def tuple2fts(S, S0, AP, L, Act, trans, name='fts',
prepend_str=None):
"""Create a Finite Transition System from a tuple of fields.
Hint
====
To remember the arg order:
1) it starts with states (S0 requires S before it is defined)
2) continues with the pair (AP, L), because states are more
fundamental than transitions
(transitions require states to be defined)
and because the state labeling L requires AP to be defined.
3) ends with the pair (Act, trans), because transitions in trans
require actions in Act to be defined.
See Also
========
L{tuple2ba}
@param S: set of states
@type S: iterable of hashables
@param S0: set of initial states, must be \\subset S
@type S0: iterable of elements from S
@param AP: set of Atomic Propositions for state labeling:
L: S-> 2^AP
@type AP: iterable of hashables
@param L: state labeling definition
@type L: iterable of (state, AP_label) pairs:
[(state0, {'p'} ), ...]
| None, to skip state labeling.
@param Act: set of Actions for edge labeling:
R: E-> Act
@type Act: iterable of hashables
@param trans: transition relation
@type trans: list of triples: [(from_state, to_state, act), ...]
where act \\in Act
@param name: used for file export
@type name: str
"""
def pair_labels_with_states(states, state_labeling):
if state_labeling is None:
return
if not isinstance(state_labeling, Iterable):
raise TypeError('State labeling function: L->2^AP must be '
'defined using an Iterable.')
state_label_pairs = True
# cannot be caught by try below
if isinstance(state_labeling[0], str):
state_label_pairs = False
if state_labeling[0] is None:
state_label_pairs = False
try:
(state, ap_label) = state_labeling[0]
except:
state_label_pairs = False
if state_label_pairs:
return state_labeling
logger.debug('State labeling L not tuples (state, ap_label),\n'
'zipping with states S...\n')
state_labeling = zip(states, state_labeling)
return state_labeling
# args
if not isinstance(S, Iterable):
raise TypeError('States S must be iterable, even for single state.')
# convention
if not isinstance(S0, Iterable) or isinstance(S0, str):
S0 = [S0]
# comprehensive names
states = S
initial_states = S0
ap = AP
state_labeling = pair_labels_with_states(states, L)
actions = Act
transitions = trans
# prepending states with given str
if prepend_str:
logger.debug('Given string:\n\t' + str(prepend_str) + '\n' +
'will be prepended to all states.')
states = prepend_with(states, prepend_str)
initial_states = prepend_with(initial_states, prepend_str)
ts = FTS()
ts.name = name
ts.states.add_from(states)
ts.states.initial |= initial_states
ts.atomic_propositions |= ap
# note: verbosity before actions below
# to avoid screening by possible error caused by action
# state labeling assigned ?
if state_labeling is not None:
for state, ap_label in state_labeling:
if ap_label is None:
ap_label = set()
ap_label = str2singleton(ap_label)
state = prepend_str + str(state)
logger.debug('Labeling state:\n\t' + str(state) + '\n' +
'with label:\n\t' + str(ap_label) + '\n')
ts.states[state]['ap'] = ap_label
# any transition labeling ?
if actions is None:
for from_state, to_state in transitions:
(from_state, to_state) = prepend_with([from_state, to_state],
prepend_str)
logger.debug('Added unlabeled edge:\n\t' + str(from_state) +
'--->' + str(to_state) + '\n')
ts.transitions.add(from_state, to_state)
else:
ts.actions |= actions
for from_state, to_state, act in transitions:
(from_state, to_state) = prepend_with([from_state, to_state],
prepend_str)
logger.debug(
'Added labeled edge (=transition):\n\t' +
str(from_state) + '---[' + str(act) + ']--->' +
str(to_state) + '\n')
ts.transitions.add(from_state, to_state, actions=act)
return ts
def tuple2ba(S,
S0,
Sa,
Sigma_or_AP,
trans,
name='ba',
prepend_str=None,
atomic_proposition_based=True):
"""Create a Buchi Automaton from a tuple of fields.
defines Buchi Automaton by a tuple (S, S0, Sa, \\Sigma, trans)
(maybe replacing \\Sigma by AP since it is an AP-based BA ?)
