def check_cex(self, fsm, explanation, agents, phi):
"""Check that the explanation is correct."""
# Get the cubes
gamma_cube = fsm.inputs_cube_for_agents(agents)
ngamma_cube = fsm.bddEnc.inputsCube - gamma_cube
# The first state satisfies the spec
self.assertTrue(explanation.state <= cex(fsm, agents, phi))
acts = BDD.false(fsm.bddEnc.DDmanager)
states = BDD.false(fsm.bddEnc.DDmanager)
for (act, succ) in explanation.successors:
ag_action = act.forsome(ngamma_cube)
# The successor satisfies phi
self.assertTrue(succ.state <= phi)
# The action is effectively possible
self.assertTrue(act <= fsm.get_inputs_between_states(
explanation.state, succ.state))
# Accumulate states and actions
acts = acts | act
states = states | succ.state
# The reached states are effectively the reachable states
# through the action
self.assertTrue(states <= fsm.post(explanation.state, ag_action))
self.assertTrue(states >= fsm.post(explanation.state, ag_action)
& fsm.bddEnc.statesMask)
# The actions are effectively all the possible actions completing ag_act
self.assertTrue(acts <= ag_action)
self.assertTrue(acts >= ag_action &
fsm.get_inputs_between_states(explanation.state, states) &
fsm.bddEnc.inputsMask)
def check_free_choice(self):
"""
Check whether this MAS satisfies the free-choice property, that is,
in every state, the choices of actions for each agent is not
constrained by the choices of other agents.
Return the set of moves that are not present in the MAS and should,
or that are present but should not.
"""
if len(self.agents) <= 0:
return BDD.false(self.bddEnc.DDmanager)
true = BDD.true(self.bddEnc.DDmanager)
protocols = {agent: self.protocol({agent}) for agent in self.agents}
enabled = (self.weak_pre(self.reachable_states) & self.reachable_states
& self.bddEnc.statesInputsMask)
for s in self.pick_all_states(self.reachable_states):
product = self.bddEnc.statesInputsMask
for agent in self.agents:
product &= protocols[agent] & s
if (enabled & s) != product:
return product.xor(enabled & s)
return BDD.false(self.bddEnc.DDmanager)
def test_get_false(self):
(fsm, enc, manager) = self.init_model()
false = BDD.false(manager)
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
false = BDD.false()
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
false = BDD.false()
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
def nfair_gamma_states(fsm, agents):
"""
Return the set of states in which agents cann avoid fair paths.
fsm -- the model
agents -- a list of agents names
"""
# NFair_Gamma = not([Gamma] G True) = <Gamma> F False
agents = frozenset(agents)
if agents not in __nfair_gamma_states:
if len(fsm.fairness_constraints) == 0:
__nfair_gamma_states[agents] = BDD.false(fsm.bddEnc.DDmanager)
else:
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f #& fsm.bddEnc.statesMask
res = res | fsm.pre_strat(fp(lambda Y :
(Z | nf) &
fsm.pre_strat(Y, agents),
BDD.true(fsm.bddEnc.DDmanager)),
agents)
return res
__nfair_gamma_states[agents] = fp(inner,
BDD.false(fsm.bddEnc.DDmanager))
return __nfair_gamma_states[agents]
def test_get_false(self):
(fsm, enc, manager) = self.init_model()
false = BDD.false(manager)
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
false = BDD.false()
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
false = BDD.false()
self.assertIsNotNone(false)
self.assertTrue(false.is_false())
self.assertFalse(false.is_true())
self.assertTrue(false.isnot_true())
self.assertFalse(false.isnot_false())
self.assertTrue(false.isnot_true())
def nfair_gamma_si(fsm, agents, strat=None):
"""
Return the set of state/inputs pairs of strat
in which agents can avoid a fair path in strat.
If strat is None, it is considered true.
fsm -- the model
agents -- a list of agents names
strat -- a BDD representing allowed state/inputs pairs, or None
"""
if not strat:
strat = BDD.true(fsm.bddEnc.DDmanager)
if len(fsm.fairness_constraints) == 0:
return BDD.false(fsm.bddEnc.DDmanager)
else:
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f & fsm.bddEnc.statesMask & strat
res = res | fsm.pre_strat_si(fp(lambda Y :
(Z | nf) &
fsm.pre_strat_si(Y, agents,
strat),
BDD.true(fsm.bddEnc.DDmanager)),
agents, strat)
return res
return fp(inner, BDD.false(fsm.bddEnc.DDmanager))
def ceu(fsm, agents, phi, psi):
"""
Return the set of states of fsm satisfying <agents>[phi U psi].
