Order of adding constraints when solving an SMT problem - smt

Question

Let's say I have a pretty simple SMT problem - some free variables and some constrains С on them. I also have an extra constraint EC. I want to prefer a solution when both C an EC are met and fallback to C-only solution if this is impossible.
How should I call check-sat in this case? Intuition tells me something like this:
(assert C)
(push)
(assert EC)
(check-sat)
<dance happy dance if it worked, or ...>
(pop)
(check-sat)
But I suspect that pop will wipe all the knowledge solver has mined, and the second check-sat will start from scratch.
I can try
(assert C)
(check-sat)
(push)
(assert EC)
(check-sat)
<dance happy dance if it worked, or ...>
(pop)
(check-sat)
The question is - can I be sure than the last (check-sat) will be a no-op, because there already was a call to check-sat with the same constraint set?

Answer 1

You write:
But I suspect that pop will wipe all the knowledge solver has mined, and the second check-sat will start from scratch.
Not necessarily. Learned clauses that depend only on C do not need to be discarded at pop(), although it is always safe to do so. This may be solver dependent.
The question is - can I be sure than the last (check-sat) will be a no-op, because there already was a call to check-sat with the same constraint set?
I wouldn't expect an SMT solver to remember that the previous check-sat was satisfiable, the previous model or even the previous sequence of decisions that lead to the SAT conclusion (after you asserted and checked something else). Nonetheless, the last check-sat should be much cheaper than the first check, because learned clauses don't need to be generated twice.
Focusing on pure SMT solvers, one option would be to use the API rather than the SMT-LIB interface so that one can simply save the SAT model after the first check-sat and there is no need of a third check-sat after pop().
What you probably want is to encode your problem as a MaxSMT problem.
Definition 2.3.4. (Partial Weighted MaxSMT, Partial MaxSMT, Weighted MaxSMT).
A Partial Weighted MaxSMT problem is a pair <φ_h, φ_s>
where φ_h is the set of "hard" T-clauses, and φ_s is a
collection of positive-weighted "soft" T-clauses of the form
<C_i, w_i>, and the goal is to find the maximum-weight set
of T-clauses ψ_s, ψ_s ⊆ φ_s, such that φ_h ∪ ψ_s is
T-satisfiable [NO06, CFG+10, ABP+11b, CGSS13a].
A Partial MaxSMT problem is a Partial Weighted MaxSMT problem
in which all "soft" T-clauses in φ_s have a unitary weight.
A Weighted MaxSMT problem is a Partial Weighted MaxSMT
problem in which the set of "hard" T-clauses φ_h is empty.
[source, p. 40]
In this case, you would assert EC as one, or more, soft clauses.
Let's say EC is a list of constraints ec_1, ..., ec_k, there are two cases:
you want all ec_1, ..., ec_k to be satisfied at the same time; then you would write:
(assert C)
(assert-soft EC)
(check-sat)
(get-model)
you want the largest possible subset of EC to be satisfied at the same time; then you would write:
(assert c)
(assert-soft ec_1)
(assert-soft ...)
(assert-soft ec_k)
(check-sat)
(get-model)
MaxSMT is supported by OMT solvers like Barcelogic, OptiMathSAT and Z3.