def ppp2ts(part):
"""Derive transition system from proposition preserving partition.
@param part: labeled polytopic partition from
which to derive the transition system
@type part: L{PropPreservingPartition}
@return: C{(ts, state_map)}
finite transition system labeled with propositions
from the given partition, and map of
polytope indices to transition system states.
@rtype: (L{transys.FTS}, \C{dict})
"""
# generate transition system and add transitions
ofts = trs.FTS()
adj = part.adj #sp.lil_matrix
n = adj.shape[0]
ofts_states = range(n)
ofts_states = trs.prepend_with(ofts_states, 's')
ofts.states.add_from(ofts_states)
ofts.transitions.add_adj(adj, ofts_states)
# decorate TS with state labels
atomic_propositions = set(part.prop_regions)
ofts.atomic_propositions.add_from(atomic_propositions)
for state, region in zip(ofts_states, part.regions):
state_prop = region.props.copy()
ofts.states.add(state, ap=state_prop)
return (ofts, ofts_states)
def ppp2ts(part):
"""Derive transition system from proposition preserving partition.
@param part: labeled polytopic partition from
which to derive the transition system
@type part: L{PropPreservingPartition}
@return: C{(ts, state_map)}
finite transition system labeled with propositions
from the given partition, and map of
polytope indices to transition system states.
@rtype: (L{transys.FTS}, \C{dict})
"""
# generate transition system and add transitions
ofts = trs.FTS()
adj = part.adj #sp.lil_matrix
n = adj.shape[0]
ofts_states = range(n)
ofts_states = trs.prepend_with(ofts_states, 's')
ofts.states.add_from(ofts_states)
ofts.transitions.add_adj(adj, ofts_states)
# decorate TS with state labels
atomic_propositions = set(part.prop_regions)
ofts.atomic_propositions.add_from(atomic_propositions)
for state, region in zip(ofts_states, part.regions):
state_prop = region.props.copy()
ofts.states.add(state, ap=state_prop)
return (ofts, ofts_states)
def test_only_mode_control():
"""Unrealizable due to non-determinism.
Switched system with 2 modes: 'left', 'right'.
Modes are controlled by the system.
States are controlled by the environment.
So only control over dynamics is through mode switching.
Transitions are thus interpreted as non-deterministic.
This can model uncertain outcomes in the real world,
e.g., due to low quality actuators or
bad low-level feedback controllers.
"""
# Create a finite transition system
env_sws = transys.FTS()
env_sws.owner = 'env'
env_sws.sys_actions.add_from({'right', 'left'})
# str states
n = 4
states = transys.prepend_with(range(n), 's')
env_sws.atomic_propositions.add_from(['home', 'lot'])
# label TS with APs
ap_labels = [set(), set(), {'home'}, {'lot'}]
for i, label in enumerate(ap_labels):
state = 's' + str(i)
env_sws.states.add(state, ap=label)
# mode1 transitions
transmat1 = np.array([[0, 1, 0, 1], [0, 1, 0, 0], [0, 1, 0, 1],
[0, 0, 0, 1]])
env_sws.transitions.add_adj(sp.lil_matrix(transmat1), states,
{'sys_actions': 'right'})
# mode2 transitions
transmat2 = np.array([[1, 0, 0, 0], [1, 0, 1, 0], [0, 0, 1, 0],
[1, 0, 1, 0]])
env_sws.transitions.add_adj(sp.lil_matrix(transmat2), states,
{'sys_actions': 'left'})
env_vars = {'park'}
env_init = {'eloc = "s0"', 'park'}
env_prog = {'!park'}
env_safe = set()
sys_vars = {'X0reach'}
sys_init = {'X0reach'}
sys_prog = {'home'}
sys_safe = {'next(X0reach) <-> lot || (X0reach && !park)'}
sys_prog |= {'X0reach'}
specs = spec.GRSpec(env_vars, sys_vars, env_init, sys_init, env_safe,
sys_safe, env_prog, sys_prog)
r = synth.is_realizable('gr1c', specs, env=env_sws, ignore_env_init=True)
