def test_rabin_trivial_loop():
a = trl.default_rabin_automaton()
a.acceptance = 'Rabin(1)'
a.declare_variables(x='bool')
a.varlist['sys'] = ['x']
# solve
assert len(a.win['<>[]']) == 1
assert len(a.win['[]<>']) == 1
zk, yki, xkijr = gr1.solve_rabin_game(a)
assert zk[-1] == a.bdd.true, zk
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, a)
# vars
assert '_goal' in a.vars, a.vars
vt = a.vars['_goal']['type']
assert vt == 'int', vt
dom = a.vars['_goal']['dom']
assert dom == (0, 0), dom
assert '_hold' in a.vars, a.vars
vt = a.vars['_hold']['type']
assert vt == 'int', vt
dom = a.vars['_hold']['dom']
assert dom == (0, 1), dom
assert 'x' in a.vars, a.vars
# init
init = a.init['impl_env']
init_ = a.add_expr('(_goal = 0) /\ (_hold = 1)')
assert init == init_, a.bdd.to_expr(init)
# action
action = a.action['impl']
s = ("(_goal = 0) /\ (_goal' = 0) /\ " "(_hold' = 0)")
action_ = a.add_expr(s)
assert action == action_, a.bdd.to_expr(action)
def test_rabin_with_safety_assumption():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['env'] = ['x']
aut.init['env'] = aut.add_expr('x')
aut.action['env'] = aut.add_expr("x' ")
aut.action['sys'] = aut.add_expr("x")
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.add_expr('x'), win_set
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = 'x /\ (_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = "((_goal = 0) /\ (_goal' = 0) /\ (_hold' = 0) /\ x)"
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# negate action to make unrealizable
aut.action['sys'] = aut.add_expr(' ~ x')
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.false, aut.bdd.to_expr(win_set)
with assert_raises(AssertionError):
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
def test_rabin_persistence():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.init['env'] = aut.add_expr(' ~ x')
aut.win['<>[]'] = [aut.add_expr('x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.true, aut.bdd.to_expr(win_set)
# tranducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1) /\ ~ x'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = ("(_goal = 0) /\ (_goal' = 0) /\ "
"ite(_hold' = 1, ~ x /\ x', x /\ x')")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# unrealizable
aut.win['[]<>'] = [aut.add_expr(' ~ x')]
zk, _, _ = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.false, aut.bdd.to_expr(win_set)
def test_rabin_persistence_2():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.init['sys'] = aut.true
aut.win['<>[]'] = [aut.add_expr('x'), aut.add_expr(' ~ x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.true, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 2)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
# enumeration.dump_relation(action, aut)
s = ("(_goal = 0) /\ (_goal' = 0) /\ "
"ite(_hold = 1,"
"(_hold' = 1) /\ ~ x',"
"ite(_hold = 0,"
"(_hold' = 0) /\ x',"
"(_hold = 2) /\ ("
"( (_hold' = 0) /\ x' ) \/ "
"( (_hold' = 1) /\ ~ x' )"
") ) )")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def test_rabin_with_safety_assumption():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['env'] = ['x']
aut.init['env'] = aut.add_expr('x')
aut.action['env'] = aut.add_expr("x' ")
aut.action['sys'] = aut.add_expr("x")
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.add_expr('x'), win_set
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = 'x /\ (_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = "((_goal = 0) /\ (_goal' = 0) /\ (_hold' = 0) /\ x)"
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# negate action to make unrealizable
aut.action['sys'] = aut.add_expr(' ~ x')
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.false, aut.bdd.to_expr(win_set)
with assert_raises(AssertionError):
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
def test_rabin_counter():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.plus_one = False
aut.qinit = '\A \A'
aut.action['sys'] = aut.add_expr("x => ~ x' ")
aut.win['[]<>'] = [aut.add_expr('x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.bdd.true, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
# regression
s = ("(_goal = 0) /\ (_goal' = 0) /\ "
"(_hold' = 0) /\ "
"ite(_hold = 0, x <=> ~ x', x => ~ x')")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def test_rabin_trivial_loop():
a = trl.default_rabin_automaton()
a.acceptance = 'Rabin(1)'
a.declare_variables(x='bool')
a.varlist['sys'] = ['x']
