Here x and k are integers
and the formula is: (50<=x+k Ʌ x+k<51)
Can it get simplified to "x+k=50"
I want the right set of tactics to solve this conjunction of inequalities.
Z3 is not a general purpose symbolic engine to simplify such expressions. Even if you got a good combination of tactics to give you what you need today, the results might change in further releases of the tool. You should look at other systems. Even a symbolic-engine like wolfram-alpha may not produce what you exactly want; but it might give you some alternative forms that might be easier to work with. See here: http://www.wolframalpha.com/input/?i=50%3C%3Dx%2Bk+%26%26+x%2Bk%3C51
Related
In constraint solver like Gecode , We can control the exploration of search space with help of branching function. for e.g. branch(home , x , INT_VAL_MIN ) This will start exploring the search space from the minimum possible value of variable x in its domain and try to find solution.(There are many such alternatives .)
For z3, do we have this kind of flexibility in-built ?? Any alternative possible??
SMT solvers usually do not allow for these sorts of "hints" to be given, they act more as black-boxes.
Having said that, each solver uses a ton of internal heuristics, and z3 itself has a number of settings that you can play with to give it hints. If you run:
z3 -pd
it will display all the options you can provide, and there are literally over 600 of them! Unfortunately, these options are not really well documented, and how they impact the solver is rather cryptic. The only reliable way to find out would be to study the source code and see what they do, which isn't for the faint of heart. But in any case, it will not be as obvious as the branch feature you cite for gecode.
There are, however, other tricks one can use to speed up solving for SMT-solvers, unfortunately, these things are usually very problem-specific. If you post specific instances, you might get better suggestions.
I am trying to find an optimal solution using the Z3 API for python. I have used set_option("verbose", 1) to print statements that Z3 generates while checking for sat. One of the statements it prints is pb.conflict statements. The statements look something like this -
pb.conflict statements.
I want to know what exactly is pb.conflict. What do these statements signify? Also, what are the two numbers that get printed along with it?
pb stands for Pseudo-boolean. A pseudo-boolean function is a function from booleans to some other domain, usually Real. A conflict happens when the choice of a variable leads to an unsatisfiable clause set, at which point the solver has to backtrack. Keeping the backtracking to a minimum is essential for efficiency, and many of the SAT engines carefully track that number. While the details are entirely solver specific (i.e., those two numbers you're asking about), in general the higher the numbers, the more conflict cases the solver met, and hence might decide to reset the state completely or take some other action. Often, there are parameters that users can set to specify when such actions are taken and exactly what those are. But again, this is entirely solver and implementation specific.
A google search on pseudo-boolean optimization will result in a bunch of scholarly articles that you might want to peruse.
If you really want to find Z3's treatment of pseudo-booleans, then your best bet is probably to look at the implementation itself: https://github.com/Z3Prover/z3/blob/master/src/smt/theory_pb.cpp
I notice that the Z3 C++ (and C) API allows you to supply the logic to be used.
I have two questions about this that I couldn't answer by looking online:
Are these supposed to be the standard SMT-LIB logics i.e. QF_LRA
When are these worth supplying i.e. when will Z3 actually use this information
My context is mainly QF no BV but everything else possible, I am using the SMT solver incrementally and I can always work out what logic I will be in at the start.
Z3 will also try to figure out what the logic is (when run with default options), but it doesn't have custom tactics for all combinations of theories (see default_tactic.cpp and smt_strategic_solver.cpp). When you are not sure what Z3 will decide to do, then it's best to set the tactic right up front, so that you will get errors if you try to use things that are not in that logic. It will also use that information to set up the smt kernel, e.g., enabling various preprocessors, various solver features, and chosing heuristics (see e.g., smt_setup.cpp).
Try it out and see!
Usually it does make a big difference. Setting the logic means the solver will use a specialized tactic to solve the formula, instead of going through the generic loop. Z3 will also try to guess the logic, but it's usually better to just provide it upfront.
I have a simple set of constraints that Z3 is not able to cope with:
http://pastebin.com/3eaLQ9wx
Is there a way to tweak the constraints in order to get the result ?
This is a simple example of a bigger set of constraints (thousands) but
I am somehow troubled that it doesn't work even on such simple example
Thanks in advance !!
Your problem has non-linear constraints. While Z3 can deal with them in most cases, the mixing of Ints and Real's seem to be putting it beyond its current capabilities. If you simply use Reals for your s_0_1, s_0_2 etc. variables, I trust Z3 will be able to solve the problem. (You seem to have enough value constraints, so I trust there won't be a modeling issue.)
I think Leonardo expressed several times that the upcoming releases will have better support for combined theories in the presence of non-linear constraints.
I'm trying to make z3 (I'm using z3py) to simplify some formulas for me (so that I can have more or less human-readable output). Using ctx-solver-simplify tactic seemed a good choice for me since in a couple of passes it would produce nice compact formulas. But soon I've run into a situation when the output of ctx-solver-simplify does not seem to be equivalent to the original formula (it looks more like being satisfiability-equivalent or so). Also, it might be the case that I'm not dealing with tactics correctly.
Here's what I was trying to do: http://rise4fun.com/Z3Py/g5sX. So, I construct a formula Set2 (everything before the definition of Set2 is just a setup needed to define it) which has a particular satisfying assignment. After applying ctx-solver-simplify, I get a single formula (as a goal) for which this assignment is not satisfying. So what am I dong wrong?
Am I wrong assuming that ctx-solver-simplify would produce an equivalent formula?
Am I handling the tactics and their output in the wrong way?
Anything else?
Thanks.
I have been looking into this, but have so far been unable to reproduce the bug directly
with our current branch. A bug in the context simplifier was fixed a little while ago, and it could
be manifesting itself with the online version of Z3.
There are still a few things I can do to double check if we can reproduce the bug
and I will update this post with what I find.