What is the most efficient way to encode pseudoboolean constraints in z3?

Question

I think there\'s two different relevant cases here:

Case 1:

I have a set of boolean variables and I want another boolean variable which is true if any of these v

Answer 1

You can currently use integers to encode PB constraints. You have to bound the variables to be in the interval 0, 1. For example:

 (set-logic QF_LIA)
 (declare-const n1 Int)
 (declare-const n2 Int)
 (assert (<= 0 n1))
 (assert (<= n1 1))
 (assert (<= 0 n2))
 (assert (<= n2 1))
 (assert (>= (+ n1 n2) 1))
 (check-sat)

If you set the logic to QF_LIA, then Z3 will automatically try to re-encode these constraints using bit-vectors. In the verbose output you will see that Z3 invokes a tactic pb2bv that does the rewriting for you

z3 ty.smt2 /v:10
(simplifier :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(propagate-values :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(ctx-simplify :num-steps 17)
(ctx-simplify :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(simplifier :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(solve_eqs :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(elim-uncnstr-vars :num-exprs 10 :num-asts 171 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(simplifier :num-exprs 10 :num-asts 173 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(pb2bv :num-exprs 4 :num-asts 180 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(simplifier :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(propagate-values :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(solve_eqs :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(max-bv-sharing :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(bit-blaster :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(aig :num-exprs 3 :num-asts 178 :time 0.00 :before-memory 0.77 :after-memory 0.77)
(ast-table :capacity 640 :size 178)
(sat-status
  :inconsistent    false
   :vars            2
  :elim-vars       0
  :lits            2
  :assigned        0
  :binary-clauses  1
  :ternary-clauses 0
  :clauses         0
  :del-clause      0
  :avg-clause-size 2.00
  :memory          0.77)