fsm -- a MAS representing the system
agents -- a list of agents names
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
"""
# phi = phi & fsm.bddEnc.statesInputsMask
# psi = psi & fsm.bddEnc.statesInputsMask
if len(fsm.fairness_constraints) == 0:
return fp(lambda Z: psi | (phi & fsm.pre_strat(Z, agents)), BDD.false(fsm.bddEnc.DDmanager))
else:
nfair = nfair_gamma_states(fsm, agents)
def inner(Z):
res = psi
for f in fsm.fairness_constraints:
nf = ~f # & fsm.bddEnc.statesMask
res = res | fsm.pre_strat(
fp(
lambda Y: (phi | psi | nfair) & (Z | nf) & (psi | fsm.pre_strat(Y, agents)),
BDD.true(fsm.bddEnc.DDmanager),
),
agents,
)
return (psi | phi | nfair) & res
return fp(inner, BDD.false(fsm.bddEnc.DDmanager))
def check_cex(self, fsm, explanation, agents, phi):
"""Check that the explanation is correct."""
# Get the cubes
gamma_cube = fsm.inputs_cube_for_agents(agents)
ngamma_cube = fsm.bddEnc.inputsCube - gamma_cube
# The first state satisfies the spec
self.assertTrue(explanation.state <= cex(fsm, agents, phi))
acts = BDD.false(fsm.bddEnc.DDmanager)
states = BDD.false(fsm.bddEnc.DDmanager)
for (act, succ) in explanation.successors:
ag_action = act.forsome(ngamma_cube)
# The successor satisfies phi
self.assertTrue(succ.state <= phi)
# The action is effectively possible
self.assertTrue(act <= fsm.get_inputs_between_states(
explanation.state, succ.state))
# Accumulate states and actions
acts = acts | act
states = states | succ.state
# The reached states are effectively the reachable states
# through the action
self.assertTrue(states <= fsm.post(explanation.state, ag_action))
self.assertTrue(states >= fsm.post(explanation.state, ag_action)
& fsm.bddEnc.statesMask)
# The actions are effectively all the possible actions completing ag_act
self.assertTrue(acts <= ag_action)
self.assertTrue(acts >= ag_action &
fsm.get_inputs_between_states(explanation.state, states) &
fsm.bddEnc.inputsMask)
def ceu(fsm, agents, phi, psi):
"""
Return the set of states of fsm satisfying <agents>[phi U psi].
fsm -- a MAS representing the system
agents -- a list of agents names
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
"""
#phi = phi & fsm.bddEnc.statesInputsMask
#psi = psi & fsm.bddEnc.statesInputsMask
if len(fsm.fairness_constraints) == 0:
return fp(lambda Z : psi | (phi & fsm.pre_strat(Z, agents)),
BDD.false(fsm.bddEnc.DDmanager))
else:
nfair = nfair_gamma_states(fsm, agents)
def inner(Z):
res = psi
for f in fsm.fairness_constraints:
nf = ~f #& fsm.bddEnc.statesMask
res = res | fsm.pre_strat(fp(lambda Y :
(phi | psi | nfair) &
(Z | nf) &
(psi | fsm.pre_strat(Y, agents)),
BDD.true(fsm.bddEnc.DDmanager)),
agents)
return (psi | phi | nfair) & res
return fp(inner, BDD.false(fsm.bddEnc.DDmanager))
def _nfair(mas, formula, agents):
"""
Return the set of states in which the given agents cannot avoid a fair path
by using the strategy encoded in these states.
"""
jump = mas.transitions[formula]["jump"]
equiv = mas.transitions[formula]["equiv"]
follow = mas.transitions[formula]["follow"]
if not mas.fairness_constraints:
return BDD.false(mas)
else:
# nfair =
# mu Z. \/_fc []_group_follow(nu Y. (Z \/ ~fc) /\ []_group_follow(Y))
def inner(Z):
# \/_fc []_group_follow(nu Y. (Z \/ ~fc) /\ []_group_follow(Y))
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc
res = res | ~follow.pre(~fixpoint(
lambda Y: (Z | nfc) & ~follow.pre(~Y), BDD.true(mas)))
return res
res = fixpoint(inner, BDD.false(mas))
return res
def check_cax(self, fsm, explanation, agents, phi):
"""Check that the explanation is correct."""
# Get the cubes
gamma_cube = fsm.inputs_cube_for_agents(agents)
ngamma_cube = fsm.bddEnc.inputsCube - gamma_cube
# The first state satisfies the spec
self.assertTrue(explanation.state <= ~cex(fsm, agents, ~phi))
acts = BDD.false(fsm.bddEnc.DDmanager)
states = BDD.false(fsm.bddEnc.DDmanager)
for (act, succ) in explanation.successors:
# The successor satisfies phi
self.assertTrue(succ.state <= phi)
# The action is effectively possible
self.assertTrue(act <= fsm.get_inputs_between_states(
explanation.state, succ.state))
# Accumulate states and actions
acts = acts | act
states = states | succ.state
# The actions are effectively all the possible ones
self.assertEqual((fsm.protocol(agents) &
explanation.state).forsome(fsm.bddEnc.statesCube).
forsome(ngamma_cube) &
fsm.bddEnc.statesMask,
acts.forsome(ngamma_cube) & fsm.bddEnc.statesMask)
def ceu(fsm, agents, phi, psi, strat=None):
"""
Return the set of states of strat satisfying <agents>[phi U psi]
under full observability in strat.
