Z3 支持非线性算术 [英] Z3 support for nonlinear arithmetic

问题描述

我知道 Z3 对非线性算术有一些支持，但想知道扩展到了什么?是否可以指定支持哪些类别的非线性算术而不支持(或可能会超时)?提前了解这些将有助于我尽早中止我的任务.

I understand that Z3 has some supports for nonlinear arith but wondering to what extends ? Is it possible to specify what classes of nonlinear arithmetics are supported and are not (or likely to give time out) ? Know these in advances will help me abort my task early.

似乎不支持与电源相关的东西，如下所示

Seems like power related stuff is not supported as shown below

def pow2(x): 
    k=Int('k')
    return Exists(k, And(k>=0,2**k==x))


prove(pow2(7))
failed to prove

推荐答案

Z3 支持非线性多项式 实数运算.因此，不支持超越函数(例如，正弦和余弦)和指数函数(例如，2^x).实际上，对于指数，Z3 可以处理可以简化为数字的指数.这是一个示例，

Z3 supports nonlinear polynomial Real arithmetic. So, there is no support for transcendental functions (e.g., sine and cosine), and exponential (e.g., 2^x). Actually, for the exponential, Z3 can handle exponents that can be simplified to numerals. Here is an example,

x = Real('x')
y = Real('y')
solve(y == 3, x**y == 2)

在此示例中，x**y 中的 y 在预处理步骤中被重写为 3.预处理后，nlsat 非线性求解器多项式实数算法被调用.关于非线性整数运算，请参阅这篇相关帖子.

In this example, the y in x**y is rewritten to 3 during a preprocessing step. After preprocessing, the nlsat solver for nonlinear polynomial real arithmetic is invoked. Regarding nonlinear integer arithmetic, see this related post.

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