def Wait(self, input_alphabet, threshold=1):
r"""
Writes ``False`` until reading the ``threshold``-th occurrence
of a true input letter; then writes ``True``.
INPUT:
- ``input_alphabet`` -- a list or other iterable.
- ``threshold`` -- a positive integer specifying how many
occurrences of ``True`` inputs are waited for.
OUTPUT:
A transducer writing ``False`` until the ``threshold``-th true
(Python's standard conversion to boolean is used to convert the
actual input to boolean) input is read. Subsequently, the
transducer writes ``True``.
EXAMPLES::
sage: T = transducers.Wait([0, 1])
sage: T([0, 0, 1, 0, 1, 0])
[False, False, True, True, True, True]
sage: T2 = transducers.Wait([0, 1], threshold=2)
sage: T2([0, 0, 1, 0, 1, 0])
[False, False, False, False, True, True]
"""
def transition(state, input):
if state == threshold:
return (threshold, True)
if not input:
return (state, False)
return (state + 1, state + 1 == threshold)
T = Transducer(transition,
input_alphabet=input_alphabet,
initial_states=[0])
for s in T.iter_states():
s.is_final = True
return T
def CountSubblockOccurrences(self, block, input_alphabet):
"""
Returns a transducer counting the number of (possibly
overlapping) occurrences of a block in the input.
INPUT:
- ``block`` -- a list (or other iterable) of letters.
- ``input_alphabet`` -- a list or other iterable.
OUTPUT:
A transducer counting (in unary) the number of occurrences of the given
block in the input. Overlapping occurrences are counted several
times.
Denoting the block by `b_0\ldots b_{k-1}`, the input word by
`i_0\ldots i_L` and the output word by `o_0\ldots o_L`, we
have `o_j = 1` if and only if `i_{j-k+1}\ldots i_{j} = b_0\ldots
b_{k-1}`. Otherwise, `o_j = 0`.
EXAMPLES:
#. Counting the number of ``10`` blocks over the alphabet
``[0, 1]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 0],
....: [0, 1])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from (1,) to (): 0|1,
Transition from (1,) to (1,): 1|0]
sage: T.input_alphabet
[0, 1]
sage: T.output_alphabet
[0, 1]
sage: T.initial_states()
[()]
sage: T.final_states()
[(), (1,)]
Check some sequence::
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T([0, 1, 0, 1, 1, 0])
[0, 0, 1, 0, 0, 1]
#. Counting the number of ``11`` blocks over the alphabet
``[0, 1]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 1],
....: [0, 1])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from (1,) to (): 0|0,
Transition from (1,) to (1,): 1|1]
Check some sequence::
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T([0, 1, 0, 1, 1, 0])
[0, 0, 0, 0, 1, 0]
#. Counting the number of ``1010`` blocks over the
alphabet ``[0, 1, 2]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 0, 1, 0],
....: [0, 1, 2])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from () to (): 2|0,
Transition from (1,) to (1, 0): 0|0,
Transition from (1,) to (1,): 1|0,
Transition from (1,) to (): 2|0,
Transition from (1, 0) to (): 0|0,
Transition from (1, 0) to (1, 0, 1): 1|0,
Transition from (1, 0) to (): 2|0,
Transition from (1, 0, 1) to (1, 0): 0|1,
Transition from (1, 0, 1) to (1,): 1|0,
Transition from (1, 0, 1) to (): 2|0]
sage: input = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2]
sage: output = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T(input) == output
True
"""
block_as_tuple = tuple(block)
def starts_with(what, pattern):
return len(what) >= len(pattern) \
and what[:len(pattern)] == pattern
def transition_function(read, input):
current = read + (input, )
if starts_with(block_as_tuple, current) \
and len(block_as_tuple) > len(current):
return (current, 0)
else:
k = 1
while not starts_with(block_as_tuple, current[k:]):
k += 1
return (current[k:], int(block_as_tuple == current))
T = Transducer(
transition_function,
input_alphabet=input_alphabet,
output_alphabet=[0, 1],
initial_states=[()])
for s in T.iter_states():
s.is_final = True
return T
def CountSubblockOccurrences(self, block, input_alphabet):
"""
Returns a transducer counting the number of (possibly
overlapping) occurrences of a block in the input.
INPUT:
- ``block`` -- a list (or other iterable) of letters.
- ``input_alphabet`` -- a list or other iterable.
OUTPUT:
A transducer counting (in unary) the number of occurrences of the given
block in the input. Overlapping occurrences are counted several
times.
Denoting the block by `b_0\ldots b_{k-1}`, the input word by
`i_0\ldots i_L` and the output word by `o_0\ldots o_L`, we
have `o_j = 1` if and only if `i_{j-k+1}\ldots i_{j} = b_0\ldots
b_{k-1}`. Otherwise, `o_j = 0`.
EXAMPLES:
#. Counting the number of ``10`` blocks over the alphabet
``[0, 1]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 0],
....: [0, 1])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from (1,) to (): 0|1,
Transition from (1,) to (1,): 1|0]
sage: T.input_alphabet
[0, 1]
sage: T.output_alphabet
[0, 1]
sage: T.initial_states()
[()]
sage: T.final_states()
[(), (1,)]
Check some sequence::
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T([0, 1, 0, 1, 1, 0])
[0, 0, 1, 0, 0, 1]
#. Counting the number of ``11`` blocks over the alphabet
``[0, 1]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 1],
....: [0, 1])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from (1,) to (): 0|0,
Transition from (1,) to (1,): 1|1]
Check some sequence::
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T([0, 1, 0, 1, 1, 0])
[0, 0, 0, 0, 1, 0]
#. Counting the number of ``1010`` blocks over the
alphabet ``[0, 1, 2]``::
sage: T = transducers.CountSubblockOccurrences(
....: [1, 0, 1, 0],
....: [0, 1, 2])
sage: sorted(T.transitions())
[Transition from () to (): 0|0,
Transition from () to (1,): 1|0,
Transition from () to (): 2|0,
Transition from (1,) to (1, 0): 0|0,
Transition from (1,) to (1,): 1|0,
Transition from (1,) to (): 2|0,
Transition from (1, 0) to (): 0|0,
Transition from (1, 0) to (1, 0, 1): 1|0,
Transition from (1, 0) to (): 2|0,
Transition from (1, 0, 1) to (1, 0): 0|1,
Transition from (1, 0, 1) to (1,): 1|0,
Transition from (1, 0, 1) to (): 2|0]
sage: input = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2]
sage: output = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]
sage: sage.combinat.finite_state_machine.FSMOldProcessOutput = False
sage: T(input) == output
True
"""
block_as_tuple = tuple(block)
def starts_with(what, pattern):
return len(what) >= len(pattern) \
and what[:len(pattern)] == pattern
def transition_function(read, input):
current = read + (input, )
if starts_with(block_as_tuple, current) \
and len(block_as_tuple) > len(current):
return (current, 0)
else:
k = 1
while not starts_with(block_as_tuple, current[k:]):
k += 1
return (current[k:], int(block_as_tuple == current))
T = Transducer(
transition_function,
input_alphabet=input_alphabet,
output_alphabet=[0, 1],
initial_states=[()])
for s in T.iter_states():
s.is_final = True
return T