If strat is None, strat is considered true.
fsm -- a MAS representing the system
agents -- a list of agents names
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
strat -- a BDD representing allowed state/inputs pairs, or None
"""
if len(fsm.fairness_constraints) == 0:
return fp(lambda Z : psi | (phi & fsm.pre_strat(Z, agents, strat)),
BDD.false(fsm.bddEnc.DDmanager))
else:
nfair = nfair_gamma(fsm, agents, strat)
def inner(Z):
res = psi
for f in fsm.fairness_constraints:
nf = ~f
res = res | fsm.pre_strat(fp(lambda Y :
(phi | psi | nfair) &
(Z | nf) &
(psi |
fsm.pre_strat(Y, agents, strat)),
BDD.true(fsm.bddEnc.DDmanager)),
agents, strat)
return (psi | phi | nfair) & res
return fp(inner, BDD.false(fsm.bddEnc.DDmanager))
def nfair_ce_moves(mas, agents, moves):
"""
mas -- a multi-agent system;
agents -- a subset of agents of mas;
moves -- a closed set of moves for agents.
"""
# If there are no fairness constraints, there are no nfair states.
if not mas.fairness_constraints:
return BDD.false(mas)
else:
def inner(Z):
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc & mas.bddEnc.statesMask
nfc_moves = nfc & mas.protocol(agents) & moves
m = stay_ce_moves(mas,
agents,
Z | nfc_moves,
BDD.false(mas),
moves)
res |= pre_ce_moves(mas, agents, m, moves)
return res
return fixpoint(inner, BDD.false(mas))
def nfair_gamma_si(fsm, agents, strat=None):
"""
Return the set of state/inputs pairs of strat
in which agents can avoid a fair path in strat.
If strat is None, it is considered true.
fsm -- the model
agents -- a list of agents names
strat -- a BDD representing allowed state/inputs pairs, or None
"""
if not strat:
strat = BDD.true(fsm.bddEnc.DDmanager)
if len(fsm.fairness_constraints) == 0:
return BDD.false(fsm.bddEnc.DDmanager)
else:
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f & fsm.bddEnc.statesMask & strat
res = res | fsm.pre_strat_si(
fp(lambda Y: (Z | nf) & fsm.pre_strat_si(Y, agents, strat),
BDD.true(fsm.bddEnc.DDmanager)), agents, strat)
return res
return fp(inner, BDD.false(fsm.bddEnc.DDmanager))
def nfair_gamma_states(fsm, agents):
"""
Return the set of states in which agents cann avoid fair paths.
fsm -- the model
agents -- a list of agents names
"""
# NFair_Gamma = not([Gamma] G True) = <Gamma> F False
agents = frozenset(agents)
if agents not in __nfair_gamma_states:
if len(fsm.fairness_constraints) == 0:
__nfair_gamma_states[agents] = BDD.false(fsm.bddEnc.DDmanager)
else:
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f # & fsm.bddEnc.statesMask
res = res | fsm.pre_strat(
fp(lambda Y: (Z | nf) & fsm.pre_strat(Y, agents), BDD.true(fsm.bddEnc.DDmanager)), agents
)
return res
__nfair_gamma_states[agents] = fp(inner, BDD.false(fsm.bddEnc.DDmanager))
return __nfair_gamma_states[agents]
def check_free_choice(self):
"""
Check whether this MAS satisfies the free-choice property, that is,
in every state, the choices of actions for each agent is not
constrained by the choices of other agents.
Return the set of moves that are not present in the MAS and should,
or that are present but should not.
"""
if len(self.agents) <= 0:
return BDD.false(self.bddEnc.DDmanager)
true = BDD.true(self.bddEnc.DDmanager)
protocols = {agent: self.protocol({agent}) for agent in self.agents}
enabled = (self.weak_pre(self.reachable_states) &
self.reachable_states & self.bddEnc.statesInputsMask)
for s in self.pick_all_states(self.reachable_states):
product = self.bddEnc.statesInputsMask
for agent in self.agents:
product &= protocols[agent] & s
if (enabled & s) != product:
return product.xor(enabled & s)
return BDD.false(self.bddEnc.DDmanager)
def check_cax(self, fsm, explanation, agents, phi):
"""Check that the explanation is correct."""
