def test_attractor():
g = TransitionSystem()
g.vars['x'] = 'bool'
g.env_vars.add('x')
g.add_path([0, 1, 2, 3])
g.add_edge(4, 1, formula='x')
aut = logicizer.graph_to_logic(g, 'loc', True)
aut.plus_one = True
aut.moore = True
aut.build()
target = aut.add_expr('loc = 2')
u = fx.attractor(aut.action['env'], aut.action['sys'], target, aut)
ok = {0: True, 1: True, 2: True, 3: False, 4: False}
for q, value in ok.items():
subs = dict(loc=q)
v = aut.let(subs, u)
assert (v == aut.true) == value, v
inside = aut.add_expr('loc > 0')
u = fx.attractor(aut.action['env'],
aut.action['sys'],
target,
aut,
inside=inside)
ok = {0: False, 1: True, 2: True, 3: False, 4: False}
for q, value in ok.items():
subs = dict(loc=q)
v = aut.let(subs, u)
assert (v == aut.true) == value, v
def counter_example():
g = TransitionSystem()
g.add_path([0, 1, 2, 3, 4])
g.add_path([5, 6, 7, 0])
g.add_edge(4, 5, formula="x")
g.add_edge(4, 1, formula="!x")
g.add_edge(1, 0)
g.add_edge(3, 2)
g.vars = dict(x='bool')
g.env_vars.add('x')
# g.dump('sys_graph_2.pdf')
#
aut_g = graph_to_logic(g, 'pc', ignore_initial=True)
#
aut = Automaton()
aut.players = dict(alice=0, bob=1)
aut.vars = dict(
pc=dict(type='saturating', dom=(0, 7), owner='alice'),
x=dict(type='bool', owner='bob'),
_i=dict(type='saturating', dom=(0, 1), owner='alice'))
aut.action['alice'] = [aut_g.action['sys'][0]]
aut.win['alice: []<>'] = ['pc = 6']
aut.win['bob: []<>'] = ['True']
fill_blanks(aut)
print(aut)
aut = aut.build()
make_assumptions(aut)
def test_attractor():
g = TransitionSystem()
g.vars['x'] = 'bool'
g.env_vars.add('x')
g.add_path([0, 1, 2, 3])
g.add_edge(4, 1, formula='x')
aut = logicizer.graph_to_logic(g, 'loc', True)
aut.plus_one = True
aut.moore = True
aut.build()
target = aut.add_expr('loc = 2')
u = fx.attractor(aut.action['env'], aut.action['sys'],
target, aut)
ok = {0: True, 1: True, 2: True, 3: False, 4: False}
for q, value in ok.items():
subs = dict(loc=q)
v = aut.let(subs, u)
assert (v == aut.true) == value, v
inside = aut.add_expr('loc > 0')
u = fx.attractor(aut.action['env'], aut.action['sys'],
target, aut, inside=inside)
ok = {0: False, 1: True, 2: True, 3: False, 4: False}
for q, value in ok.items():
subs = dict(loc=q)
v = aut.let(subs, u)
assert (v == aut.true) == value, v
def counter_example():
g = TransitionSystem()
g.add_path([0, 1, 2, 3, 4])
g.add_path([5, 6, 7, 0])
g.add_edge(4, 5, formula="x")
g.add_edge(4, 1, formula="~ x")
g.add_edge(1, 0)
g.add_edge(3, 2)
g.vars = dict(x='bool')
g.env_vars.add('x')
# g.dump('sys_graph_2.pdf')
#
aut_g = graph_to_logic(g, 'pc', ignore_initial=True)
#
aut = sym.Automaton()
aut.players = dict(alice=0, bob=1)
table = dict(pc=dict(type='saturating', dom=(0, 7), owner='alice'),
x=dict(type='bool', owner='bob'),
_i=dict(type='saturating', dom=(0, 1), owner=None))
aut.add_vars(table, flexible=True)
aut.varlist = dict(alice=['pc'], bob=['x'])
aut.init_expr = dict(alice='TRUE', bob='TRUE')
aut.action_expr = dict(alice=aut_g.action['sys'][0], bob='TRUE')
aut.win_expr = dict(alice={'[]<>': ['pc = 6']}, bob={'[]<>': ['True']})
# TODO: sym.fill_blanks(aut)
print(aut)
