布尔可满足性检查我的代码

Question

我在我的代码中得到了错误的答案。

n 是变量的数量，而 formula 是一个包含子句的列表。

给定一个有 'n' 个变量和用列表 'formula' 编码的子句的 SAT 实例，如果这个实例是可满足的，就返回 'satisfiable'，否则返回 'unsatisfiable'。'formula' 中的每个元素代表一个子句，它是一个整数列表，其中整数 i 表示子句中存在字面量 Xi，而整数 -i 表示子句中存在字面量 ~Xi。举个例子，子句 "X1 v ~X11 v X7" 可以用列表 [1, -11, 7] 来表示。

import itertools
n = 4 
formula = [[1, -2, 3], [-1, 3], [-3], [2, 3]]


booleanValues = [True,False] * n

allorderings = set(itertools.permutations(booleanValues, n)) #create possible combinations of variables that can check if formula is satisfiable or not

print(allorderings)

for potential in allorderings:
    l = [] #boolean value for each variable / different combination for each iteration
    for i in potential:
        l.append(i)
    #possible = [False]*n
    aclause = []
    for clause in formula:
        something = []
        #clause is [1,2,3]
        for item in clause:
            if item > 0:
                something.append(l[item-1]) 
            else:
                item = item * -1
                x = l[item-1]
                if x == True:
                    x = False
                else:
                    x = True
                something.append(x)
        counter = 0
        cal = False
        for thingsinclause in something:
            if counter == 0:
                cal = thingsinclause
                counter = counter + 1
            else:
                cal = cal and thingsinclause
                counter = counter + 1

        aclause.append(cal)

    counter2 = 0
    formcheck = False
    for checkformula in aclause:
        if counter2 == 0:
            formcheck = checkformula
            counter2 = counter2 + 1
        else:
            formcheck = formcheck or checkformula
    print("this combination works", checkformula)

Answer 1

这是一个修正后的版本：

import itertools
n = 4 
formula = [[1, -2, 3], [-1, 3], [-3], [2, 3]]

allorderings = itertools.product ([False, True], repeat = n)

for potential in allorderings:
    print ("Initial values:", potential)
    allclauses = []
    for clause in formula:
        curclause = []
        for item in clause:
            x = potential[abs (item) - 1]
            curclause.append (x if item > 0 else not x)
        cal = any (curclause)
        allclauses.append (cal)
    print ("Clauses:", allclauses)
    formcheck = all (allclauses)
    print ("This combination works:", formcheck)

需要考虑的几点：

1. 与其引入一些复杂且错误的逻辑来寻找与或运算，不如使用 any 和 all。这样更简洁，也更不容易出错。

2. 最自然的循环对象是 itertools.product([False, True], repeat = n)，也就是可能的布尔值集合 [False, True] 的 n 次方。换句话说，就是 [False, True] 的 n 份的 笛卡尔积。这里是 itertools.product 的文档。

3. 我增加了一些输出，以便查看情况。以下是我在 Python3 中得到的输出（Python2 会加上括号，但基本输出是一样的）：

---

Initial values: (False, False, False, False)
Clauses: [True, True, True, False]
This combination works: False
Initial values: (False, False, False, True)
Clauses: [True, True, True, False]
This combination works: False
Initial values: (False, False, True, False)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (False, False, True, True)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (False, True, False, False)
Clauses: [False, True, True, True]
This combination works: False
Initial values: (False, True, False, True)
Clauses: [False, True, True, True]
This combination works: False
Initial values: (False, True, True, False)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (False, True, True, True)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (True, False, False, False)
Clauses: [True, False, True, False]
This combination works: False
Initial values: (True, False, False, True)
Clauses: [True, False, True, False]
This combination works: False
Initial values: (True, False, True, False)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (True, False, True, True)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (True, True, False, False)
Clauses: [True, False, True, True]
This combination works: False
Initial values: (True, True, False, True)
Clauses: [True, False, True, True]
This combination works: False
Initial values: (True, True, True, False)
Clauses: [True, True, False, True]
This combination works: False
Initial values: (True, True, True, True)
Clauses: [True, True, False, True]
This combination works: False