def _build_automata(self):
rows = self.row_symbols
atoms = [AtomicFormula(r) for r in rows]
alphabet = Alphabet(set(rows))
ldlf = LDLf_EmptyTraces(alphabet)
f = PathExpressionEventually(
PathExpressionSequence.chain([
PathExpressionStar(
And.chain([Not(atoms[0]),
Not(atoms[1]),
Not(atoms[2])])),
PathExpressionStar(
And.chain([atoms[0],
Not(atoms[1]),
Not(atoms[2])])),
# Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
PathExpressionStar(
And.chain([atoms[0], atoms[1],
Not(atoms[2])])),
# Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2]]), # Not(atoms[3]), Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], Not(atoms[4]), Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], atoms[4], Not(atoms[5])]),
# And.chain([atoms[0], atoms[1], atoms[2], atoms[3], atoms[4], atoms[5] ])
]),
And.chain([atoms[0], atoms[1], atoms[2]]))
nfa = ldlf.to_nfa(f)
dfa = _to_pythomata_dfa(nfa)
return dfa
def expand_formula(self, f: Formula):
"""Manage the case when we have a propositional formula."""
# Check first if it is a propositional
pl = PL(self.alphabet)
if pl.is_formula(f):
return super().expand_formula(
PathExpressionEventually(f, LogicalTrue()))
else:
return super().expand_formula(f)
def _expand_formula(self, f: Formula):
if isinstance(f, AtomicFormula):
return f
elif isinstance(f, And):
return And(self.expand_formula(f.f1), self.expand_formula(f.f2))
elif isinstance(f, Not):
return Not(self.expand_formula(f.f))
elif isinstance(f, PathExpressionEventually):
return PathExpressionEventually(f.p, self.expand_formula(f.f))
else:
raise ValueError("Not valid Formula to expand")
def _truth(self, f: Formula, trace: FiniteTrace, position: int):
assert trace.alphabet == self.alphabet
truth = self._truth
# LDLfFormulas
if isinstance(f, AtomicFormula):
return f.symbol in trace.get(position)
elif isinstance(f, Not):
return not self.truth(f.f, trace, position)
elif isinstance(f, And):
return self.truth(f.f1, trace, position) and self.truth(f.f2, trace, position)
elif isinstance(f, PathExpressionEventually):
path = f.p
assert self._is_path(path)
if isinstance(path, PathExpressionTest):
return truth(path.f, trace, position) and truth(f.f, trace, position)
elif isinstance(path, PathExpressionUnion):
return truth(PathExpressionEventually(path.p1, f.f), trace, position) or truth(
PathExpressionEventually(path.p2, f.f), trace, position)
elif isinstance(path, PathExpressionSequence):
return truth(PathExpressionEventually(path.p1, PathExpressionEventually(path.p2, f.f)), trace, position)
elif isinstance(path, PathExpressionStar):
return truth(f.f, trace, position) or (
position < trace.last()
and truth(PathExpressionEventually(path.p, PathExpressionEventually(path, f.f)), trace, position)
and not self._is_testonly(path)
)
# Should be a Propositional Formula
else:
pl, I = PL._from_set_of_propositionals(trace.get(position), trace.alphabet)
return position < trace.last() and pl.truth(path, I) and truth(f.f, trace, position + 1)
else:
raise ValueError("Argument not a valid Formula")
def to_equivalent_formula(self, derived_formula: Formula):
if isinstance(derived_formula, Or):
return Not(And(Not(derived_formula.f1), Not(derived_formula.f2)))
elif isinstance(derived_formula, PathExpressionAlways):
return Not(PathExpressionEventually(derived_formula.p, Not(derived_formula.f)))
elif isinstance(derived_formula, FalseFormula):
return And(Not(DUMMY_ATOMIC), DUMMY_ATOMIC)
elif isinstance(derived_formula, TrueFormula):
return Not(FalseFormula())