# solve
assert len(a.win['<>[]']) == 1
assert len(a.win['[]<>']) == 1
zk, yki, xkijr = gr1.solve_rabin_game(a)
assert zk[-1] == a.bdd.true, zk
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, a)
# vars
assert '_goal' in a.vars, a.vars
vt = a.vars['_goal']['type']
assert vt == 'int', vt
dom = a.vars['_goal']['dom']
assert dom == (0, 0), dom
assert '_hold' in a.vars, a.vars
vt = a.vars['_hold']['type']
assert vt == 'int', vt
dom = a.vars['_hold']['dom']
assert dom == (0, 1), dom
assert 'x' in a.vars, a.vars
# init
init = a.init['impl_env']
init_ = a.add_expr('(_goal = 0) /\ (_hold = 1)')
assert init == init_, a.bdd.to_expr(init)
# action
action = a.action['impl']
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"(_hold' = 0)")
action_ = a.add_expr(s)
assert action == action_, a.bdd.to_expr(action)
def test_rabin_persistence_2():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.init['sys'] = aut.true
aut.win['<>[]'] = [aut.add_expr('x'), aut.add_expr(' ~ x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.true, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 2)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
# enumeration.dump_relation(action, aut)
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"ite(_hold = 1,"
"(_hold' = 1) /\ ~ x',"
"ite(_hold = 0,"
"(_hold' = 0) /\ x',"
"(_hold = 2) /\ ("
"( (_hold' = 0) /\ x' ) \/ "
"( (_hold' = 1) /\ ~ x' )"
") ) )")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def test_rabin_persistence():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.init['env'] = aut.add_expr(' ~ x')
aut.win['<>[]'] = [aut.add_expr('x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.true, aut.bdd.to_expr(win_set)
# tranducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1) /\ ~ x'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"ite(_hold' = 1, ~ x /\ x', x /\ x')")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# unrealizable
aut.win['[]<>'] = [aut.add_expr(' ~ x')]
zk, _, _ = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.false, aut.bdd.to_expr(win_set)
def test_rabin_counter():
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.plus_one = False
aut.qinit = '\A \A'
aut.action['sys'] = aut.add_expr("x => ~ x' ")
aut.win['[]<>'] = [aut.add_expr('x')]
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.bdd.true, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
# regression
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"(_hold' = 0) /\ "
"ite(_hold = 0, x <=> ~ x', x => ~ x')")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def test_streett_with_liveness_assumption():
aut = trl.default_streett_automaton()
aut.declare_variables(x='bool', y=(0, 2))
aut.varlist = dict(env=['x'], sys=['y'])
aut.init['env'] = aut.add_expr('y < 2')
aut.action['sys'] = aut.add_expr(
"""
/\ ( ((y = 0) /\ ~ x) => (y' = 0) )
/\ ((y = 0) => (y' < 2))
/\ ((y = 1) => (y' = 0))
/\ ((y = 2) => FALSE)
/\ y \in 0..2
""")
aut.win['<>[]'] = [aut.add_expr(' ~ x')]
aut.win['[]<>'] = [aut.add_expr('y = 1')]
# solve
z, yij, xijk = gr1.solve_streett_game(aut)
z_ = aut.add_expr('y < 2')
e = aut.bdd.to_expr(z)
e_ = aut.bdd.to_expr(z_)
assert z == z_, (e, e_)
# transducer
gr1.make_streett_transducer(z, yij, xijk, aut)
assert action_refined(aut)
init = aut.init['impl_env']
assert init == aut.add_expr('(y < 2) /\ (_goal = 0)'), aut.bdd.to_expr(init)
action = aut.action['impl']
s = (
"( (y = 0) => ite(x, (y' = 1), (y' = 0)) ) /\ "
"( (y = 1) => (y' = 0) ) /\ "
"( (_goal = 0) /\ (_goal' = 0) ) /\ "
"( (y /= 2) /\ (y /= 3) )")
action_ = aut.add_expr(s)
sat = list(aut.bdd.pick_iter(action))
sys_action = aut.action['sys']
sys_action = gr1._copy_bdd(sys_action, aut.bdd, aut.bdd)
u = aut.apply('=>', action, sys_action)
assert u == aut.bdd.true, u
assert action == action_, (action, action_, pprint.pprint(sat))
#
# test complement
b = trl.default_rabin_automaton()
b.acceptance = 'Rabin(1)'
b.declare_variables(x='bool', y=(0, 2))
b.varlist = dict(env=['y'], sys=['x'])
b.action['env'] = gr1._copy_bdd(aut.action['sys'], aut.bdd, b.bdd)
b.win['<>[]'] = [b.add_expr('y /= 1')]
b.win['[]<>'] = [b.add_expr('x')]
zk, yki, xkijr = gr1.solve_rabin_game(b)
rabin_win_set = zk[-1]
bdd = b.bdd
streett_win_set = gr1._copy_bdd(z, aut.bdd, bdd)
assert rabin_win_set == bdd.apply('not', streett_win_set)
with assert_raises(AssertionError):
gr1.make_rabin_transducer(zk, yki, xkijr, b)
def test_streett_with_liveness_assumption():