# Get the cubes
gamma_cube = fsm.inputs_cube_for_agents(agents)
ngamma_cube = fsm.bddEnc.inputsCube - gamma_cube
# The first state satisfies the spec
self.assertTrue(explanation.state <= ~cex(fsm, agents, ~phi))
acts = BDD.false(fsm.bddEnc.DDmanager)
states = BDD.false(fsm.bddEnc.DDmanager)
for (act, succ) in explanation.successors:
# The successor satisfies phi
self.assertTrue(succ.state <= phi)
# The action is effectively possible
self.assertTrue(act <= fsm.get_inputs_between_states(
explanation.state, succ.state))
# Accumulate states and actions
acts = acts | act
states = states | succ.state
# The actions are effectively all the possible ones
self.assertEqual((fsm.protocol(agents) &
explanation.state).forsome(fsm.bddEnc.statesCube).
forsome(ngamma_cube) &
fsm.bddEnc.statesMask,
acts.forsome(ngamma_cube) & fsm.bddEnc.statesMask)
def inner(Z):
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc & mas.bddEnc.statesMask
states = stay_ce(mas, agents, Z | nfc, BDD.false(mas), moves)
res |= pre_ce(mas, agents, states, moves)
return res
def test_init(self):
fsm = self.init_model()
manager = fsm.bddEnc.DDmanager
init = fsm.init
initState = fsm.pick_one_state(init)
self.assertTrue(BDD.false(manager) <= init <= BDD.true(manager))
self.assertTrue(BDD.false(manager) < initState <= init)
def eval_strat_FSF(fsm, spec):
"""
Return the BDD representing the set of states of fsm satisfying spec.
spec is a strategic operator <G> pi.
Implement a variant of the algorithm that
filters, splits and then filters.
fsm -- a MAS representing the system;
spec -- an AST-based ATLK specification with a top strategic operator.
"""
if type(spec) is CAX:
# [g] X p = ~<g> X ~p
newspec = CEX(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAG:
# [g] G p = ~<g> F ~p
newspec = CEF(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAU:
# [g][p U q] = ~<g>[ ~q W ~p & ~q ]
newspec = CEW(spec.group,
Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAF:
# [g] F p = ~<g> G ~p
newspec = CEG(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAW:
# [g][p W q] = ~<g>[~q U ~p & ~q]
newspec = CEU(spec.group,
Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat_FSF(fsm, newspec)
sat = BDD.false(fsm.bddEnc.DDmanager)
agents = {atom.value for atom in spec.group}
# First filtering
winning = filter_strat(fsm, spec, variant="FSF")
if winning.is_false(): # no state/inputs pairs are winning => return false
return winning
return split_eval(fsm, spec, BDD.false(fsm.bddEnc.DDmanager),
winning)
def inner(Z):
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc & mas.bddEnc.statesMask
nfc_moves = nfc & mas.protocol(agents) & moves
m = stay_ce_moves(mas,
agents,
Z | nfc_moves,
BDD.false(mas),
moves)
res |= pre_ce_moves(mas, agents, m, moves)
return res
def eval_strat_FSF(fsm, spec):
"""
Return the BDD representing the set of states of fsm satisfying spec.
spec is a strategic operator <G> pi.
Implement a variant of the algorithm that
filters, splits and then filters.
fsm -- a MAS representing the system;
spec -- an AST-based ATLK specification with a top strategic operator.
"""
if type(spec) is CAX:
# [g] X p = ~<g> X ~p
newspec = CEX(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAG:
# [g] G p = ~<g> F ~p
newspec = CEF(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAU:
# [g][p U q] = ~<g>[ ~q W ~p & ~q ]
newspec = CEW(spec.group, Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAF:
# [g] F p = ~<g> G ~p
newspec = CEG(spec.group, Not(spec.child))
return ~eval_strat_FSF(fsm, newspec)
elif type(spec) is CAW:
# [g][p W q] = ~<g>[~q U ~p & ~q]
newspec = CEU(spec.group, Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat_FSF(fsm, newspec)
sat = BDD.false(fsm.bddEnc.DDmanager)
agents = {atom.value for atom in spec.group}
# First filtering
winning = filter_strat(fsm, spec, variant="FSF")
if winning.is_false(): # no state/inputs pairs are winning => return false
return winning
return split_eval(fsm, spec, BDD.false(fsm.bddEnc.DDmanager), winning)
def split_eval(fsm, spec, common, rest):
"""
Split strats into all its non-conflicting greatest subsets and compute
the states that satisfy spec in strats.
fsm -- the model
strats -- a BDD representing a set of states/inputs pairs
spec -- an AST-based ATLK specification with a top strategic operator.