See Also
========
L{tuple2fts}
@param S: set of states
@param S0: set of initial states, must be \\subset S
@param Sa: set of accepting states
@param Sigma_or_AP: Sigma = alphabet
@param trans: transition relation, represented by list of triples::
[(from_state, to_state, guard), ...]
where guard \\in \\Sigma.
@param name: used for file export
@type name: str
@rtype: L{BuchiAutomaton}
"""
# args
if not isinstance(S, Iterable):
raise TypeError('States S must be iterable, even for single state.')
if not isinstance(S0, Iterable) or isinstance(S0, str):
S0 = [S0]
if not isinstance(Sa, Iterable) or isinstance(Sa, str):
Sa = [Sa]
# comprehensive names
states = S
initial_states = S0
accepting_states = Sa
alphabet_or_ap = Sigma_or_AP
transitions = trans
# prepending states with given str
if prepend_str:
logger.debug('Given string:\n\t' + str(prepend_str) + '\n' +
'will be prepended to all states.')
states = prepend_with(states, prepend_str)
initial_states = prepend_with(initial_states, prepend_str)
accepting_states = prepend_with(accepting_states, prepend_str)
ba = BuchiAutomaton(atomic_proposition_based=atomic_proposition_based)
ba.name = name
ba.states.add_from(states)
ba.states.initial |= initial_states
ba.states.accepting |= accepting_states
if atomic_proposition_based:
ba.alphabet.math_set |= alphabet_or_ap
else:
ba.alphabet.add(alphabet_or_ap)
for transition in transitions:
(from_state, to_state, guard) = transition
[from_state, to_state] = prepend_with([from_state, to_state],
prepend_str)
# convention
if atomic_proposition_based:
if guard is None:
guard = set()
guard = str2singleton(guard)
ba.transitions.add(from_state, to_state, letter=guard)
return ba
def prepend_with_check(states, prepend_str, expected):
assert labeled_graphs.prepend_with(states, prepend_str) == expected
def tuple2fts(S, S0, AP, L, Act, trans, name='fts',
prepend_str=None):
"""Create a Finite Transition System from a tuple of fields.
Hint
====
To remember the arg order:
1) it starts with states (S0 requires S before it is defined)
2) continues with the pair (AP, L), because states are more
fundamental than transitions
(transitions require states to be defined)
and because the state labeling L requires AP to be defined.
3) ends with the pair (Act, trans), because transitions in trans
require actions in Act to be defined.
See Also
========
L{tuple2ba}
@param S: set of states
@type S: iterable of hashables
@param S0: set of initial states, must be \\subset S
@type S0: iterable of elements from S
@param AP: set of Atomic Propositions for state labeling:
L: S-> 2^AP
@type AP: iterable of hashables
@param L: state labeling definition
@type L: iterable of (state, AP_label) pairs:
[(state0, {'p'} ), ...]
| None, to skip state labeling.
@param Act: set of Actions for edge labeling:
R: E-> Act
@type Act: iterable of hashables
@param trans: transition relation
@type trans: list of triples: [(from_state, to_state, act), ...]
where act \\in Act
@param name: used for file export
@type name: str
"""
def pair_labels_with_states(states, state_labeling):
if state_labeling is None:
return
if not isinstance(state_labeling, Iterable):
raise TypeError('State labeling function: L->2^AP must be '
'defined using an Iterable.')
state_label_pairs = True
# cannot be caught by try below
if isinstance(state_labeling[0], str):
state_label_pairs = False
if state_labeling[0] is None:
state_label_pairs = False
try:
(state, ap_label) = state_labeling[0]
except:
state_label_pairs = False
if state_label_pairs:
return state_labeling
logger.debug('State labeling L not tuples (state, ap_label),\n'
'zipping with states S...\n')
state_labeling = zip(states, state_labeling)
return state_labeling
# args
if not isinstance(S, Iterable):
raise TypeError('States S must be iterable, even for single state.')
