Z3Py example from checking beliefs in dynamic networks

Question

For a better understanding of Z3 (or more specific of Z3Py) I wanted to implement the straight forward example from the Paper Checking Beliefs in dynamic Networks.

Here is my working code:

from z3 import *

fp = Fixedpoint()

dst = BitVec('dst', 3)
src = BitVec('src', 3)
dst_next = BitVec('dst_next', 3)
src_next = BitVec('src_next', 3)

fp.declare_var(dst, src, dst_next, src_next)

rels = {}

for c in ['A', 'R1', 'R2', 'R3', 'B', 'D']:
    f = Function(c, BitVecSort(3), BitVecSort(3), BoolSort())
    rels[c] = f
    fp.register_relation(f)
    fp.set_predicate_representation(f, 'doc')

# Guards
g12 = And(Extract(2, 1, dst) == 0b10, Extract(2, 1, dst) == 0b01)
g13 = And(Not(g12), Extract(2, 2, dst) == 0b1)
g2b = Extract(2, 1, dst) == 0b10
g3d = Extract(2, 2, src) == 0b1
g32 = And(Not(g3d), Extract(2, 2, dst) == 0b1)
ld = And(src_next == src, dst_next == dst)
set0 = And(src_next == src, dst_next == dst & 0b101)

# Relations
fp.rule(rels['R1'](dst_next, src_next), And(rels['R2'](dst, src), g12, ld))
fp.rule(rels['R1'](dst_next, src_next), And(rels['R3'](dst, src), g13, ld))
fp.rule(rels['R2'](dst_next, src_next), And(rels['B'](dst, src), g2b, ld))
fp.rule(rels['R3'](dst_next, src_next), And(rels['D'](dst, src), g3d, ld))
fp.rule(rels['R3'](dst_next, src_next), And(rels['R2'](dst, src), g32, set0))
fp.rule(rels['A'](dst, src), rels['R1'](dst, src))

fp.fact(rels['B'](dst, src))

#print(fp)
print(fp.query(rels['A'](dst, src)))
print(fp.get_answer())

This prints the correct Answer:

sat
Or(And(Var(0) == 5, Var(1) == 2),
   And(Var(0) == 4, Var(1) == 2),
   And(Var(0) == 4, Var(1) == 3),
   And(Var(0) == 5, Var(1) == 1),
   And(Var(0) == 4, Var(1) == 0),
   And(Var(0) == 5, Var(1) == 3),
   And(Var(0) == 5, Var(1) == 0),
   And(Var(0) == 4, Var(1) == 1))

So my question is now can Z3Py do some Bitvector "compression" of the result and print something like And(Var(0) == 10*, Var(1) == 0** ? And if I wanted to get all packets from B to A over R3 can I simply fp.query(rels['A'](dst, src), rels['R3'](dst, src)) or do I have to remove the relation R2 to R1?

Thanks!

Answer 1

It should be able to. You need to set default_relation=doc (to enable the difference of cubes representation described in that paper). (not sure exactly how to do it from Python, but I hope the API supports that; otherwise let us know).