CODEWITHSUNDEEP
c++z3smt
user3003525
user3003525

Reputation: 55

Z3 SMT Solver : Is there a way to generate a Model with a Specific Set of Variables

I'm working on a problem where I have a large number of variables (around 500) defined in Z3. I'm interested in finding a multiple models ( working on multiple solutions ) that satisfies my constraints, but I only need the values of a specific subset of these variables.

Is there a way to instruct Z3 to check the constraints and generate a model that only includes specific set of variables? I'm looking for a solution that would avoid generating values for all 500 variables, as this is unnecessary for my problem and could potentially slow down the solver.

Any advice or guidance with simple example would be greatly appreciated.

Thank you.

I am using following approach ( a simple example ) like below for my project. The API model would get solution for all variables but interested in generating a model with specific variables. While getting all solutions, it slows down.

# Define a large number of variables
variables = [Int('x{}'.format(i)) for i in range(500)]

# Define some constraints
constraints = [var > 0 for var in variables]

# Create a solver and add the constraints
s = Solver()
s.add(constraints)

# Find 500 solutions
for i in range( 500 ):
    if s.check() == sat:
        m = s.model()

        # Print the values of x0, x1, and x2
        for j in range(3):
            print(m[variables[j]])

        # Add a constraint that negates the current solution for x0, x1, and x2
        s.add(Or(variables[0] != m[variables[0]], variables[1] != m[variables[1]], variables[2] != m[variables[2]]))
    else:
        print("No more solutions")
        break

Upvotes: 0

Views: 229

Answers (1)

alias
alias

Reputation: 30525

In general, you need not worry about variables that don't contribute to a solution: If they do not matter, then the underlying solver will figure that out and won't waste its time in determining whether the problem is SAT or UNSAT. (During model creation, it'll assign values to these variables, but that's a relatively cheap operation once you get to a SAT state.)

It seems to me, however, what you want is a bit different. You're saying that even though change in these "extra" variables can give you a new model, you don't really care about those. In your example, the only interesting models to you are when x0, x1, and x2 are different. That is, you don't care about differing models where x0, x1, x2 are the same and the changes are in the remaining 497 variables.

If that's the case (and that's a legitimate use case indeed), you should use the fast all-sat algorithm instead. See https://theory.stanford.edu/~nikolaj/programmingz3.html#sec-blocking-evaluations, and in particular the function all_smt. (Also see (Z3Py) checking all solutions for equation)

In particular, the second argument to all_smt (named initial_terms) is exactly what you want to use. You want to pass [x0, x1, x2] as an argument to that. See https://stackoverflow.com/a/76494971/936310 for a discussion on the correct use of all_smt.

Upvotes: 0

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