aut.build()
make_assumptions(aut)
def test_logicizer_env():
g = TransitionSystem()
g.vars['x'] = 'bool'
g.owner = 'env'
g.add_edge(0, 1, x=True)
g.add_edge(1, 2, formula="x'")
g.add_edge(2, 1)
(env_init, env_act, sys_init,
sys_act) = logicizer._graph_to_formulas(g,
nodevar='k',
ignore_initial=True,
self_loops=True)
s = stx.conj(env_act)
e1 = "(((((k = 0)) => (((x <=> True)) /\ ((k' = 1)))) \n"
e2 = "(((((k = 0)) => (((k' = 1)) /\ ((x <=> True)))) \n"
assert s.startswith(e1) or s.startswith(e2), s
e3 = ("/\ (((k = 1)) => ((x') /\ ((k' = 2))))) \n"
"/\ (((k = 2)) => ((k' = 1)))) \/ (k' = k)")
assert s.endswith(e3), s
# test automaton
aut = logicizer.graph_to_logic(g, nodevar='k', ignore_initial=True)
assert 'x' in aut.vars, aut.vars
assert 'k' in aut.vars, aut.vars
xtype = aut.vars['x']['type']
ktype = aut.vars['k']['type']
assert xtype == 'bool', xtype
assert ktype == 'int', ktype
def test_descendants():
g = TransitionSystem()
g.add_path([0, 1, 2])
aut = logicizer.graph_to_logic(g, 'pc', True)
source = aut.add_expr('pc = 0')
constrain = aut.true
v = fx.descendants(source, constrain, aut)
assert v == aut.add_expr('pc_0 <=> ~ pc_1'), _to_expr(v, aut)
def test_descendants():
g = TransitionSystem()
g.add_path([0, 1, 2])
aut = logicizer.graph_to_logic(g, 'pc', True)
source = aut.add_expr('pc = 0')
constrain = aut.true
v = fx.descendants(source, constrain, aut)
assert v == aut.add_expr('pc_0 <=> ~ pc_1'), _to_expr(v, aut)
def test_ee_image_only_sys():
g = TransitionSystem()
g.add_path([0, 1, 2])
aut = logicizer.graph_to_logic(g, 'pc', True)
u = aut.add_expr('pc = 0')
v = fx.ee_image(u, aut)
v_ = aut.add_expr('pc = 1')
assert v == v_, _to_expr(v, aut)
v = fx.ee_image(v, aut)
v_ = aut.add_expr('pc = 2')
assert v == v_, _to_expr(v, aut)
def test_ee_image_only_sys():
g = TransitionSystem()
g.add_path([0, 1, 2])
aut = logicizer.graph_to_logic(g, 'pc', True)
u = aut.add_expr('pc = 0')
v = fx.ee_image(u, aut)
v_ = aut.add_expr('pc = 1')
assert v == v_, _to_expr(v, aut)
v = fx.ee_image(v, aut)
v_ = aut.add_expr('pc = 2')
assert v == v_, _to_expr(v, aut)
def test_ee_image():
g = TransitionSystem()
g.vars = dict(x='bool')
g.env_vars = {'x'}
g.add_edge(0, 1, formula='x')
g.add_edge(0, 1, formula=' ~ x')
g.add_edge(0, 2, formula='x')
aut = logicizer.graph_to_logic(g, 'pc', True)
source = aut.add_expr('pc = 0')
u = fx.ee_image(source, aut)
u_ = aut.add_expr('(pc = 1) \/ (pc = 2)')
assert u == u_, _to_expr(u, aut)
def test_ee_image():
g = TransitionSystem()
g.vars = dict(x='bool')
g.env_vars = {'x'}
g.add_edge(0, 1, formula='x')
g.add_edge(0, 1, formula=' ~ x')
g.add_edge(0, 2, formula='x')
aut = logicizer.graph_to_logic(g, 'pc', True)
source = aut.add_expr('pc = 0')
u = fx.ee_image(source, aut)
u_ = aut.add_expr('(pc = 1) \/ (pc = 2)')
assert u == u_, _to_expr(u, aut)
def grid_world_example():
# robot a
a = TransitionSystem()
a.add_path([0, 1, 2, 3, 4, 5, 0])
a.initial_nodes.add(4)
n_a = len(a) - 1
aut_a = graph_to_logic(a, 'a', ignore_initial=False, self_loops=True)
# robot b
b = TransitionSystem()
b.add_path([5, 4, 3, 2, 1, 0, 5])