assert not r
###############################
# Switched system with 4 modes:
###############################
# In this scenario we have limited actions "left, right, up, down" with
# certain (nondeterministic) outcomes
# Create a finite transition system
sys_sws = transys.FTS()
sys_sws.actions.add_from({'right','up','left','down'})
# str states
n = 6
states = transys.prepend_with(range(n), 's')
sys_sws.states.add_from(set(states) )
sys_sws.states.initial.add_from({'s0', 's3'})
sys_sws.atomic_propositions.add_from(['home','lot'])
state_labels = [{'home'}, set(), set(), set(), set(), {'lot'}]
# Add states and decorate TS with state labels (aka atomic propositions)
for state, label in zip(states, state_labels):
sys_sws.states.add(state, ap=label)
# mode1 transitions
transmat1 = np.array([[0,1,0,0,1,0],
[0,0,1,0,0,1],
[0,0,1,0,0,0],
[0,1,0,0,1,0],
# In this scenario we have limited actions "left, right, up, down" with
# uncertain (nondeterministics) outcomes (e.g., due to bad actuators or
# bad low-level feedback controllers)
# Only control over the dynamics is through mode switching
# Transitions should be interpreted as nondeterministic
# Create a finite transition system
env_sws = transys.FTS()
env_sws.owner = 'env'
env_sws.sys_actions.add_from({'right', 'up', 'left', 'down'})
# str states
n = 6
states = transys.prepend_with(range(n), 's')
env_sws.states.add_from(set(states))
env_sws.states.initial.add('s0')
env_sws.atomic_propositions.add_from(['home', 'lot'])
state_labels = [{'home'}, set(), set(), set(), set(), {'lot'}]
# Add states and decorate TS with state labels (aka atomic propositions)
for state, label in zip(states, state_labels):
env_sws.states.add(state, ap=label)
# mode1 transitions
transmat1 = np.array([[0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0,
1], [0, 0, 1, 0, 0, 0],
[0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1],
[0, 0, 0, 0, 0, 1]])
def test_only_mode_control():
"""Unrealizable due to non-determinism.
Switched system with 2 modes: 'left', 'right'.
Modes are controlled by the system.
States are controlled by the environment.
So only control over dynamics is through mode switching.
Transitions are thus interpreted as non-deterministic.
This can model uncertain outcomes in the real world,
e.g., due to low quality actuators or
bad low-level feedback controllers.
"""
# Create a finite transition system
env_sws = transys.OpenFTS()
env_sws.sys_actions.add_from({'right','left'})
# str states
n = 4
states = transys.prepend_with(range(n), 's')
env_sws.atomic_propositions.add_from(['home','lot'])
# label TS with APs
ap_labels = [set(),set(),{'home'},{'lot'}]
for i, label in enumerate(ap_labels):
state = 's' + str(i)
env_sws.states.add(state, ap=label)
# mode1 transitions
transmat1 = np.array([[0,1,0,1],
[0,1,0,0],
[0,1,0,1],
[0,0,0,1]])
env_sws.transitions.add_adj(
sp.lil_matrix(transmat1), states, {'sys_actions':'right'}
)
# mode2 transitions
transmat2 = np.array([[1,0,0,0],
[1,0,1,0],
[0,0,1,0],
[1,0,1,0]])
env_sws.transitions.add_adj(
sp.lil_matrix(transmat2), states, {'sys_actions':'left'}
)
env_vars = {'park'}
env_init = {'eloc = 0', 'park'}
env_prog = {'!park'}
env_safe = set()
sys_vars = {'X0reach'}
sys_init = {'X0reach'}
sys_prog = {'home'}
sys_safe = {'next(X0reach) <-> lot || (X0reach && !park)'}
sys_prog |= {'X0reach'}
specs = spec.GRSpec(env_vars, sys_vars, env_init, sys_init,
env_safe, sys_safe, env_prog, sys_prog)
r = synth.is_realizable('gr1c', specs, env=env_sws, ignore_env_init=True)
assert(not r)