Question

The following code terminates after 8 iterations (while it should iterate 14 times) why?

The code encodes a linear hybrid automata, it should run for the designated number of iterations but doesn’t.

from z3 import *
x,t,t1,t2,x_next=Reals ('x t t1 t2 x_next')

location=[None]
location='off'
x=20
t1=0

s=Solver()
#set_option(precision=10)
k=14
for   i in range(k):

  print location 
  if location=='off':
      s.add((10*x_next)>=(3*t1)-(3*t2)+(10*x),(10*x_next)<=(10*x)-(t2-t1),x_next>=18,(t2-t1)>0)
  elif location=='on':
      s.add(10*x_next>=(t2-t1)+(10*x),(5*x_next)<=(5*x)+(t2-t1),x_next<=22,(t2-t1)>0)


  if  [location=='off' and x_next<19] :
      location='on'
  elif [location=='on' and x_next>21]:
       location='off'

  if s.check()==unsat:
      break

  m=s.model()
  #print s.check()
  print i
  print location
  print s.model()

  print "value of x_next"
  print m[x_next].as_decimal(10)

  x=m[x_next]
  t1=m[t2]

Answer 1

The program stops because the set of assertions is unsatisfiable after iteration 8, and in your loop you have the statements:

if s.check()==unsat:
    break

In the first iteration you add the assertion:

10*x_next <= 200 - t2 - 0

In the last iteration, you add:

10*x_next >= t2 - Q(40,3) + 10*Q(56,3),
t2 - Q(40,3) > 0

where, the command Q(a, b) is used to create the rational number a/b.
That is, t1 is 40/3 and x is 56/3 at iteration 8.
The three assertions above are unsatisfiable. The first two imply that t2 <= 40/3, and the last t2 > 40/3.

BTW, the following statement seems to be incorrect. That is, I do not believe it reflects your intention. Note that, this is orthogonal problem.

if  [location=='off' and x_next<19] :

The expression x_next<19 does not evaluate to True or False. It creates the Z3 (symbolic) expression x_next < 19. I believe, you want to evaluate whether this expression is true in a model m. If that is the case, you should write:

if  location=='off' and is_true(m.evaluate(x_next<19)) :

The command m.evaluate(t) evaluates the expression t in the model m. The result is a Z3 expression. The function is_true(t) returns True if t is the Z3 expression true.