"""
if (common | rest).is_false():
return common | rest
else:
gamma = {atom.value for atom in spec.group}
sat = BDD.false(fsm.bddEnc.DDmanager)
for newcommon, splitted, newrest in split_one(fsm, rest, gamma):
if splitted.is_false():
# newcommon contains a partial uniform strategy
# we can extract the winning states
# from newcommon | common
# first, filter
winning = (filter_strat(fsm, spec, common | newcommon, "SF")
.forsome(fsm.bddEnc.inputsCube))
# then, get equiv sat
sat = sat | all_equiv_sat(fsm, winning, gamma)
gc.collect()
else:
sat = sat | split_eval(fsm, spec, common | newcommon | splitted,
newrest)
return sat
def test_size(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
noadmin = eval_simple_expression(fsm, "admin = none")
alice = eval_simple_expression(fsm, "admin = alice")
processing = eval_simple_expression(fsm, "state = processing")
self.assertEqual(BDD.true().size, 1)
self.assertEqual(BDD.false().size, 1)
self.assertEqual(fsm.pick_one_state(BDD.true()).size,
len(fsm.bddEnc.get_variables_ordering("bits")) + 1)
self.assertEqual(init.size, 5)
self.assertEqual(processing.size, 3)
def get_equiv_class(fsm, gamma, state, semantics="group"):
"""
Return the equivalence class for gamma state belongs to. The equivalence
class depends on semantics; if semantics is individual, the common
knowledge based equivalence class for gamma containing state is returned;
otherwise (assuming semantics is group), the distributed knowledge based
equivalence fo gamma containing state is returned.
fsm -- the model
gamma -- a set of agents of fsm
semantics -- the semantic to use (group or individual);
if not "individual", "group" semantics is used
"""
if semantics == "individual":
old = BDD.false(fsm.bddEnc.DDmanager)
eq = state
while old != eq:
old = eq
for agent in gamma:
eq |= (fsm.equivalent_states(old, {agent}) &
fsm.reachable_states)
return eq
else:
return fsm.equivalent_states(state, gamma) & fsm.reachable_states
def inner(Z):
res = phi
for f in fsm.fairness_constraints:
res = res & fsm.pre(fp(lambda Y : (Z & f) |
(phi & fsm.pre(Y)),
BDD.false(fsm.bddEnc.DDmanager)))
return res
def get_equiv_class(fsm, gamma, state, semantics="group"):
"""
Return the equivalence class for gamma state belongs to. The equivalence
class depends on semantics; if semantics is individual, the common
knowledge based equivalence class for gamma containing state is returned;
otherwise (assuming semantics is group), the distributed knowledge based
equivalence fo gamma containing state is returned.
fsm -- the model
gamma -- a set of agents of fsm
semantics -- the semantic to use (group or individual);
if not "individual", "group" semantics is used
"""
if semantics == "individual":
old = BDD.false(fsm.bddEnc.DDmanager)
eq = state
while old != eq:
old = eq
for agent in gamma:
eq |= (fsm.equivalent_states(old, {agent}) &
fsm.reachable_states)
return eq
else:
return fsm.equivalent_states(state, gamma) & fsm.reachable_states
def split_one_all(mas, agents, agent, moves):
"""
Split one equivalence class of moves and return couples composed of
a split and the rest of moves to split; the last couple is the rest of
moves to split only, the split being empty.
mas -- a multi-agents system;
agents -- a subset of agents of mas;
agent -- an agent of agents;
moves -- a subset of moves for agents.
Return a generator of all couples of splits and rest of moves, the last
couple containing an empty split.
"""
if moves.is_false():
yield (moves, moves)
return
else:
# Get one equivalence class
si = mas.pick_one_state_inputs(moves)
s = si.forsome(mas.bddEnc.inputsCube)
eqs = get_equiv_class(mas, [agent], s)
eqcl = moves & eqs
# Remove it from strats
moves = moves - eqcl
# The current equivalence class is conflicting
for non_conflicting in split_conflicting(mas, agents, agent, eqcl):
yield (non_conflicting, moves)
yield (BDD.false(mas.bddEnc.DDmanager), moves)
return
def inner(Z):
res = phi
for f in fsm.fairness_constraints:
res = res & fsm.pre_nstrat(
fp(lambda Y: (Z & f) | (phi & fsm.pre_nstrat(Y, agents)), BDD.false(fsm.bddEnc.DDmanager)), agents
)
return res
def inner(Z):
res = Z
for f in fsm.fairness_constraints:
res = res & fixpoint(lambda Y : (Z & f) | (phi &
fsm.weak_pre(Y.forsome(fsm.bddEnc.inputsCube))),
BDD.false(fsm.bddEnc.DDmanager))
return phi & fsm.weak_pre(res.forsome(fsm.bddEnc.inputsCube))
def test_size(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
noadmin = eval_simple_expression(fsm, "admin = none")
alice = eval_simple_expression(fsm, "admin = alice")
processing = eval_simple_expression(fsm, "state = processing")
self.assertEqual(BDD.true().size, 1)
self.assertEqual(BDD.false().size, 1)
self.assertEqual(
fsm.pick_one_state(BDD.true()).size,
len(fsm.bddEnc.get_variables_ordering("bits")) + 1)
self.assertEqual(init.size, 5)
self.assertEqual(processing.size, 3)
def test_false(self):
ast = negation_normal_form(
parse_ctlq("A['admin = bob' oW A['admin = alice' oU AG ?]]"))
self.assertTrue(check_ctlqx(ast))
fsm = self.init_model()
self.assertEqual(solve_ctlqx(fsm, ast),
BDD.false(fsm.bddEnc.DDmanager))
def split_eval(fsm, spec, common, rest):
"""
Split strats into all its non-conflicting greatest subsets and compute
the states that satisfy spec in strats.
fsm -- the model
strats -- a BDD representing a set of states/inputs pairs
spec -- an AST-based ATLK specification with a top strategic operator.