b.add_path([2, 6, 2])
b.add_path([0, 7, 0])
b.initial_nodes.add(0)
n_b = len(b) - 1
aut_b = graph_to_logic(b, 'b', ignore_initial=False, self_loops=True)
# interleaving repr
aut = Automaton()
aut.players = dict(car_a=0, car_b=1)
n = len(aut.players)
aut.vars = dict(
a=dict(type='saturating', dom=(0, n_a), owner='car_a'),
b=dict(type='saturating', dom=(0, n_b), owner='car_b'),
_i=dict(type='saturating', dom=(0, n - 1), owner=None))
aut.init['car_a'] = [aut_a.init['sys'][0]]
aut.init['car_b'] = [aut_b.init['sys'][0]]
aut.action['car_a'] = [aut_a.action['sys'][0]]
aut.action['car_b'] = [aut_b.action['sys'][0]]
# avoid collisions
s = "(a != b) & (a' != b)"
# & ((a = 4) -> (a' != 4))
aut.action['car_a'].append(s)
s = "(a != b) & (a != b')"
# & ((a = 4) -> (b = 1))
aut.action['car_b'].append(s)
aut.win['car_a: []<>'] = ['(a = 4)', '(b = 1)']
aut.win['car_b: []<>'] = ['True']
fill_blanks(aut)
print(aut)
aut = aut.build()
make_assumptions(aut)
def test_ue_image_no_constrain():
g = TransitionSystem()
g.vars = dict(x='bool')
g.env_vars = {'x'}
g.add_edge(0, 1, formula='x')
g.add_edge(0, 2, formula=' ~ x')
aut = logicizer.graph_to_logic(g, 'pc', True)
# source constrained to x
source = aut.add_expr('x /\ (pc = 0)')
u = fx.ee_image(source, aut)
assert u == aut.add_expr('pc = 1')
# source contains both x and ~ x
source = aut.add_expr('pc = 0')
u = fx.ee_image(source, aut)
assert u == aut.add_expr('(pc = 1) \/ (pc = 2)')
def test_ue_image_no_constrain():
g = TransitionSystem()
g.vars = dict(x='bool')
g.env_vars = {'x'}
g.add_edge(0, 1, formula='x')
g.add_edge(0, 2, formula=' ~ x')
aut = logicizer.graph_to_logic(g, 'pc', True)
# source constrained to x
source = aut.add_expr('x /\ (pc = 0)')
u = fx.ee_image(source, aut)
assert u == aut.add_expr('pc = 1')
# source contains both x and ~ x
source = aut.add_expr('pc = 0')
u = fx.ee_image(source, aut)
assert u == aut.add_expr('(pc = 1) \/ (pc = 2)')
def semi_symbolic():
"""Example using a semi-enumerated state machine.
Instructive variants:
- `formula = "x'"`
- `self_loops = True`
- `aut.moore = False`
"""
g = TransitionSystem()
g.owner = 'sys'
g.vars = dict(x='bool')
g.env_vars.add('x')
g.add_path(range(11))
g.add_edge(10, 10)
g.add_edge(10, 0, formula="x")
# symbolic
aut = logicizer.graph_to_logic(
g, 'nd', ignore_initial=True, self_loops=False)
aut.init['env'] = 'nd = 1'
aut.win['<>[]'] = aut.bdds_from(' ~ x')
aut.win['[]<>'] = aut.bdds_from('nd = 0')
aut.qinit = '\A \A'
aut.moore = True
aut.plus_one = True
print(aut)
# compile to BDD
z, yij, xijk = gr1.solve_streett_game(aut)
gr1.make_streett_transducer(z, yij, xijk, aut)
# print t.bdd.to_expr(t.action['sys'][0])
r = aut.action['sys']
# aut.bdd.dump('bdd.pdf', roots=[r])
g = enumerate_controller(aut)
h, _ = sym_enum._format_nx(g)
pd = nx.drawing.nx_pydot.to_pydot(h)
pd.write_pdf('game_states.pdf')
print('Enumerated strategy has {n} nodes.'.format(
n=len(g)))
print(('Winning set:', aut.bdd.to_expr(z)))
print('{n} BDD nodes in total'.format(
n=len(aut.bdd)))
def semi_symbolic():
"""Example using a semi-enumerated state machine.
