问题
I'm a new guy to work with the Z3.
Would like to know how I can calculate the maximum value of a set and two different sets.
For example:
[1, 6, 5] - The greater is 6
[1, 6, 5] e [10, 7, 2] - The greater is 6
I use the following code to set:
(declare-sort Set 0)
(declare-fun contains (Set Int) bool)
( declare-const set Set )
( declare-const distinct_set Set )
( declare-const A Int )
( declare-const B Int )
( declare-const C Int )
( assert ( = A 0 ) )
( assert ( = B 1 ) )
( assert ( = C 2 ) )
( assert ( distinct A C) )
( assert ( distinct set distinct_set ) )
(assert
(forall ((x Int))
(= (contains set x) (or (= x A) (= x C)))))
And now would like to know how can I calculate the largest value in the set (set) and the largest value in sets (set and distinct_set).
If it was for all integers was only because it was easy to do:
(define-fun max ((x Int) (y Int)) Int
(ite (< x y) y x))
But I can not leave with sets by their integers, ie, get the values that have set.
Can you help me?
Thanks
回答1:
Is the following encoding reasonable for your purposes? It is also available online here.
; We Enconde each set S of integers as a function S : Int -> Bool
(declare-fun S1 (Int) Bool)
; To assert that A and C are elements of S1, we just assert (S1 A) and (S1 C)
(declare-const A Int)
(declare-const C Int)
(assert (S1 A))
(assert (S1 C))
; To say that B is not an element of S1, we just assert (not (S1 B))
(declare-const B Int)
(assert (not (S1 B)))
; Now, let max_S1 be the max value in S1
(declare-const max_S1 Int)
; Then, we now that max_S1 is an element of S1, that is
(assert (S1 max_S1))
; All elements in S1 are smaller than or equal to max_S1
(assert (forall ((x Int)) (=> (S1 x) (not (>= x (+ max_S1 1))))))
; Now, let us define a set S2 and S3
(declare-fun S2 (Int) Bool)
(declare-fun S3 (Int) Bool)
; To assert that S3 is equal to the union of S1 and S2, we just assert
(assert (forall ((x Int)) (= (S3 x) (or (S1 x) (S2 x)))))
; To assert that S3 is not equal to S1 we assert
(assert (exists ((x Int)) (not (= (S3 x) (S1 x)))))
(check-sat)
; Now let max_S3 be the maximal value of S3
(declare-const max_S3 Int)
(assert (S3 max_S3))
(assert (forall ((x Int)) (=> (S3 x) (not (>= x (+ max_S3 1))))))
; the set of constraints is still satisfiable
(check-sat)
; Now, let us assert that max_S3 < max_S1.
; It should be unsat, since S3 is a super set of S1
(assert (< max_S3 max_S1))
(check-sat)
来源：https://stackoverflow.com/questions/15398403/max-value-in-set-z3