"""
if (common | rest).is_false():
return common | rest
else:
gamma = {atom.value for atom in spec.group}
sat = BDD.false(fsm.bddEnc.DDmanager)
for newcommon, splitted, newrest in split_one(fsm, rest, gamma):
if splitted.is_false():
# newcommon contains a partial uniform strategy
# we can extract the winning states
# from newcommon | common
# first, filter
winning = (filter_strat(fsm, spec, common | newcommon,
"SF").forsome(fsm.bddEnc.inputsCube))
# then, get equiv sat
sat = sat | all_equiv_sat(fsm, winning, gamma)
gc.collect()
else:
sat = sat | split_eval(fsm, spec,
common | newcommon | splitted, newrest)
return sat
def inner(Z):
res = BDD.true(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
res = res & run.pre(
fixpoint(lambda Y: (Z & fc) | run.pre(Y), BDD.false(mas)))
return res
def test_false(self):
ast = negation_normal_form(
parse_ctlq("A['admin = bob' oW A['admin = alice' oU AG ?]]")
)
self.assertTrue(check_ctlqx(ast))
fsm = self.init_model()
self.assertEqual(solve_ctlqx(fsm, ast),
BDD.false(fsm.bddEnc.DDmanager))
def eg(fsm, phi):
res = BDD.true(fsm.bddEnc.DDmanager)
old = BDD.false(fsm.bddEnc.DDmanager)
while res != old:
old = res
new = ex(fsm, res)
res = res & new & phi & fsm.reachable_states
return res
def eg(fsm, phi):
res = BDD.true(fsm.bddEnc.DDmanager)
old = BDD.false(fsm.bddEnc.DDmanager)
while res != old:
old = res
new = ex(fsm, res)
res = res & new & phi & fsm.reachable_states
return res
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f # & fsm.bddEnc.statesMask
res = res | fsm.pre_strat(
fp(lambda Y: (Z | nf) & fsm.pre_strat(Y, agents), BDD.true(fsm.bddEnc.DDmanager)), agents
)
return res
def inner(Z):
res = BDD.false(fsm.bddEnc.DDmanager)
for f in fsm.fairness_constraints:
nf = ~f & fsm.bddEnc.statesMask & strat
res = res | fsm.pre_strat_si(
fp(lambda Y: (Z | nf) & fsm.pre_strat_si(Y, agents, strat),
BDD.true(fsm.bddEnc.DDmanager)), agents, strat)
return res
def reach(mas, states):
"""
Return the set of states reachable from states in mas.
mas -- a multi-agents system;
states -- a subset of states of mas.
"""
return fixpoint(lambda Z: states | mas.post(Z), BDD.false(mas))
def inner(Z):
res = Z
for f in fsm.fairness_constraints:
res = res & fixpoint(
lambda Y: (Z & f) |
(phi & fsm.weak_pre(Y.forsome(fsm.bddEnc.inputsCube))),
BDD.false(fsm.bddEnc.DDmanager))
return phi & fsm.weak_pre(res.forsome(fsm.bddEnc.inputsCube))
def inner(Z):
res = BDD.true(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
res = res & run.pre(
fixpoint(
lambda Y: (states_2 & _fair(mas))
| (Z & fc) | (states_1 & run.pre(Y)), BDD.false(mas)))
return (res & states_1) | (states_2 & _fair(mas))
def inner(Z):
# \/_fc []_group_follow(nu Y. (Z \/ ~fc) /\ []_group_follow(Y))
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc
res = res | ~follow.pre(~fixpoint(
lambda Y: (Z | nfc) & ~follow.pre(~Y), BDD.true(mas)))
return res
def filter_ceu_moves(mas, agents, moves_1, moves_2, moves):
"""
mas -- a multi-agent system;
agents -- a subset of agents of mas;
moves_1 -- a subset of moves for agents;
moves_2 -- a subset of moves for agents;
moves -- a closed set of moves for agents.
