], condition,[])
])
formulas.append(finish_run_of_trace)
return formulas
def apply(net1, m01, mf1, net2, m02, mf2, size_of_run, d, silent_label=None):
vars = vg.VariablesGenerator()
#we=add_wait_net_end(net1,"wf")
w1 = add_wait_net(net1, "wf")
adapted_size_of_run = size_of_run * size_of_run + size_of_run
pn1_formula, pn1_places, pn1_transitions, pn1_silent_transitions = petri_net_to_SAT(
net1,
m01,
mf1,
vars,
adapted_size_of_run,
reach_final=True,
label_m=BOOLEAN_VAR_MARKING_PN_1,
label_t=BOOLEAN_VAR_FIRING_TRANSITION_PN_1,
silent_transition=silent_label,
space_between_fired=1 + size_of_run)
print("etape1")
pn1_force_wait_transitions = force_wait_transition(vars, w1,
pn1_transitions,
adapted_size_of_run,
size_of_run + 1)
print("etape2")
w2 = add_wait_net(net2, "wf")
pn2_formula, pn2_places, pn2_transitions, pn2_silent_transitions = petri_net_to_SAT(
net2,
m02,
mf2,
vars,
adapted_size_of_run,
reach_final=True,
label_m=BOOLEAN_VAR_MARKING_PN_2,
label_t=BOOLEAN_VAR_FIRING_TRANSITION_PN_2,
silent_transition=silent_label)
dist_formulas = distanceNets(
vars, adapted_size_of_run,
vars.getFunction(BOOLEAN_VAR_FIRING_TRANSITION_PN_1),
vars.getFunction(BOOLEAN_VAR_FIRING_TRANSITION_PN_2), pn1_transitions,
pn2_transitions, w1, w2)
print("etape3")
maxDist_formulas = maxDistance(vars, vars.getFunction(BOOLEAN_VAR_DIFF1),
vars.getFunction(BOOLEAN_VAR_DIFF2), d,
adapted_size_of_run)
#notTooManyW=numberOfWaitInRun(vars,size_of_run,vars.getFunction(BOOLEAN_VAR_FIRING_TRANSITION_PN_1),pn1_transitions,w1,we)
print("etape4")
from pm4py.visualization.petrinet import factory as vizu
#vizu.apply(net2,m02,mf2).view()
listOfForAll = vars.getAll(BOOLEAN_VAR_MARKING_PN_1) + vars.getAll(
BOOLEAN_VAR_FIRING_TRANSITION_PN_1)
listOfExist = vars.getAll(BOOLEAN_VAR_MARKING_PN_2) + vars.getAll(
BOOLEAN_VAR_FIRING_TRANSITION_PN_2) + vars.getAll(
BOOLEAN_VAR_DIFF1) + vars.getAll(BOOLEAN_VAR_DIFF2)
full_formula = Or([], [], [
And([], [], [pn1_formula, pn1_force_wait_transitions]).negation(),
And([], [], [dist_formulas, maxDist_formulas, pn2_formula])
])
print("etape5")
cnf = full_formula.operatorToCnf(vars.iterator)
print("etape6")
listOfExist += list(range(vars.iterator, full_formula.nbVars))
writeQDimacs(full_formula.nbVars, listOfForAll, listOfExist, cnf)
print("mais voila")
runCadet()
positives, negatives = cadetOutputQDimacs()
for var in positives:
if vars.getVarName(var) != None and vars.getVarName(var).startswith(
"tau1_ia"):
print(
vars.getVarName(var), pn1_transitions[int(
vars.getVarName(var).split(", ")[1].split("]")[0])])
print("....")
for var in negatives:
if vars.getVarName(var) != None and vars.getVarName(var).startswith(
"tau1_ia"):
print(
vars.getVarName(var), pn1_transitions[int(
vars.getVarName(var).split(", ")[1].split("]")[0])])