elif isinstance(derived_formula, LDLfLast):
return PathExpressionAlways(TrueFormula(), FalseFormula())
else:
raise ValueError("Derived formula not recognized")
def test_to_nnf(self):
f1 = Not(
PathExpressionEventually(
PathExpressionSequence(PathExpressionTest(Not(self.a_and_b)),
PathExpressionStar(TrueFormula())),
self.abc))
nnf_f1 = PathExpressionAlways(
PathExpressionSequence(
PathExpressionTest(Or(Not(self.a), Not(self.b))),
# PathExpressionStar(Or(DUMMY_ATOMIC, Not(DUMMY_ATOMIC)))
PathExpressionStar(TrueFormula())),
Or(Not(self.a), Or(Not(self.b), Not(self.c))))
self.assertEqual(self.ldlf.to_nnf(f1), nnf_f1)
def _is_formula(self, f: Formula):
"""Check if a formula is legal in the current formal system"""
# Check first if it is a propositional
pl = PL(self.alphabet)
if pl.is_formula(f):
return self.is_formula(PathExpressionEventually(f, LogicalTrue()))
elif isinstance(f, LogicalTrue):
return True
elif isinstance(f, Not):
return self.is_formula(f.f)
elif isinstance(f, And):
return self.is_formula(f.f1) and self.is_formula(f.f2)
elif isinstance(f, PathExpressionEventually):
return self._is_path(f.p) and self.is_formula(f.f)
else:
return False
def _not_to_nnf(self, not_formula: Not):
subformula = not_formula.f
if isinstance(subformula, AtomicFormula):
return not_formula
if isinstance(subformula, Not):
# skip two consecutive Not
new_formula = subformula.f
return self.to_nnf(new_formula)
elif isinstance(subformula, And):
return Or(self.to_nnf(Not(subformula.f1)), self.to_nnf(Not(subformula.f2)))
elif isinstance(subformula, Or):
return And(self.to_nnf(Not(subformula.f1)), self.to_nnf(Not(subformula.f2)))
elif isinstance(subformula, PathExpressionEventually):
return PathExpressionAlways(self.to_nnf_path(subformula.p), self.to_nnf(Not(subformula.f)))
elif isinstance(subformula, PathExpressionAlways):
return PathExpressionEventually(self.to_nnf_path(subformula.p), self.to_nnf(Not(subformula.f)))
else:
raise ValueError
def to_equivalent_formula(self, derived_formula: Formula):
# make lines shorter
ef = self.to_equivalent_formula
if isinstance(derived_formula, AtomicFormula):
return PathExpressionEventually(derived_formula, LogicalTrue())
elif isinstance(derived_formula, LogicalFalse):
return Not(LogicalTrue())
elif isinstance(derived_formula, Or):
return Not(And(Not(derived_formula.f1), Not(derived_formula.f2)))
elif isinstance(derived_formula, PathExpressionAlways):
return Not(
PathExpressionEventually(derived_formula.p,
Not(derived_formula.f)))
elif isinstance(derived_formula, Next):
return PathExpressionEventually(
TrueFormula(), And(derived_formula.f, Not(ef(End()))))
elif isinstance(derived_formula, End):
return ef(PathExpressionAlways(TrueFormula(), ef(LogicalFalse())))
elif isinstance(derived_formula, Until):
return PathExpressionEventually(
PathExpressionStar(
PathExpressionSequence(
PathExpressionTest(derived_formula.f1),
ef(TrueFormula()))),
And(derived_formula.f2, Not(ef(End()))))
elif isinstance(derived_formula, FalseFormula):
return FalseFormula()
elif isinstance(derived_formula, TrueFormula):
return TrueFormula()
elif isinstance(derived_formula, LDLfLast):
return PathExpressionEventually(ef(TrueFormula()), ef(End()))
# propositional
elif isinstance(derived_formula, Formula):
pl = PL(self.alphabet)
assert pl.is_formula(derived_formula)
f = pl.to_nnf(derived_formula)
return PathExpressionEventually(f, LogicalTrue())
else:
raise ValueError("Derived formula not recognized")
def delta(self, f: Formula, action: FrozenSet[Symbol], epsilon=False):