"""
# Abstract away actions of states
states_1 = moves_1.forsome(mas.bddEnc.inputsCube)
states_2 = moves_2.forsome(mas.bddEnc.inputsCube)
states_1 = states_1 & mas.bddEnc.statesMask
states_2 = states_2 & mas.bddEnc.statesMask
moves_1 = states_1 & mas.protocol(agents)
moves_2 = states_2 & mas.protocol(agents)
# If there are no fairness constraints, the computation is simpler
if not mas.fairness_constraints:
# mu Q'. moves_2 & moves | (moves_1 & moves & pre_ce_moves(Q'))
return fixpoint(lambda Z: moves_2 & moves |
(moves_1 &
moves &
pre_ce_moves(mas, agents, Z, moves)),
BDD.false(mas))
else:
moves_1_2_n = moves_1 | moves_2 | nfair_ce_moves(mas, agents, moves)
moves_1_2_n = moves_1_2_n & moves
def inner(Z):
res = moves_2 & moves
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc & mas.bddEnc.statesMask
moves_nfc = nfc & mas.protocol(agents) & moves
m = stay_ce_moves(mas,
agents,
moves_1_2_n & (Z | moves_nfc),
moves_2 & moves & (Z | moves_nfc),
moves)
res |= pre_ce_moves(mas, agents, m, moves)
return res & moves_1_2_n
return fixpoint(inner, BDD.false(mas))
def eval_ceu(mas, formula, agents, states_1, states_2):
jump = mas.transitions[formula]["jump"]
equiv = mas.transitions[formula]["equiv"]
follow = mas.transitions[formula]["follow"]
reachable = mas.reachable_states
if not mas.fairness_constraints:
# <group>i[p U q] =
# <>_group_jump []_group_equiv
# (reachable => mu Z . q \/ (p /\ []_group_follow Z))
return jump.pre(~equiv.pre(~(reachable.imply(
fixpoint(lambda Z: states_2 |
(states_1 & ~follow.pre(~Z)), BDD.false(mas))))))
else:
nfair = _nfair(mas, formula, agents)
# <group>i fair [p U q] =
# <>_group_jump []_group_equiv
# reachable =>
# mu Z. (p \/ q \/ ~ifair) /\
# (q \/_fc []_group_follow
# (nu Y. (Z \/ ~fc) /\
# (p \/ q \/ ~ifair) /\
# (q \/ []_group_follow(Y))))
def inner(Z):
# (p \/ q \/ ~ifair) /\
# (q \/_fc []_group_follow
# (nu Y. (Z \/ ~fc) /\
# (p \/ q \/ ~ifair) /\
# (q \/ []_group_follow(Y))))
res = BDD.false(mas)
for fc in mas.fairness_constraints:
fc = fc.forsome(mas.bddEnc.inputsCube)
nfc = ~fc
# []_group_follow (nu Y. (Z \/ ~fc) /\
# (p \/ q \/ ~ifair) /\
# (q \/ []_group_follow(Y)))
res = res | ~follow.pre(~(fixpoint(
lambda Y: ((Z | nfc) & (states_1 | states_2 | nfair) &
(states_2 | ~follow.pre(~Y))), BDD.true(mas))))
return ((states_1 | states_2 | nfair) & (states_2 | res))
return jump.pre(
~equiv.pre(~(reachable.imply(fixpoint(inner, BDD.false(mas))))))
def eval_strat(fsm, spec):
"""
Return the BDD representing the set of states of fsm satisfying spec.
spec is a strategic operator <G> pi.
fsm -- a MAS representing the system;
spec -- an AST-based ATLK specification with a top strategic operator.
"""
if type(spec) is CAX:
# [g] X p = ~<g> X ~p
newspec = CEX(spec.group, Not(spec.child))
return ~eval_strat(fsm, newspec)
elif type(spec) is CAG:
# [g] G p = ~<g> F ~p
newspec = CEF(spec.group, Not(spec.child))
return ~eval_strat(fsm, newspec)
elif type(spec) is CAU:
# [g][p U q] = ~<g>[ ~q W ~p & ~q ]
newspec = CEW(spec.group,
Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat(fsm, newspec)
elif type(spec) is CAF:
# [g] F p = ~<g> G ~p
newspec = CEG(spec.group, Not(spec.child))
return ~eval_strat(fsm, newspec)
elif type(spec) is CAW:
# [g][p W q] = ~<g>[~q U ~p & ~q]
newspec = CEU(spec.group,
Not(spec.right),
And(Not(spec.left), Not(spec.right)))
return ~eval_strat(fsm, newspec)
sat = BDD.false(fsm.bddEnc.DDmanager)
agents = {atom.value for atom in spec.group}
return split_eval(fsm, spec, BDD.false(fsm.bddEnc.DDmanager),
fsm.protocol(agents) & fsm.reachable_states)
def ceu(fsm, agents, phi, psi):
"""
Return the set of states of fsm satisfying <agents>[phi U psi].
fsm -- a MAS representing the system
agents -- a list of agents names
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
"""
return fp(lambda Y: psi | (phi & fsm.pre_strat(Y, agents)), BDD.false(fsm.bddEnc.DDmanager))
def eu(fsm, phi, psi):
"""
Return the set of states of fsm satisfying E[ phi U psi ].
