SAT scaled score ranges between 890 and 2400. In conclusion, once you have all this information, you can see how complex the SAT test can be. Organizing your study is a key factor, and this SAT Score Calculator can be a powerful tool to be aware of your weak areas before is too late.
This system provides CryptoMiniSat, an advanced incremental SAT solver. The system has 3interfaces: command-line, C++ library and python. The command-line interfacetakes a cnf as aninput in the DIMACSformat with the extension of XOR clauses. The C++ and python interface mimics this and alsoallows for incremental use: assumptions and multiple solve
calls.A C compatible wrapper is also provided.
When citing, always reference our SAT 2009 conference paper, bibtex record is here.
License
Please read LICENSE.txt for a discussion. Everything that is needed to build is MIT licensed. The M4RI library (not included) is GPL, so in case you have M4RI installed, you must build with -DNOM4RI=ON
or -DMIT=ON
in case you need a pure MIT build.
Docker usage
To run on file myfile.cnf
:
To run on a hand-written CNF:
To run on the file /home/myfolder/myfile.cnf.gz
by mounting it (may be faster):
To build and run locally:
To build and run the web interface:
Compiling in Linux
To build and install, issue:
Compiling in Mac OSX
First, you must get Homebew from https://brew.sh/ then:
Compiling in Windows
You will need python installed, then for Visual Studio 2015:
You now have the static binary under C:cmsbuildReleasecryptominisat5.exe
Command-line usage
Let's take the file:
The file has 3 variables and 3 clauses, this is reflected in the headerp cnf 3 3
which gives the number of variables as the first number and the number of clauses as the second.Every clause is ended by '0'. The clauses say: 1 must be True, 2must be False, and either 1 has to be False, 2 has to be True or 3 has to beTrue. The only solution to this problem is:
![Sat solver python Sat solver python](https://www.researchgate.net/profile/Andrei_Tchernykh/publication/320911023/figure/fig4/AS:558113939628033@1510076140637/General-structure-for-the-3-sat-mapreduce-solver-see-online-version-for-colours.png)
Which means, that setting variable 1 True, variable 2 False and variable 3 True satisfies the set of constraints (clauses) in the CNF. If the file had contained:
Then there is no solution and the solver returns s UNSATISFIABLE
.
Incremental Python Usage
The python module works with both Python 2 and Python 3. It must be compiled as per (notice 'python-dev'):
You can then use it in incremental mode as:
We can also try to assume any variable values for a single solver run:
For more detailed usage instructions, please see the README.rst under the python
directory.
Incremental Library Usage
The library uses a variable numbering scheme that starts from 0. Since 0 cannotbe negated, the class Lit
is used as: Lit(variable_number, is_negated)
. Assuch, the 1st CNF above would become:
The library usage also allows for assumptions. We can add these lines justbefore the return 0;
above:
Since we assume that variable 2 must be false, there is no solution. However,if we solve again, without the assumption, we get back the original solution.Assumptions allow us to assume certain literal values for a specific run butnot all runs -- for all runs, we can simply add these assumptions as 1-longclauses.
Multiple solutions
To find multiple solutions to your problem, just run the solver in a loopand ban the previous solution found:
The above loop will run as long as there are solutions. It is highlysuggested to only add into the new clause(bad_solutions
above) thevariables that are 'important' or 'main' to your problem. Variables that wereonly used to translate the original problem into CNF should not be added.This way, you will not get spurious solutions that don't differ in the main,important variables.
Rust binding
To build the Rust binding, download the prerequisites as before, go into the 'Rust' subfolder and use cargo:
Now you can use your Rust bindings as:
The above solves the same problem as above in Python and C++.
Preprocessor usage
Run cryptominisat5 as:
where some_sat_solver
is a SAT solver of your choice that outputs a solution in the format of:
or
You can tune the schedule of simplifications by issuing --sched 'X,Y,Z...'
. The default schedule for preprocessing is:
It is a good idea to put renumber
as late as possible, as it renumbers the variables for memory usage reduction.
Gaussian elimination
For building with Gaussian Elimination, you need to build as per:
To use Gaussian elimination, provide a CNF with xors in it (either in CNF or XOR+CNF form) and tune the gaussian parameters. Use --hhelp
to find all the gaussian elimination options:
If any of these options seem to be non-existent, then either you forgot to compile the SAT solver with the above options, or you forgot to re-install it with sudo make install
.
Testing
For testing you will need the GIT checkout and build as per:
Fuzzing
Build for test as per above, then:
![Sat Sat](https://slideplayer.com/slide/9795053/31/images/41/Progress+of+a+SAT+solver.jpg)
Configuring a build for a minimal binary&library
The following configures the system to build a bare minimal binary&library. It needs a compiler, but nothing much else:
CMake Arguments
The following arguments to cmake configure the generated build artifacts. To use, specify options prior to running make in a clean subdirectory: cmake <options> ..
-DSTATICCOMPILE=<ON/OFF>
-- statically linked library and binary-DUSE_GAUSS=<ON/OFF>
-- Gauss-Jordan Elimination support-DSTATS=<ON/OFF>
-- advanced statistics (slower)-DENABLE_TESTING=<ON/OFF>
-- test suite support-DMIT=<ON/OFF>
-- MIT licensed components only-DNOM4RI=<ON/OFF>
-- without toplevel Gauss-Jordan Elimination support-DREQUIRE_M4RI=<ON/OFF>
-- abort if M4RI is not present-DNOZLIB=<ON/OFF>
-- no gzip DIMACS input support-DONLY_SIMPLE=<ON/OFF>
-- only the simple binary is built-DNOVALGRIND=<ON/OFF>
-- no extended valgrind memory checking support-DLARGEMEM=<ON/OFF>
-- more memory available for clauses (but slower on most problems)
Trying different configurations
Try solving using different reconfiguration values between 1..15 as per:
These configurations are designed to be relatively orthogonal. Check if any of them solve a lot faster. If it does, try using that for similar problems going forward. Please do come back to the author with what you have found to work best for you.
Getting learnt clauses
As an experimental feature, you can get the learnt clauses from the system with the following code, where lits
is filled with learnt clauses every time get_next_small_clause
is called. The example below will eventually return all clauses of size 4 or less. You can call end_getting_small_clauses
at any time.
C usage
See src/cryptominisat_c.h.in for details. This is an experimental feature.
You've learned the basic algorithms now and are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset.