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- Parses multiple implication tables from magic
- Speed improvements to model closure
- Make use of prior model_closure computations
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Brandon Rozek 2024-05-12 13:03:28 -04:00
parent cf636eb7fd
commit 2fa8aa9c15
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GPG key ID: 26E457DA82C9F480
3 changed files with 187 additions and 92 deletions
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93
model.py
View file

@ -8,7 +8,7 @@ Operation, Conjunction, Disjunction, Implication
)
from typing import Set, Dict, Tuple, Optional
from functools import lru_cache
from itertools import combinations, chain, product
from itertools import combinations, chain, product, permutations
from copy import deepcopy
@ -32,6 +32,8 @@ class ModelValue:
def __lt__(self, other):
assert isinstance(other, ModelValue)
return ModelOrderConstraint(self, other)
def __deepcopy__(self, memo):
return ModelValue(self.name)
class ModelFunction:
@ -195,66 +197,47 @@ def satisfiable(logic: Logic, model: Model, interpretation: Dict[Operation, Mode
return True
from itertools import combinations_with_replacement
from collections import defaultdict
def model_closure(initial_set: Set[ModelValue], mfunctions: Set[ModelFunction]):
last_set: Set[ModelValue] = set()
current_set: Set[ModelValue] = initial_set
closure_set: Set[ModelValue] = initial_set
last_new = initial_set
changed = True
while last_set != current_set:
last_set = deepcopy(current_set)
while changed:
changed = False
new_elements = set()
old_closure = closure_set - last_new
# arity -> args
cached_args = defaultdict(list)
for mfun in mfunctions:
# Get output for every possible input configuration
# from last_set
for args in product(last_set, repeat=mfun.arity):
current_set.add(mfun(*args))
return current_set
# Use cached args if this arity was looked at before
if mfun.arity in cached_args:
for args in cached_args[mfun.arity]:
element = mfun(*args)
if element not in closure_set:
new_elements.add(element)
# Move onto next function
continue
def has_vsp(model: Model, interpretation: Dict[Operation, ModelFunction]) -> bool:
"""
Tells you whether a model violates the
variable sharing property.
"""
# Iterate over how many new elements would be within the arguments
# NOTE: To not repeat work, there must be at least one new element
for num_new in range(1, mfun.arity + 1):
new_args = combinations_with_replacement(last_new, r=num_new)
old_args = combinations_with_replacement(old_closure, r=mfun.arity - num_new)
for new_arg, old_arg in product(new_args, old_args):
for args in permutations(new_arg + old_arg):
cached_args[mfun.arity].append(args)
element = mfun(*args)
if element not in closure_set:
new_elements.add(element)
impfunction = interpretation[Implication]
# Compute I the set of tuples (x, y) where
# x -> y does not take a designiated value
I: Set[Tuple[ModelValue, ModelValue]] = set()
for (x, y) in product(model.carrier_set, model.carrier_set):
if impfunction(x, y) not in model.designated_values:
I.add((x, y))
# Construct the powerset without the empty set
s = list(I)
I_power = chain.from_iterable(combinations(s, r) for r in range(1, len(s) + 1))
# ((x1, y1)), ((x1, y1), (x2, y2)), ...
for xys in I_power:
# Compute the closure of all operations
# with just the xs
xs = {xy[0] for xy in xys}
carrier_set_left: Set[ModelValue] = model_closure(xs, model.logical_operations)
# Compute the closure of all operations
# with just the ys
ys = {xy[1] for xy in xys}
carrier_set_right: Set[ModelValue] = model_closure(ys, model.logical_operations)
# If the carrier set intersects, then we violate VSP
if len(carrier_set_left & carrier_set_right) > 0:
continue
invalid = False
for (x2, y2) in product(carrier_set_left, carrier_set_right):
if impfunction(x2, y2) in model.designated_values:
invalid = True
break
if not invalid:
return True
return False
closure_set.update(new_elements)
changed = len(new_elements) > 0
last_new = new_elements
return closure_set

