z3 - z3 是否忽略了我的一些限制？

Question

stackoverflow-ers(?),

我正在玩 z3，我正在尝试解决以下限制：

(declare-const A (_ BitVec 32))
(declare-const B (_ BitVec 32))
(declare-const C (_ BitVec 32))
(declare-const D (_ BitVec 32))
(declare-const E (_ BitVec 32))
(declare-const F (_ BitVec 32))

(assert (<= A #xFFFFFFFF))
(assert (<= B #xFFFFFFFF))
(assert (<= C #xFFFFFFFF))


(assert (> A #x00000000))

;(Commented) Restriction #1 (assert (> B #x00000000))
(assert (> C #x00000000))

(assert (= D (bvand (bvmul (bvmul A B) #x00000008) #xFFFFFFFF) ))
(assert (<= D #xFFFFFFFF))

(assert (= E (bvand (bvmul (bvmul A C) #x00000008) #xFFFFFFFF)))
(assert (<= D E))

(assert (= F (bvand (bvmul A #x00000008) #xFFFFFFFF)))    

;(Uncommented) Restriction #2
(assert (> (bvand (bvmul F B) #xFFFFFFFF) D))

(assert (< (bvand (bvmul A B) #xFFFFFFFF) #x7FFFFFFF))
(assert (< (bvand (bvmul A C) #xFFFFFFFF) #x7FFFFFFF))


(assert (< D #x01000000))

(check-sat)

(get-value(A))
(get-value(B))
(get-value(C))
(get-value(D))
(get-value(F))

我在这些约束方面遇到了一些麻烦：a）第一个问题是 z3 忽略了“Restriction #2”

(assert (> (bvand (bvmul F B) #xFFFFFFFF) D))

，我得到的值如下：

A: #x000070e0
B: #x0000000a
C: #x00000014
D: #x00234600
F: #x00038700

尽管有限制，但 F*B = D。

b）如果我取消注释“限制 #1”

(assert (> B #x00000000))

我得到以下结果：

A: #x0000a000
B: #x00000007
C: #x00000000

它是椅子 - 键盘界面错误吗？我究竟做错了什么？

在 Z3 上在线运行。

提前致谢！

Answer 1

为了比较位向量，您应该始终使用相应的有符号/无符号变体：bvult, bvugt, bvule,bvuge表示无符号，bvslt, bvsgt, bvsle,bvsge表示有符号。<等的使用>无效。因此，您的“限制”实际上目前被简单地忽略了。如果我在命令行上运行你的基准测试，我会得到以下输出：

(error "line 8 column 24: Sort mismatch at argument #1 for function (declare-fun <= (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 9 column 24: Sort mismatch at argument #1 for function (declare-fun <= (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 10 column 24: Sort mismatch at argument #1 for function (declare-fun <= (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 13 column 23: Sort mismatch at argument #1 for function (declare-fun > (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 16 column 24: Sort mismatch at argument #1 for function (declare-fun > (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 19 column 24: Sort mismatch at argument #1 for function (declare-fun <= (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 22 column 15: Sort mismatch at argument #1 for function (declare-fun <= (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 27 column 44: Sort mismatch at argument #1 for function (declare-fun > (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 29 column 52: Sort mismatch at argument #1 for function (declare-fun < (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 30 column 52: Sort mismatch at argument #1 for function (declare-fun < (Int Int) Bool) supplied sort is (_ BitVec 32)")
(error "line 33 column 23: Sort mismatch at argument #1 for function (declare-fun < (Int Int) Bool) supplied sort is (_ BitVec 32)")
sat
((A #x00000000))
((B #x00000000))
((C #x00000000))
((D #x00000000))
((F #x00000000))

我不确定为什么“在线”求解器没有类似的抱怨。