Instructive variants:
- `formula = "x'"`
- `self_loops = True`
- `aut.moore = False`
"""
g = TransitionSystem()
g.owner = 'sys'
g.vars = dict(x='bool')
g.env_vars.add('x')
nx.add_path(g, range(11))
g.add_edge(10, 10)
g.add_edge(10, 0, formula="x")
# symbolic
aut = logicizer.graph_to_logic(g,
'nd',
ignore_initial=True,
self_loops=False)
aut.init['env'] = 'nd = 1'
aut.win['<>[]'] = aut.bdds_from(' ~ x')
aut.win['[]<>'] = aut.bdds_from('nd = 0')
aut.qinit = '\A \A'
aut.moore = True
aut.plus_one = True
print(aut)
# compile to BDD
z, yij, xijk = gr1.solve_streett_game(aut)
gr1.make_streett_transducer(z, yij, xijk, aut)
# print t.bdd.to_expr(t.action['sys'][0])
r = aut.action['sys']
# aut.bdd.dump('bdd.pdf', roots=[r])
g = enumerate_controller(aut)
h, _ = sym_enum._format_nx(g)
pd = nx.drawing.nx_pydot.to_pydot(h)
pd.write_pdf('game_states.pdf')
print('Enumerated strategy has {n} nodes.'.format(n=len(g)))
print(('Winning set:', aut.bdd.to_expr(z)))
print('{n} BDD nodes in total'.format(n=len(aut.bdd)))
def gridworld_example():
# car a
a = TransitionSystem()
a.add_path([0, 1, 2, 3, 4, 5, 0])
a.initial_nodes.add(4)
n_a = len(a) - 1
aut_a = graph_to_logic(a, 'a', ignore_initial=False, self_loops=True)
# car b
b = TransitionSystem()
b.add_path([5, 4, 3, 2, 1, 0, 5])
b.add_path([2, 6, 2])
b.add_path([0, 7, 0])
b.initial_nodes.add(0)
n_b = len(b) - 1
aut_b = graph_to_logic(b, 'b', ignore_initial=False, self_loops=True)
# interleaving repr
aut = sym.Automaton()
aut.players = dict(car_a=0, car_b=1)
n = len(aut.players)
table = dict(a=dict(type='int', dom=(0, n_a), owner='car_a'),
b=dict(type='int', dom=(0, n_b), owner='car_b'),
_i=dict(type='int', dom=(0, n - 1), owner='scheduler'))
aut.add_vars(table, flexible=True)
aut.varlist['car_a'] = ['a']
aut.varlist['car_b'] = ['b']
s = r'''
InitA == ({init_a}) /\ (a \in 0 .. {n_a})
InitB == ({init_b}) /\ (b \in 0 .. {n_b})
NextA ==
/\ ({action_a})
# type invariance action
/\ a \in 0 .. {n_a}
/\ a' \in 0 .. {n_a}
# avoid collisions
/\ (a != b) /\ (a' != b)
/\ ((a = 4) => (a' != 4))
NextB ==
/\ ({action_b})
# type invariance action
/\ b \in 0 .. {n_b}
/\ b' \in 0 .. {n_b}
# avoid collisions
/\ (a != b) /\ (a != b')
RecurA1 == (a = 4)
RecurA2 == (b = 1)
RecurB == True
'''.format(n_a=n_a,
n_b=n_b,
init_a=aut_a.init['sys'][0],
init_b=aut_b.init['sys'][0],
action_a=aut_a.action['sys'][0],
action_b=aut_b.action['sys'][0])
aut.define(s)
aut.init_expr = dict(car_a='InitA', car_b='InitB')
aut.action_expr = dict(car_a='NextA', car_b='NextB')
aut.win_expr = dict(car_a={'[]<>': ['RecurA1', 'RecurA2']},
car_b={'[]<>': ['RecurB']})
print(aut)
aut.build()
make_assumptions(aut)