72
parse_magic.py
View file

@ -13,6 +13,7 @@ from logic import (
Negation,
Disjunction
)
from vsp import has_vsp
def parse_matrices(infile: TextIO) -> List[Tuple[Model, Dict]]:
next(infile) # Skip header line
@ -42,12 +43,11 @@ def parse_matrices(infile: TextIO) -> List[Tuple[Model, Dict]]:
if designated_values is None:
break
while True:
result = parse_implication(infile, size)
if result is None:
break
mimplication, hasnext = result
results = parse_implication(infile, size)
if result is None:
break
for mimplication in results:
logical_operations = {
mnegation, mconjunction, mdisjunction,
mimplication
@ -60,10 +60,7 @@ def parse_matrices(infile: TextIO) -> List[Tuple[Model, Dict]]:
Implication: mimplication
}
solutions.append((model, interpretation))
print(f"Parsed {len(solutions)} so far")
if not hasnext:
break
return solutions
def carrier_set_from_size(size: int):
@ -78,7 +75,7 @@ def parse_size(infile: TextIO) -> Optional[int]:
return None
assert size > 0, "Unexpected size"
return size
def parse_negation(infile: TextIO, size: int) -> Optional[ModelFunction]:
line = next(infile).strip()
if line == '-1':
@ -87,12 +84,12 @@ def parse_negation(infile: TextIO, size: int) -> Optional[ModelFunction]:
row = line.split(" ")
assert len(row) == size + 1, "Negation table doesn't match size"
mapping = {}
for i, j in zip(range(size + 1), row):
x = mvalue_from_index(i)
y = parse_mvalue(j)
mapping[(x, )] = y
return ModelFunction(1, mapping, "Negation")
@ -118,7 +115,7 @@ def determine_cresult(size: int, ordering: Dict[ModelValue, ModelValue], a: Mode
if ordering[(c, d)]:
if ordering[(d, a)] and ordering [(d, b)]:
invalid = True
if not invalid:
return c
@ -131,7 +128,7 @@ def determine_dresult(size: int, ordering: Dict[ModelValue, ModelValue], a: Mode
continue
if not ordering[(b, c)]:
continue
invalid = False
for j in range(size + 1):
@ -148,8 +145,8 @@ def determine_dresult(size: int, ordering: Dict[ModelValue, ModelValue], a: Mode
def parse_order(infile: TextIO, size: int) -> Optional[Tuple[ModelFunction, ModelFunction]]:
line = next(infile).strip()
if line == '-1':
return None
return None
table = line.split(" ")
assert len(table) == (size + 1)**2
@ -186,7 +183,7 @@ def parse_designated(infile: TextIO, size: int) -> Optional[Set[ModelValue]]:
line = next(infile).strip()
if line == '-1':
return None
row = line.split(" ")
assert len(row) == size + 1, "Designated table doesn't match size"
@ -200,44 +197,45 @@ def parse_designated(infile: TextIO, size: int) -> Optional[Set[ModelValue]]:
return designated_values
def parse_implication(infile: TextIO, size: int) -> Optional[Tuple[ModelFunction, bool]]:
def parse_implication(infile: TextIO, size: int) -> Optional[List[ModelFunction]]:
line = next(infile).strip()
if line == '-1':
return None
table = line.split(" ")
has_next = True
if table[-1] == '-1':
has_next = False
table = table[:-1]
assert len(table) == (size + 1)**2
# Split and remove the last '-1' character
table = line.split(" ")[:-1]
mapping = {}
assert len(table) % (size + 1)**2 == 0
table_i = 0
mimplications: List[ModelFunction] = []
for i in range(size + 1):
x = mvalue_from_index(i)
for j in range(size + 1):
y = mvalue_from_index(j)
for _ in range(len(table) // (size + 1)**2):
mapping = {}
r = parse_mvalue(table[table_i])
table_i += 1
for i in range(size + 1):
x = mvalue_from_index(i)
for j in range(size + 1):
y = mvalue_from_index(j)
mapping[(x, y)] = r
r = parse_mvalue(table[table_i])
table_i += 1
mimplication = ModelFunction(2, mapping, "Implication")
return mimplication, has_next
mapping[(x, y)] = r
mimplication = ModelFunction(2, mapping, "Implication")
mimplications.append(mimplication)
return mimplications
if __name__ == "__main__":
from model import has_vsp
solutions: List[Model] = parse_matrices(sys.stdin)
print(f"Parsed {len(solutions)} matrices")
for model, interpretation in solutions:
for i, (model, interpretation) in enumerate(solutions):
# print(model)
if has_vsp(model, interpretation):
print(model)
print("Has VSP")
else:
print("Model", i, "does not have VSP")

