我开始使用Z3,我给它一个玩具问题。我们的想法是为所有分配(A,B,C),中的至少一个(FA(B,C)==一个,FB(A,C)== B,FC(A,B)== c)中必须是真实的。
该模型报告
[fc = [else -> And(Not(Var(1)), Var(0))],
fa = [else -> And(Var(1), Var(0))],
fb = [else -> False]]
这似乎并没有满足该约束的(A =假,B =真,C =真)的情况下,如在下面的表中报告。
我在做什么错了,我怎么能得到满足约束条件,如第二个表格呈现规则的解决方案吗?
import pandas as pd
from z3 import Bools, Function, BoolSort, Solver, ForAll, Or
a, b, c = Bools("a b c")
fa = Function("fa", BoolSort(), BoolSort(), BoolSort())
fb = Function("fb", BoolSort(), BoolSort(), BoolSort())
fc = Function("fc", BoolSort(), BoolSort(), BoolSort())
s = Solver()
s.add(ForAll([a, b, c], Or(fa(b, c) == a, fb(a, c) == b, fc(a, b) == c)))
def tabulate(fa, fb, fc):
mi = pd.MultiIndex.from_product(
[[False, True] for _ in range(3)], names=["a", "b", "c"]
)
df = pd.DataFrame(index=mi).reset_index()
return (
df.assign(fa=fa, fb=fb, fc=fc)
.assign(
fb_correct=lambda x: x.fb == x.b,
fa_correct=lambda x: x.fa == x.a,
fc_correct=lambda x: x.fc == x.c,
)
.assign(any_correct=lambda x: x.fb_correct | x.fa_correct | x.fc_correct)
.astype(int)
)
print(s.check())
print(s.model())
# sat
# [fc = [else -> And(Not(Var(1)), Var(0))],
# fa = [else -> And(Var(1), Var(0))],
# fb = [else -> False]]
print(tabulate(fb=False, fa=lambda x: x.b & x.c, fc=lambda x: x.a & ~x.b))
# a b c fa fb fc fb_correct fa_correct fc_correct any_correct
# 0 0 0 0 0 0 0 1 1 1 1
# 1 0 0 1 0 0 0 1 1 0 1
# 2 0 1 0 0 0 0 0 1 1 1
# 3 0 1 1 1 0 0 0 0 0 0
# 4 1 0 0 0 0 1 1 0 0 1
# 5 1 0 1 0 0 1 1 0 1 1
# 6 1 1 0 0 0 0 0 0 1 1
# 7 1 1 1 1 0 0 0 1 0 1
# Correct answer:
print(
tabulate(fb=lambda x: ~x.a | x.b, fa=lambda x: x.b & x.c, fc=lambda x: x.a & ~x.b)
)
# a b c fa fb fc fb_correct fa_correct fc_correct any_correct
# 0 0 0 0 0 1 0 0 1 1 1
# 1 0 0 1 0 1 0 0 1 0 1
# 2 0 1 0 0 1 0 1 1 1 1
# 3 0 1 1 1 1 0 1 0 0 1
# 4 1 0 0 0 0 1 1 0 0 1
# 5 1 0 1 0 0 1 1 0 1 1
# 6 1 1 0 0 1 0 1 0 1 1
# 7 1 1 1 1 1 0 1 1 0 1
版本:Z3-求解== 4.8.0.0.post1
我不能复制这一点。当我运行程序时,我得到:
[fc = [else -> And(Var(0), Var(1))],
fa = [else -> And(Var(0), Not(Var(1)))],
fb = [else -> False]]
这似乎是正确的模式。请注意,这不同于你在说什么,因为它似乎交换fc
和fa
你的情况。
这很可能是一个已经修正了一个错误;我使用的是从GitHub源新鲜编译Z3。你可以升级你的Z3安装,看看问题是否会消失?