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112 lines
3.6 KiB
Python
112 lines
3.6 KiB
Python
"""
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Check to see if the model has the variable
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sharing property.
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"""
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from itertools import product
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from typing import Dict, List, Optional, Set, Tuple
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from common import set_to_str
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from model import (
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Model, model_closure, ModelFunction, ModelValue
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)
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class VSP_Result:
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def __init__(
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self, has_vsp: bool, model_name: Optional[str] = None,
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subalgebra1: Optional[Set[ModelValue]] = None,
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subalgebra2: Optional[Set[ModelValue]] = None):
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self.has_vsp = has_vsp
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self.model_name = model_name
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self.subalgebra1 = subalgebra1
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self.subalgebra2 = subalgebra2
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def __str__(self):
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if not self.has_vsp:
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return f"Model {self.model_name} does not have the variable sharing property."
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return f"""Model {self.model_name} has the variable sharing property.
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Subalgebra 1: {set_to_str(self.subalgebra1)}
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Subalgebra 2: {set_to_str(self.subalgebra2)}
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"""
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def has_vsp(model: Model, impfunction: ModelFunction,
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negation_defined: bool) -> VSP_Result:
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"""
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Checks whether a model has the variable
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sharing property.
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"""
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# NOTE: No models with only one designated
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# value satisfies VSP
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if len(model.designated_values) == 1:
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return VSP_Result(False, model.name)
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assert model.ordering is not None, "Expected ordering table in model"
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top = model.ordering.top()
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bottom = model.ordering.bottom()
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C: Dict[ModelValue, Set[ModelValue]] = {}
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for x in model.designated_values:
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# Discard ({⊥} ∪ A', B) subalgebras
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if bottom is not None and x == bottom:
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continue
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# Discard ({⊤} ∪ A', B) subalgebras when negation is defined
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if top is not None and negation_defined and x == top:
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continue
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if x not in C:
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C[x] = model_closure({x,}, model.logical_operations, None)
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Xs = C[x]
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# Discard ({⊥} ∪ A', B) subalgebras
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if bottom is not None and bottom in Xs:
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continue
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# Discard ({⊤} ∪ A', B) subalgebras when negation is defined
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if top is not None and negation_defined and top in Xs:
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continue
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for y in model.designated_values - Xs:
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# Discard (A, {⊤} ∪ B') subalgebras
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if top is not None and y == top:
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continue
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# Discard (A, {⊥} ∪ B') subalgebras when negation is defined
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if bottom is not None and negation_defined and y == bottom:
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continue
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# Discard ({a} ∪ A', {b} ∪ B') subalgebras when a <= b
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if model.ordering.is_lt(x, y):
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continue
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# Discard ({a} ∪ A', {b} ∪ B') subalgebras when b <= a and negation is defined
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if negation_defined and model.ordering.is_lt(y, x):
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continue
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if y not in C:
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C[y] = model_closure({y,}, model.logical_operations, None)
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Ys = C[y]
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# Discard (A, {⊤} ∪ B') subalgebras
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if top is not None and top in Ys:
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continue
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# Discard (A, {⊥} ∪ B') subalgebras when negation is defined
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if bottom is not None and negation_defined and bottom in Ys:
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continue
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if not Xs.isdisjoint(Ys):
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continue
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falsified = True
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for (xi, yi) in product(Xs, Ys):
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if impfunction(xi, yi) in model.designated_values:
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falsified = False
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break
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if falsified:
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return VSP_Result(True, model.name, Xs, Ys)
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return VSP_Result(False, model.name)
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