114
vsp.py Normal file
View file

@ -0,0 +1,114 @@
"""
Check to see if the model has the variable
sharing property.
"""
from itertools import chain, combinations, product
from typing import Dict, Set, Tuple, List
from model import (
Model, ModelFunction, ModelValue, model_closure
)
from logic import Implication, Operation
def preseed(initial_set: Set[ModelValue], cache:List[Tuple[Set[ModelValue], Set[ModelValue]]]):
"""
Cache contains caches of model closure calls:
Ex:
{1, 2, 3} -> {....}
If {1,2,3} is a subset of initial set,
then {....} is the subset of the output of model_closure.
We'll use the output to speed up the saturation procedure
"""
candidate_preseed: Tuple[Set[ModelValue], int] = (None, None)
for i, o in cache:
if i < initial_set:
cost = len(initial_set - i)
if candidate_preseed[1] is None or cost < candidate_preseed[1]:
candidate_preseed = o, cost
same_set = candidate_preseed[1] == 0
return candidate_preseed[0], same_set
def has_vsp(model: Model, interpretation: Dict[Operation, ModelFunction]) -> bool:
"""
Tells you whether a model has the
variable sharing property.
"""
impfunction = interpretation[Implication]
# Compute I the set of tuples (x, y) where
# x -> y does not take a designiated value
I: Set[Tuple[ModelValue, ModelValue]] = set()
for (x, y) in product(model.carrier_set, model.carrier_set):
if impfunction(x, y) not in model.designated_values:
I.add((x, y))
# Construct the powerset of I without the empty set
s = list(I)
I_power = chain.from_iterable(combinations(s, r) for r in range(1, len(s) + 1))
# ((x1, y1)), ((x1, y1), (x2, y2)), ...
# Closure cache
closure_cache: List[Tuple[Set[ModelValue], Set[ModelValue]]] = []
# Find the subalgebras which falsify implication
for xys in I_power:
xs = {xy[0] for xy in xys}
orig_xs = xs
cached_xs = preseed(xs, closure_cache)
if cached_xs[0] is not None:
xs |= cached_xs[0]
ys = {xy[1] for xy in xys}
orig_ys = ys
cached_ys = preseed(ys, closure_cache)
if cached_ys[0] is not None:
ys |= cached_ys[0]
# NOTE: Optimziation before model_closure
# If the carrier set intersects, then move on to the next
# subalgebra
if len(xs & ys) > 0:
continue
# Compute the closure of all operations
# with just the xs
carrier_set_left: Set[ModelValue] = model_closure(xs, model.logical_operations)
# Save to cache
if cached_xs[0] is not None and not cached_ys[1]:
closure_cache.append((orig_xs, carrier_set_left))
# Compute the closure of all operations
# with just the ys
carrier_set_right: Set[ModelValue] = model_closure(ys, model.logical_operations)
# Save to cache
if cached_ys[0] is not None and not cached_ys[1]:
closure_cache.append((orig_ys, carrier_set_right))
# If the carrier set intersects, then move on to the next
# subalgebra
if len(carrier_set_left & carrier_set_right) > 0:
continue
# See if for all pairs in the subalgebras, that
# implication is falsified
falsified = True
for (x2, y2) in product(carrier_set_left, carrier_set_right):
if impfunction(x2, y2) in model.designated_values:
falsified = False
break
if falsified:
return True
return False