使用 Z3 和 SMT-LIB 获得最多两个值 [英] Use Z3 and SMT-LIB to get a maximum of two values

问题描述

如何使用 smt-lib2 获得公式的最大值?

How do I get the maximum of a formula using smt-lib2?

我想要这样的东西:

(declare-fun x () Int)
(declare-fun y () Int)
(declare-fun z () Int)
(assert (= x 2))
(assert (= y 4))
(assert (= z (max x y))
(check-sat)
(get-model)
(exit)

当然，smtlibv2 不知道max".那么，如何才能做到这一点?

Of course, 'max' is unknown to smtlibv2. So, how can this be done?

推荐答案

在 Z3 中，您可以轻松定义宏 max 并使用它来获取两个值的最大值:

In Z3, you can easily define a macro max and use it for getting maximum of two values:

(define-fun max ((x Int) (y Int)) Int
  (ite (< x y) y x))

还有一个使用未解释函数对 max 建模的技巧，这将有助于与 Z3 API 一起使用:

There is another trick to model max using uninterpreted functions, which will be helpful to use with Z3 API:

(declare-fun max (Int Int) Int)
(assert (forall ((x Int) (y Int))
    (= (max x y) (ite (< x y) y x))))

注意你必须设置(set-option :macro-finder true)，这样Z3就可以在检查可满足性时用函数体替换全称量词.

Note that you have to set (set-option :macro-finder true), so Z3 is able to replace universal quantifiers with body of the function when checking satisfiability.

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