（Z3Py）檢查公式的所有解

Question

在Z3Py中，如何檢查給定約束的方程是否只有一個解？

如果不止一個解決方案，我怎麼能列舉出來？

Answer 1

你可以通過添加新的限制，阻止該模型由Z3返回。例如，假設在由Z3返回的模型中，我們有x = 0和y = 1。然後，我們可以通過添加約束Or(x != 0, y != 1)來阻止此模型。 以下腳本可以解決這個問題。 您可以在線試用：http://rise4fun.com/Z3Py/4blB

請注意，以下腳本有一些限制。輸入公式不能包含未解釋的函數，數組或未解釋的排序。

from z3 import * 

# Return the first "M" models of formula list of formulas F 
def get_models(F, M): 
    result = [] 
    s = Solver() 
    s.add(F) 
    while len(result) < M and s.check() == sat: 
     m = s.model() 
     result.append(m) 
     # Create a new constraint the blocks the current model 
     block = [] 
     for d in m: 
      # d is a declaration 
      if d.arity() > 0: 
       raise Z3Exception("uninterpreted functions are not supported") 
      # create a constant from declaration 
      c = d() 
      if is_array(c) or c.sort().kind() == Z3_UNINTERPRETED_SORT: 
       raise Z3Exception("arrays and uninterpreted sorts are not supported") 
      block.append(c != m[d]) 
     s.add(Or(block)) 
    return result 

# Return True if F has exactly one model. 
def exactly_one_model(F): 
    return len(get_models(F, 2)) == 1 

x, y = Ints('x y') 
s = Solver() 
F = [x >= 0, x <= 1, y >= 0, y <= 2, y == 2*x] 
print get_models(F, 10) 
print exactly_one_model(F) 
print exactly_one_model([x >= 0, x <= 1, y >= 0, y <= 2, 2*y == x]) 

# Demonstrate unsupported features 
try: 
    a = Array('a', IntSort(), IntSort()) 
    b = Array('b', IntSort(), IntSort()) 
    print get_models(a==b, 10) 
except Z3Exception as ex: 
    print "Error: ", ex 

try: 
    f = Function('f', IntSort(), IntSort()) 
    print get_models(f(x) == x, 10) 
except Z3Exception as ex: 
    print "Error: ", ex