fsm -- a MAS representing the system
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
"""
return fp(lambda Z: (psi | (phi & fsm.pre(Z))),
BDD.false(fsm.bddEnc.DDmanager))
def eu(fsm, phi, psi):
"""
Return the set of states of fsm satisfying E[ phi U psi ].
fsm -- a MAS representing the system
phi -- a BDD representing the set of states of fsm satisfying phi
psi -- a BDD representing the set of states of fsm satisfying psi
"""
return fp(lambda Z: (psi | (phi & fsm.pre(Z))),
BDD.false(fsm.bddEnc.DDmanager))
def explain_ceu(fsm, state, agents, phi, psi, states=None):
"""
Explain why state of fsm satisfies <agents> phi U psi.
fsm -- the fsm;
state -- a state of fsm satisfying <agents> phi U psi;
agents -- the agents of the specification;
phi -- the set of states of fsm satifying phi;
psi -- the set of states of fsm satifying psi;
states -- a dictionary of state->explanation pairs.
"""
# <agents> phi U psi = mu Y. psi | (phi & fsm.pre_strat(Y, agents))
# To show that state satisfies <agents> phi U psi
# if state in psi, return Explanation(state) because state is its own
# explanation
# otherwise, compute the fixpoint, until state is in the last set
# then choose one action always leading to states of the previous set
# (it is possible because state is added because it can go one step in
# the right direction), and recursively explain why the found states
# satisfy <agents> phi U psi.
# states is used to store already explained states and create a directed
# acyclic graph instead of the pure execution tree, to avoid a blow up
# in terms of number of states.
if states is None:
states = {}
if state in states:
return states[state]
if state <= psi:
new = Explanation(state)
states[state] = new
return new
else:
f = lambda Y : psi | (phi & fsm.pre_strat(Y, agents))
old = BDD.false(fsm.bddEnc.DDmanager)
new = psi
while not state <= new:
old = new
new = f(old)
expl = explain_cex(fsm, state, agents, old)
successors = set()
for action, succ in expl.successors:
successors.add((action,
explain_ceu(fsm, succ.state, agents,
phi, psi, states)))
new = Explanation(state, successors)
states[state] = new
return new
def test_true_false_equalities(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
self.assertTrue(false != true)
self.assertFalse(false == true)
self.assertTrue(false == false)
self.assertTrue(true == true)
self.assertTrue((false != true) == (not false == true))
def inner(Z):
res = phi
for f in fsm.fairness_constraints:
res = res & fsm.pre_nstrat(
fp(
lambda Y: (psi & fair_gamma_states(fsm, agents)) | (Z & f) | (phi & fsm.pre_nstrat(Y, agents)),
BDD.false(fsm.bddEnc.DDmanager),
),
agents,
)
return (psi & fair_gamma_states(fsm, agents)) | res
def test_true_false_xor(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
self.assertTrue(true ^ false == true)
self.assertTrue(true ^ true == false)
self.assertTrue(false ^ false == false)
self.assertTrue(init ^ true == ~init)
self.assertTrue(init ^ false == init)
def test_true_false_not(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
self.assertTrue(~true == -true)
self.assertTrue(~false == -false)
self.assertTrue(~true == false)
self.assertTrue(~false == true)
self.assertTrue(false < ~init < true)
def test_true_false_or(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
self.assertTrue((true | false) == (true + false))
self.assertTrue(true | false == true)
self.assertTrue(true | true == true)
self.assertTrue(false | false == false)
self.assertTrue(init | true == true)
self.assertTrue(init | false == init)
def test_true_false_and(self):
(fsm, enc, manager) = self.init_model()
true = BDD.true(manager)
false = BDD.false(manager)
init = fsm.init
self.assertTrue((true & false) == (true * false))
self.assertTrue(true & false == false)
self.assertTrue(true & true == true)
self.assertTrue(false & false == false)
self.assertTrue(init & true == init)
self.assertTrue(init & false == false)
def test_pick_states_inputs(self):
fsm = self.model()
false = BDD.false(fsm.bddEnc.DDmanager)
true = BDD.true(fsm.bddEnc.DDmanager)
p = evalSexp(fsm, "p")
q = evalSexp(fsm, "q")
a = evalSexp(fsm, "a")
pstates = fsm.pick_all_states_inputs(p & a)
self.assertEqual(len(pstates), 2)
for pstate in pstates:
self.assertTrue(false < pstate < p)
def test_fairness(self):
fsm = BddFsm.from_filename("tests/pynusmv/models/counters-fair.smv")
self.assertIsNotNone(fsm)
false = BDD.false(fsm.bddEnc.DDmanager)
true = BDD.true(fsm.bddEnc.DDmanager)
rc1 = evalSexp(fsm, "run = rc1")
rc2 = evalSexp(fsm, "run = rc2")
fairBdds = fsm.fairness_constraints
self.assertEqual(len(fairBdds), 2)
for fair in fairBdds:
self.assertTrue(fair == rc1 or fair == rc2)