Z3 最小化-无穷大答案

Question

I'm currently using the c++ API of z3 and have a problem minimizing the sum of integer variables.

There are some integer variables ( rv_i ) and each of them becomes some positive number or 0 depending on whether the boolean variable r_i is true or false. I want to minimize the sum of rv_i s and asserted the expressions like the below code. I think the minimized value of the sum of rv_i s should be 0 if all r_i s are false or should be some positive value if some of r_i s are true, but z3 gives the minus infinity ( (* (- 1) oo) ) when printing the minimized result. why z3 gives the minus infinity to the minimized value of the below code? (check result is sat)

(declare-fun rv_10 () Int)
(declare-fun r_10 () Bool)
(declare-fun rv_9 () Int)
(declare-fun r_9 () Bool)
(declare-fun rv_8 () Int)
(declare-fun r_8 () Bool)
(declare-fun rv_7 () Int)
(declare-fun r_7 () Bool)
(declare-fun rv_6 () Int)
(declare-fun r_6 () Bool)
(declare-fun rv_5 () Int)
(declare-fun r_5 () Bool)
(declare-fun rv_4 () Int)
(declare-fun r_4 () Bool)
(declare-fun rv_3 () Int)
(declare-fun r_3 () Bool)
(declare-fun rv_2 () Int)
(declare-fun r_2 () Bool)
(declare-fun rv_1 () Int)
(declare-fun r_1 () Bool)
(declare-fun rv_0 () Int)
(declare-fun r_0 () Bool)
(declare-fun p_1 () Bool)
(declare-fun p_2 () Bool)
(declare-fun p_3 () Bool)
...
(assert (and (=> r_0 (= rv_0 1))
     (=> r_1 (= rv_1 3))
     (=> r_2 (= rv_2 5))
     (=> r_3 (= rv_3 2))
     (=> r_4 (= rv_4 2))
     (=> r_5 (= rv_5 3))
     (=> r_6 (= rv_6 5))
     (=> r_7 (= rv_7 5))
     (=> r_8 (= rv_8 5))
     (=> r_9 (= rv_9 5))
     (=> r_10 (= rv_10 5))
(assert (and (=> (not r_0) (= rv_0 0))
     (=> (not r_1) (= rv_1 0))
     (=> (not r_2) (= rv_2 0))
     (=> (not r_3) (= rv_3 0))
     (=> (not r_4) (= rv_4 0))
     (=> (not r_5) (= rv_5 0))
     (=> (not r_6) (= rv_6 0))
     (=> (not r_7) (= rv_7 0))
     (=> (not r_8) (= rv_8 0))
     (=> (not r_9) (= rv_9 0))
     (=> (not r_10) (= rv_10 0))
(assert (>= rv_0 0))
(assert (>= rv_1 0))
(assert (>= rv_2 0))
(assert (>= rv_3 0))
(assert (>= rv_4 0))
(assert (>= rv_5 0))
(assert (>= rv_6 0))
(assert (>= rv_7 0))
(assert (>= rv_8 0))
(assert (>= rv_9 0))
(assert (>= rv_10 0))
(assert (=> p_1 (and (or (not r_1) (not r_2)))))
(assert (=> p_2 (and (or r_0) (or r_1 r_2) (or r_3))))
(assert (=> p_3 (or r_6 r_7 r_8 r_9 r_10)))
...
(minimize (+ rv_0
   rv_1
   rv_2
   rv_3
   rv_4
   rv_5
   rv_6
   rv_7
   rv_8
   rv_9
   rv_10))
(check-sat)

Answer 1

I cannot replicate this. Your input has a few ... 's in them, if you remove those and insert parenthesis to close the corresponding expressions, and add the following line at the very end (after check-sat ):

(get-objectives)

then z3 says:

sat
(objectives
 ((+ rv_0 rv_1 rv_2 rv_3 rv_4 rv_5 rv_6 rv_7 rv_8 rv_9 rv_10) 0)
)

So, either the parts you've ... 'd have code that change this behavior (unlikely), or since you're programming this using the C++ API, you're not quite using the C++ API correctly (more likely).

But without seeing the actual full input that causes the issue, it's impossible to tell what's going on wrong. I doubt z3 is at fault here; you should really post an MWE (minimal-workable-example); see here: https://stackoverflow.com/help/minimal-reproducible-example