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bif_to_cnf.py
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bif_to_cnf.py
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#!/usr/bin/python3
import sys
import argparse
import itertools
import sympy
from deps.bif_parser import BIFParser as BIFP
from sympy.logic.boolalg import Not, And, Or, Equivalent, Implies, to_cnf
# variables are tuple: (sympy var, node name, var state name)
# conditional variables have an extra element:
# (sympy var, node name, var state name, (conditional var 1, ...))
# for cnf: clauses are tuples (Boolean, variable)
# with boolean == False <=> not(var)
# and variable as defined above
LATEX_NAMES = False
def get_combinations(list_of_lists):
"""
Returns all posible combinations of the given lists
used to create all conditional variables
"""
return itertools.product(*list_of_lists)
def create_var(node, state):
"""
Creates a variable representing that the given node is in the given state
"""
if LATEX_NAMES:
var_name = "\\lambda_{" + node.getName() + "\\_" + state + "}"
else:
var_name = node.getName() + '_' + state
return (sympy.Symbol(var_name), node.getName(), state)
def create_conditional_var(node, state, conds, parents):
"""
Creates a conditional probability variable of the node in the given state
assumings all conds states of parents
"""
if LATEX_NAMES:
cond_names = ",".join([b.getName() + "\\_" + a for a, b in zip(conds, parents)])
var_name = "\\theta_{" + node.getName() + "\\_" + state + "|" + cond_names+ "}"
else:
var_name = node.getName() + "_" + state + "|" + "_".join(conds)
return (sympy.Symbol(var_name), node.getName(), state, tuple(conds))
def get_state_vars(node):
""" Creates all state variables of the given node """
return [create_var(node, s) for s in node.getStates()]
def get_all_cond_vars(node):
""" Creates all conditional state variables """
cond_list = [node.getStates()]
parents = node.getParents()
for parent in parents:
cond_list.append(parent.getStates())
pairs = get_combinations(cond_list)
return [create_conditional_var(node, p[0], p[1:], parents) for p in pairs]
def create_variables(nodes, enc1):
""" creates required all variables """
variables = []
queries = []
for node in nodes:
states = node.getStates()
# each state gets one variable
svars = get_state_vars(node)
parents = node.getParents()
# per state and state of each parent -> one variable
if enc1:
cond_list = [states]
else:
cond_list = [states[:-1]]
for parent in parents:
cond_list.append(parent.getStates())
pairs = get_combinations(cond_list)
pvars = [create_conditional_var(node, p[0], p[1:], parents) for p in pairs]
for v in svars:
queries.append(v[0].name)
# add all variables
for v in svars + pvars:
variables.append(v[0].name)
return variables, queries
def create_indicator_cnf(node):
""" Creates the indicator clauses """
cnf = []
svars = get_state_vars(node)
# the disjunction of all states:
cnf.append(Or(*[s[0] for s in svars]))
# negation:
l = len(svars)
for j in range(l):
for i in range(j):
sa = svars[j][0]
sb = svars[i][0]
cnf.append(~sa | ~sb)
return cnf
def toEnc1(nodes):
""" Creates the ENC 1 encoding of the given nodes """
cnf = []
for node in nodes:
cnf += create_indicator_cnf(node)
parents = node.getParents()
cond_list = [node.getStates()]
for parent in parents:
cond_list.append(parent.getStates())
pairs = get_combinations(cond_list)
nodes = [node] + parents
# create parameter clauses
for pair in pairs:
par_var = create_conditional_var(node, pair[0], pair[1:], parents)
rl = par_var[0]
ll = And(*[create_var(nodes[i], s)[0] for i, s in enumerate(pair)])
cnf.append(Equivalent(ll, rl))
return And(*cnf)
def toEnc2(nodes):
""" Creates the ENC 2 encoding of the given nodes """
cnf = []
for node in nodes:
states = node.getStates()
cnf += create_indicator_cnf(node)
cond_list = [states]
parents = node.getParents()
for parent in parents:
cond_list.append(parent.getStates())
pairs = itertools.product(*cond_list)
nodes = [node] + parents
for pair in pairs:
# pair[0] is the state of the node
# pair[1:] are the state of all conditionals
ll = [create_var(nodes[i+1], s)[0] for i, s in enumerate(pair[1:])]
ll += [~(create_conditional_var(node, s, pair[1:], parents)[0]) for s in states[:states.index(pair[0])]]
if pair[0] != states[-1]:
ll += [create_conditional_var(node, pair[0], pair[1:], parents)[0]]
ll = And(*ll)
rl = create_var(node, pair[0])[0]
#print(ll, '=>', rl)
cnf.append(Implies(ll, rl))
return And(*cnf)
def assign_weights_enc1(nodes):
weights = {}
for node in nodes:
cpd = node.getDist()
cvars = get_all_cond_vars(node)
for cvar in cvars:
# cpd[state_of_node + state_of_conditionals]
prob = cpd[(cvar[2],) + cvar[3]]
weights[cvar[0].name] = prob
return weights
def assign_weights_enc2(nodes):
weights = {}
for node in nodes:
states = node.getStates()
cpd = node.getDist()
cvars = get_all_cond_vars(node)
for cvar in cvars:
prob = cpd[(cvar[2],) + cvar[3]]
# index of state
idx = states.index(cvar[2])
divisor = 1
for i in range(idx):
divisor -= cpd[(states[i],) + cvar[3]]
# TODO: 0 or 1 if divisor == 0
weights[cvar[0].name] = prob / divisor if divisor > 0 else 0
return weights
def weights_to_dict(weights, variables, enc1):
ws = {}
for var in variables:
if var in weights:
weight = weights[var]
ws[var] = (weight, 1 if enc1 else (1 - weight))
else:
ws[var] = (1, 1)
return ws
def latex_print(s):
if type(s) is And:
return " \\wedge ".join([latex_print(a) for a in s.args])
elif type(s) is Or:
return " \\vee ".join([latex_print(a) for a in s.args])
elif type(s) is Equivalent:
return latex_print(s.args[0]) + " \\Leftrightarrow " + latex_print(s.args[1])
elif type(s) is Implies:
return latex_print(s.args[0]) + " \\Rightarrow " + latex_print(s.args[1])
elif type(s) is Not:
return " \\neg " + latex_print(s.args[0])
else:
return s.name
def parse_bif(contents, enc1, verbose):
nodes = None
bif_w = contents.splitlines()
bif = BIFP.fixWhiteSpace(bif_w)
nodes = BIFP.parseBIF(bif)
if nodes is None:
print("error parsing bif")
return -1
if verbose:
print(">bif info:")
for n in nodes:
n.printNode()
# create variables
# map from name to int
variables, queries = create_variables(nodes, enc1)
if verbose:
print("variables:")
for v in variables:
print(v)
# create cnf
cnf = toEnc1(nodes) if enc1 else toEnc2(nodes)
if verbose:
print("enc:")
clauses = cnf.args
for clause in clauses:
p = "$ "
p += latex_print(clause)
p += " $"
print(p)
print()
cnf = to_cnf(cnf)
if verbose:
print("cnf:")
print(cnf)
# assign weights
weights = assign_weights_enc1(nodes) if enc1 else assign_weights_enc2(nodes)
weights = weights_to_dict(weights, variables, enc1)
# if verbose:
# print("weights:")
# keys = weights.keys()
# for key in keys:
# print("$ " + key + " $ & " + str(weights[key][0]) + "&" + str(weights[key][1]) + " \\\\")
return variables, cnf, weights, queries