I have downloaded z3 and find a mini_ic3.py program? I think it is for ic3--an inductive invariant -based formal verification program.
is there some reference paper to recommend for understanding mini_ic3.py in z3 directory
Not much directly describing that particular implementation, I'm afraid. Your best bet is to read through https://theory.stanford.edu/~nikolaj/programmingz3.html#sec-bounded-model-checking
The original IC3 papers themselves would help as well. The following is a great introduction: http://theory.stanford.edu/~arbrad/papers/Understanding_IC3.pdf
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I am using Z3 to solve a problem and I find it is very slow.
Are there any general principles or guidelines about the acceleration of Z3 solver? Such as:
Try to reduce the number of constraints.
Try specifying the tactics.
...
There are no generally applicable rules; otherwise we would have implemented and automated them. Without further information about the problem, there is no way to help you. A good place for performance investigations is a Z3 GitHub discussion.
As Christoph mentioned, there's no "one-size-fits-all" advice that applies uniformly to all problems. However, this sort of performance question comes up often enough, and there has been previous discussion on stack-overflow with a summary of how to think about scalability before: Scalability of z3
I'd start by reviewing this answer, and see if you have specific questions. In particular, sharing the particulars of your actual problem and how you modeled it in z3 will be essential to get better guidance.
Currently, I have a somewhat superficial understanding of how SMT solvers work (the basics of algorithms like E-matching, MBQI, and CVC4/5's inductive reasoning). However, it's very frustrating to debug by trial-and-error.
Is there any guidance on how to debug SMT scripts that make heavy use of quantifiers?
A badly-written script often goes into infinite loop but I cannot tell if it's my mistake, or it's just taking too long to respond.
The SMT solvers tend to hide internals from users, so it's quite hard to figure out why it's stuck. Is there any way to print the "solving context"?
Or maybe I'm using SMT solvers the wrong way? I should design my own verification algorithm, only employing SMT solvers for local decisions?
Any help is appreciated!
This is a very subjective question, and largely opinion based. But a couple of general remarks:
Don't directly program in SMTLib. It is not meant to be for human-consumption. Instead, use a higher-level API, and script them from a language that you're more familiar with. There are bindings available from any number of languages, including C/C++/Java/Python/O'Caml/Haskell/Scala etc. Just doing this will get rid of most of the mundane mistakes you make.
Turn on verbosity output of the solver. You might be able to notice patterns in the log output. Unfortunately this is very solver specific, and can be hard to decipher; but can also indicate if, for instance, you're stuck in an e-matching loop in the presence of quantifiers.
If there's a custom algorithm for your verification problem (Hoare triples, separation logic, abstract interpretation, ...), then you first have to apply these techniques and delegate local/sub-lemmas to an SMT solver. Do not expect the SMT solver to be able to do large proofs, and anything that requires actual induction out-of-the box.
Try reducing complexity by putting in over-constraints and see which ones help. Based on your findings you might be able to do a case-split, for instance, if the over-constraints enumerate a reasonably small search-space.
Again, these are very general remarks and whether they'll apply for your specific problem is anyone's guess. But I'd start with coding in a higher-level API if you aren't already doing so.
I'm a beginner with Z3. I just have tried some of the examples released in Z3 package, and I have no the other experience any more. I am working with a problem about shortest path in a graph. Can I do it by Z3 ? Thanks you all.
You can express such queries in logic, but maybe you can just use a dedicated algorithm (Dijktra or variants) for such problems.
For an introduction to using Z3, take a look at the tutorial linked from
http://rise4fun.com/z3
I am trying to Code a genetic algorithm in Matlab but really dont know how it works in images and how to proceed? Is there any basic tutorial that can help me understand how to apply GA on images (starting from 2d to multidimentional images ).
That will be a great help for me.
Thanking everyone in anticipations.
Kind Regards.
For GA you need two things: a fitness function that can evaluate any solution and tell how good it is, and a representation of your solution so that you can do crossover and mutation. Once you have these, you are good to go. I'm not an expert on image processing so I can't help you with that exactly.
Look at the book Essentials of metaheuristics which is a very good resource for start with evolutionary computation (and not only that) in general. It's free.
There is a paper on this subject which you can find at the IEEE library. I believe it solves the problem you vaguely describe.
Do you know is there any smt tool other than Z3 that supports fixpoint?
By fixpoint, I presume you mean solving for Horn clause queries. There are many tools that solve problems of a similar nature, but perhaps not with precisely the same format.
Philippe Suter's Leon tool uses different algorithms and can solve many correctness queries over recursive programs. Andrey Rybalchenko's ARMC tool solves Horn formulas with linear real arithmetic as well. It can also establish termination conditions. CLP systems with tabling should also be amenable to solving queries in a format that is similar to Z3's (both use Horn formulas as their input format). There are also many symbolic model checking solvers that could be used depending on your context.