# convention
if not isinstance(S0, Iterable) or isinstance(S0, str):
S0 = [S0]
# comprehensive names
states = S
initial_states = S0
ap = AP
state_labeling = pair_labels_with_states(states, L)
actions = Act
transitions = trans
# prepending states with given str
if prepend_str:
logger.debug('Given string:\n\t' + str(prepend_str) + '\n' +
'will be prepended to all states.')
states = prepend_with(states, prepend_str)
initial_states = prepend_with(initial_states, prepend_str)
ts = FTS()
ts.name = name
ts.states.add_from(states)
ts.states.initial |= initial_states
ts.atomic_propositions |= ap
# note: verbosity before actions below
# to avoid screening by possible error caused by action
# state labeling assigned ?
if state_labeling is not None:
for state, ap_label in state_labeling:
if ap_label is None:
ap_label = set()
ap_label = str2singleton(ap_label)
state = prepend_str + str(state)
logger.debug('Labeling state:\n\t' + str(state) + '\n' +
'with label:\n\t' + str(ap_label) + '\n')
ts.states[state]['ap'] = ap_label
# any transition labeling ?
if actions is None:
for from_state, to_state in transitions:
(from_state, to_state) = prepend_with([from_state, to_state],
prepend_str)
logger.debug('Added unlabeled edge:\n\t' + str(from_state) +
'--->' + str(to_state) + '\n')
ts.transitions.add(from_state, to_state)
else:
ts.actions |= actions
for from_state, to_state, act in transitions:
(from_state, to_state) = prepend_with([from_state, to_state],
prepend_str)
logger.debug(
'Added labeled edge (=transition):\n\t' +
str(from_state) + '---[' + str(act) + ']--->' +
str(to_state) + '\n')
ts.transitions.add(from_state, to_state, actions=act)
return ts
def prepend_with_check(states, prepend_str, expected):
assert labeled_graphs.prepend_with(states, prepend_str) == expected
def tuple2ba(S, S0, Sa, Sigma_or_AP, trans, name='ba', prepend_str=None,
atomic_proposition_based=True):
"""Create a Buchi Automaton from a tuple of fields.
defines Buchi Automaton by a tuple (S, S0, Sa, \\Sigma, trans)
(maybe replacing \\Sigma by AP since it is an AP-based BA ?)
See Also
========
L{tuple2fts}
@param S: set of states
@param S0: set of initial states, must be \\subset S
@param Sa: set of accepting states
@param Sigma_or_AP: Sigma = alphabet
@param trans: transition relation, represented by list of triples::
[(from_state, to_state, guard), ...]
where guard \\in \\Sigma.
@param name: used for file export
@type name: str
@rtype: L{BuchiAutomaton}
"""
# args
if not isinstance(S, Iterable):
raise TypeError('States S must be iterable, even for single state.')
if not isinstance(S0, Iterable) or isinstance(S0, str):
S0 = [S0]
if not isinstance(Sa, Iterable) or isinstance(Sa, str):
Sa = [Sa]
# comprehensive names
states = S
initial_states = S0
accepting_states = Sa
alphabet_or_ap = Sigma_or_AP
transitions = trans
# prepending states with given str
if prepend_str:
logger.debug('Given string:\n\t' + str(prepend_str) + '\n' +
'will be prepended to all states.')
states = prepend_with(states, prepend_str)
initial_states = prepend_with(initial_states, prepend_str)
accepting_states = prepend_with(accepting_states, prepend_str)
ba = BuchiAutomaton(atomic_proposition_based=atomic_proposition_based)
ba.name = name
ba.states.add_from(states)
ba.states.initial |= initial_states
ba.states.accepting |= accepting_states
if atomic_proposition_based:
ba.alphabet.math_set |= alphabet_or_ap
else:
ba.alphabet.add(alphabet_or_ap)
for transition in transitions:
(from_state, to_state, guard) = transition
[from_state, to_state] = prepend_with([from_state, to_state],
prepend_str)
# convention
if atomic_proposition_based:
if guard is None:
guard = set()
guard = str2singleton(guard)
ba.transitions.add(from_state, to_state, letter=guard)
return ba