# TODO: should return [True|False]Formula or simply True/False?
pl, I = PL._from_set_of_propositionals(action, self.alphabet)
if pl.is_formula(f):
return self.delta(PathExpressionEventually(f, LogicalTrue()),
action, epsilon)
elif isinstance(f, LogicalTrue):
return TrueFormula()
elif isinstance(f, LogicalFalse):
return FalseFormula()
elif isinstance(f, And):
return And(self.delta(f.f1, action),
self.delta(f.f2, action, epsilon))
elif isinstance(f, Or):
return Or(self.delta(f.f1, action),
self.delta(f.f2, action, epsilon))
elif isinstance(f, PathExpressionEventually):
if pl.is_formula(f.p):
if not epsilon and pl.truth(f.p, I):
return self._expand(f.f)
else:
return FalseFormula()
elif isinstance(f.p, PathExpressionTest):
return And(self.delta(f.p.f, action, epsilon),
self.delta(f.f, action, epsilon))
elif isinstance(f.p, PathExpressionUnion):
return Or(
self.delta(PathExpressionEventually(f.p.p1, f.f), action,
epsilon),
self.delta(PathExpressionEventually(f.p.p2, f.f), action,
epsilon))
elif isinstance(f.p, PathExpressionSequence):
e2 = PathExpressionEventually(f.p.p2, f.f)
e1 = PathExpressionEventually(f.p.p1, e2)
return self.delta(e1, action, epsilon)
elif isinstance(f.p, PathExpressionStar):
o1 = self.delta(f.f, action, epsilon)
o2 = self.delta(PathExpressionEventually(f.p.p, F(f)), action,
epsilon)
return Or(o1, o2)
elif isinstance(f, PathExpressionAlways):
if pl.is_formula(f.p):
if not epsilon and pl.truth(f.p, I):
return self._expand(f.f)
else:
return TrueFormula()
elif isinstance(f.p, PathExpressionTest):
o1 = self.delta(self.to_nnf(Not(f.p.f)), action, epsilon)
o2 = self.delta(f.f, action, epsilon)
return Or(o1, o2)
elif isinstance(f.p, PathExpressionUnion):
return And(
self.delta(PathExpressionAlways(f.p.p1, f.f), action,
epsilon),
self.delta(PathExpressionAlways(f.p.p2, f.f), action,
epsilon))
elif isinstance(f.p, PathExpressionSequence):
return self.delta(
PathExpressionAlways(f.p.p1,
PathExpressionAlways(f.p.p2, f.f)),
action, epsilon)
elif isinstance(f.p, PathExpressionStar):
a1 = self.delta(f.f, action, epsilon)
a2 = self.delta(PathExpressionAlways(f.p.p, T(f)), action,
epsilon)
return And(a1, a2)
elif isinstance(f, F):
return FalseFormula()
elif isinstance(f, T):
return TrueFormula()
else:
raise ValueError
def setUp(self):
"""Set up test fixtures, if any."""
# Symbols
self.a_sym = Symbol("a")
self.b_sym = Symbol("b")
self.c_sym = Symbol("c")
# Propositions
self.a = AtomicFormula(self.a_sym)
self.b = AtomicFormula(self.b_sym)
self.c = AtomicFormula(self.c_sym)
# Propositionals
self.not_a = Not(self.a)
self.not_b = Not(self.b)
self.not_c = Not(self.c)
self.a_and_b = And(self.a, self.b)
self.a_and_c = And(self.a, self.c)
self.b_and_c = And(self.b, self.c)
self.abc = And(self.a, And(self.b, self.c))
self.b_or_c = Or(self.b, self.c)
self.a_or_b = Or(self.a, self.b)
self.not_abc = Not(And(self.a, And(self.b, self.c)))
### Path expression
# Tests
self.test_a = PathExpressionTest(self.a)
self.test_b = PathExpressionTest(self.b)
self.test_not_a = PathExpressionTest(self.not_a)
self.test_not_b = PathExpressionTest(self.not_b)
# Union
self.path_a_or_b = PathExpressionUnion(self.a, self.b)
self.path_b_or_c = PathExpressionUnion(self.b, self.c)
# Sequence
self.path_seq_a_and_b__a_and_c = PathExpressionSequence(
self.a_and_b, self.a_and_c)
self.path_a_or_b__b_or_c = PathExpressionSequence(
self.path_a_or_b, self.path_b_or_c)
# Stars
self.path_b_or_c_star = PathExpressionStar(self.path_b_or_c)
self.path_not_abc = PathExpressionStar(self.not_abc)
# Modal connective
self.eventually_propositional_a_and_b__a_and_c = PathExpressionEventually(
self.a_and_b, self.a_and_c)
self.eventually_test_a__c = PathExpressionEventually(
self.test_a, self.c)
self.eventually_test_a__b = PathExpressionEventually(
self.test_a, self.b)
self.eventually_seq_a_and_b__a_and_c__not_c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.not_c)
self.eventually_seq_a_and_b__a_and_c__c = PathExpressionEventually(
self.path_seq_a_and_b__a_and_c, self.c)
self.eventually_b_or_c_star__b_and_c = PathExpressionEventually(
self.path_b_or_c_star, self.b_and_c)
self.next_a_and_c = PathExpressionEventually(TrueFormula(),
self.a_and_c)
self.liveness_b_and_c = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.b_and_c)
self.liveness_abc = PathExpressionEventually(
PathExpressionStar(TrueFormula()), self.abc)
self.always_true__a = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.a)
self.always_true__b_or_c = PathExpressionAlways(
PathExpressionStar(TrueFormula()), self.b_or_c)
self.alphabet = Alphabet({self.a_sym, self.b_sym, self.c_sym})
# Traces
self.ldlf = LDLf(self.alphabet)
self.trace_1_list = [
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.a_sym, self.b_sym},
{self.a_sym, self.c_sym},
{self.b_sym, self.c_sym},
]
self.trace_1 = FiniteTrace(self.trace_1_list, self.alphabet)