aut = trl.default_streett_automaton()
aut.declare_variables(x='bool', y=(0, 2))
aut.varlist = dict(env=['x'], sys=['y'])
aut.init['env'] = aut.add_expr('y < 2')
aut.action['sys'] = aut.add_expr("""
/\ ( ((y = 0) /\ ~ x) => (y' = 0) )
/\ ((y = 0) => (y' < 2))
/\ ((y = 1) => (y' = 0))
/\ ((y = 2) => FALSE)
/\ y \in 0..2
""")
aut.win['<>[]'] = [aut.add_expr(' ~ x')]
aut.win['[]<>'] = [aut.add_expr('y = 1')]
# solve
z, yij, xijk = gr1.solve_streett_game(aut)
z_ = aut.add_expr('y < 2')
e = aut.bdd.to_expr(z)
e_ = aut.bdd.to_expr(z_)
assert z == z_, (e, e_)
# transducer
gr1.make_streett_transducer(z, yij, xijk, aut)
assert action_refined(aut)
init = aut.init['impl_env']
assert init == aut.add_expr('(y < 2) /\ (_goal = 0)'), aut.bdd.to_expr(
init)
action = aut.action['impl']
s = ("( (y = 0) => ite(x, (y' = 1), (y' = 0)) ) /\ "
"( (y = 1) => (y' = 0) ) /\ "
"( (_goal = 0) /\ (_goal' = 0) ) /\ "
"( (y /= 2) /\ (y /= 3) )")
action_ = aut.add_expr(s)
sat = list(aut.bdd.pick_iter(action))
sys_action = aut.action['sys']
sys_action = gr1._copy_bdd(sys_action, aut.bdd, aut.bdd)
u = aut.apply('=>', action, sys_action)
assert u == aut.bdd.true, u
assert action == action_, (action, action_, pprint.pprint(sat))
#
# test complement
b = trl.default_rabin_automaton()
b.acceptance = 'Rabin(1)'
b.declare_variables(x='bool', y=(0, 2))
b.varlist = dict(env=['y'], sys=['x'])
b.action['env'] = gr1._copy_bdd(aut.action['sys'], aut.bdd, b.bdd)
b.win['<>[]'] = [b.add_expr('y /= 1')]
b.win['[]<>'] = [b.add_expr('x')]
zk, yki, xkijr = gr1.solve_rabin_game(b)
rabin_win_set = zk[-1]
bdd = b.bdd
streett_win_set = gr1._copy_bdd(z, aut.bdd, bdd)
assert rabin_win_set == bdd.apply('not', streett_win_set)
with assert_raises(AssertionError):
gr1.make_rabin_transducer(zk, yki, xkijr, b)
def test_rabin_always_x():
# always x
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.acceptance = 'Rabin(1)'
aut.action['sys'] = aut.add_expr("x' ")
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.bdd.true, win_set
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
# init
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
# action
action = aut.action['impl']
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"(_hold' = 0) /\ "
"x' ")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# always ~ x
aut.init['env'] = aut.add_expr(' ~ x')
aut.action['sys'] = aut.add_expr(' ~ x')
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
win_set_ = aut.add_expr(' ~ x')
assert win_set == win_set_, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = (
'(_goal = 0) /\ (_hold = 1) /\ '
' ~ x')
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = (
"(_goal = 0) /\ (_goal' = 0) /\ "
"(_hold' = 0) /\ "
" ~ x /\ ~ x'")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def test_rabin_always_x():
# always x
aut = trl.default_rabin_automaton()
aut.declare_variables(x='bool')
aut.varlist['sys'] = ['x']
aut.acceptance = 'Rabin(1)'
aut.action['sys'] = aut.add_expr("x' ")
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
assert win_set == aut.bdd.true, win_set
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
# init
init = aut.init['impl_env']
s = '(_goal = 0) /\ (_hold = 1)'
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
# action
action = aut.action['impl']
s = ("(_goal = 0) /\ (_goal' = 0) /\ " "(_hold' = 0) /\ " "x' ")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
#
# always ~ x
aut.init['env'] = aut.add_expr(' ~ x')
aut.action['sys'] = aut.add_expr(' ~ x')
# solve
zk, yki, xkijr = gr1.solve_rabin_game(aut)
win_set = zk[-1]
win_set_ = aut.add_expr(' ~ x')
assert win_set == win_set_, aut.bdd.to_expr(win_set)
# transducer
gr1.make_rabin_transducer(zk, yki, xkijr, aut)
assert action_refined(aut)
init = aut.init['impl_env']
s = ('(_goal = 0) /\ (_hold = 1) /\ ' ' ~ x')
init_ = aut.add_expr(s)
assert init == init_, aut.bdd.to_expr(init)
action = aut.action['impl']
s = ("(_goal = 0) /\ (_goal' = 0) /\ " "(_hold' = 0) /\ " " ~ x /\ ~ x'")
action_ = aut.add_expr(s)
assert action == action_, aut.bdd.to_expr(action)
def synthesize_rabin_controller(b):
"""Return enumerated graph with steps as edges.
after solving Rabin(1) game.
@param b: game with <>[] & []<> winning
@type b: `symbolic.Automaton`
"""
qinit = b.qinit
aut_rabin = b.build()
zk, yki, xkijr = gr1.solve_rabin_game(aut_rabin)
t= gr1.make_rabin_transducer(zk, yki, xkijr, aut_rabin)
g = enum.action_to_steps(t, qinit=qinit)
return g
