def test_implicates_implicants_negation_rule_example():
"""These failed an old version of the previous test. See issue #3."""
sentence = Or({And({~Var(1), Var(2)}), And({~Var(3), Var(1)})})
assert (sentence.negate().implicants().negate().children >=
sentence.implicates().children)
assert (sentence.negate().implicates().negate().children <=
sentence.implicants().children)
def encode_circuit_search(original_theory, num_gates, models=[]):
########
# Vars #
########
# Inputs to the circuit are the variables of the input theory
inputs = [Var(v) for v in original_theory.vars()]
if models:
input_clones = clone_varset(models, inputs, inputs)
else:
input_clones = {}
# Gates are either & | or ~
gates = []
gate_modalities = {}
for i in range(num_gates):
gates.append(Var(Gate(i)))
gate_modalities[gates[-1]] = {}
for m in ['and', 'or', 'not']:
gate_modalities[gates[-1]][m] = Var(GateType(gates[-1], m))
if models:
gate_clones = clone_varset(models, inputs, gates)
else:
gate_clones = {}
# Single (arbitrary) gate is the circuit output
output = gates[0]
# Connections between inputs/gates to gates, and transitivity
connections = {}
unconnections = {}
for src in inputs + gates[1:]:
connections[src] = {}
for dst in gates:
if src != dst:
connections[src][dst] = Var(Connection(src, dst))
if dst not in unconnections:
unconnections[dst] = {}
unconnections[dst][src] = connections[src][dst]
C = connections # convenience
orders = {}
for src in gates:
orders[src] = {}
for dst in gates:
orders[src][dst] = Var(Order(src,dst))
###############
# Constraints #
###############
''' add decorators for simplifying adding constraints (i.e. a conjunct)'''
conjuncts = []
# Orderings (to forbid cycles in the circuit)
for g1 in gates:
# Connection implies orders
for src in connections:
for dst in connections[src]:
if isinstance(src.name, Gate) and isinstance(dst.name, Gate):
conjuncts.append(~connections[src][dst] | orders[src][dst])
# Can't order before yourself
conjuncts.append(~orders[g1][g1])
# Transitive closure
for g2 in gates:
for g3 in gates:
conjuncts.append(~orders[g1][g2] | ~orders[g2][g3] | orders[g1][g3])
if FORCE_TREE:
# At max one outgoing connection on a gate
for src in gates[1:]:
for dst1 in connections[src]:
for dst2 in connections[src]:
if dst1 != dst2:
conjuncts.append(~connections[src][dst1] | ~connections[src][dst2])
# Every gate has at least one input
for dst in unconnections:
conjuncts.append(Or(unconnections[dst].values()))
# Every gate has at most two inputs and negation gates have at most one
for j in gates:
for i1 in inputs+gates[1:]:
for i2 in inputs+gates[1:]:
if not unique([j,i1,i2]):
continue
conjuncts.append(~gate_modalities[j]['not'] | ~C[i1][j] | ~C[i2][j])
for i3 in inputs+gates[1:]:
if not unique([j,i1,i2,i3]):
continue
conjuncts.append(~C[i1][j] | ~C[i2][j] | ~C[i3][j])
# Every gate has exactly one modality
for g in gates:
# At least one
conjuncts.append(Or(gate_modalities[g].values()))
# At most one
for m1 in ['and', 'or', 'not']:
remaining = set(['and', 'or', 'not']) - set([m1])
conjuncts.append(Or([~gate_modalities[g][m2] for m2 in remaining]))
# Re-usable theories
notneg_cache = {}
def notneg(src, dst, cloned_src=None):
if not cloned_src:
cloned_src = src
if (cloned_src,dst) not in notneg_cache:
notneg_cache[(cloned_src,dst)] = ~C[src][dst] | cloned_src
return notneg_cache[(cloned_src,dst)]
notpos_cache = {}
def notpos(src, dst, cloned_src=None):
if not cloned_src:
cloned_src = src
if (cloned_src,dst) not in notpos_cache:
notpos_cache[(cloned_src,dst)] = ~C[src][dst] | ~cloned_src
return notpos_cache[(cloned_src,dst)]
# Implement the gates
for g in gates:
ins = [i for i in inputs+gates[1:] if i != g]
conjuncts.append(~gate_modalities[g]['and'] | iff(g, And([notneg(src,g) for src in ins])))
t = Or([notpos(src,g).negate() for src in ins])
conjuncts.append(~gate_modalities[g]['or'] | iff(g, t))
conjuncts.append(~gate_modalities[g]['not'] | iff(g, t.negate()))
for m in models:
bitvec = model_to_bitvec(m, inputs)
orig_mapping = {**{input_clones[bitvec][i]: i for i in inputs if i != g},
**{gate_clones[bitvec][i]: i for i in gates[1:] if i != g}}
ins = orig_mapping.keys()
conjuncts.append(~gate_modalities[g]['and'] | iff(gate_clones[bitvec][g],
And([notneg(orig_mapping[src],g,src) for src in ins])))
t = Or([notpos(orig_mapping[src],g,src).negate() for src in ins])
conjuncts.append(~gate_modalities[g]['or'] | iff(gate_clones[bitvec][g], t))
conjuncts.append(~gate_modalities[g]['not'] | iff(gate_clones[bitvec][g], t.negate()))
# Finally, lock in the models
if models:
for m in models:
bitvec = model_to_bitvec(m, inputs)
for var in m:
if m[var]:
conjuncts.append(input_clones[bitvec][Var(var)])
else:
conjuncts.append(~input_clones[bitvec][Var(var)])
if original_theory.satisfied_by(m):
conjuncts.append(gate_clones[bitvec][output])
else:
conjuncts.append(~gate_clones[bitvec][output])
else:
for model in all_models(original_theory.vars()):
t = false # negating the conjunction because of the implication: flips the signs
for var,val in model.items():
if val:
t |= ~Var(var)
else:
t |= Var(var)
if original_theory.satisfied_by(model):
t |= output
else:
t |= ~output
conjuncts.append(t)
versions = {}
example = {}
for c in conjuncts:
cn = c.simplify().to_CNF()
stats = "(%d / %d / %d) > (%d / %d / %d)" % (c.simplify().size(), c.simplify().height(), len(c.simplify().vars()),
cn.size(), cn.height(), len(cn.vars()))
example[stats] = str(c.simplify())
versions[stats] = versions.get(stats, 0) + 1
print("Conjunct stats:")
for k in versions:
print("\n - (%d) %s: %s" % (versions[k], k, example[k]))
T = And(conjuncts)
return T.simplify(), inputs, gates, output, connections, unconnections, gate_modalities