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This is a library for building and querying a compressed form of set-membership filters, named k-XORSAT filters. These filters can be used similar to how one would use a Bloom filter but with one restriction --- items cannot be added after the filter is built. So, this is an 'offline' or 'static' filter, whereas Bloom filters are considered 'online' or 'dynamic'. The advantage is that k-XORSAT filters achieve very near the optimal memory usage. That is, they use much less memory than Bloom filters, making them desirable for either large data sets (save space) or data sets that are provided to a large user base (save bandwidth).

The advantage of k-XORSAT filters over other filters with small memory footprint is that the near-optimal compression of k-XORSAT filters is reliably achieved, and the query speed is comparable to Bloom filters for high false positive rates, and faster than Bloom filters for small false positive rates.


This package depends on pthreads and standard C math libraries.

This project also relies on a few git submodules. To get these modules, clone the repository by doing either

git clone --recursive


git clone
cd XORSATFilter
git submodule update --init --recursive


Run make in the project root directory. The library file libxorsatfilter.a will (assuming successful compilation) be created in this package's lib directory.


k-XORSAT filters are built in two separate phases. The first step is to add elements to a builder object. The second phase is to create a querier object from a builder object. Once completed, the querier object may be queried ad infinitum.

A builder is first allocated using XORSATFilterBuilderAlloc, like so:

  XORSATFilterBuilder *xsfb = XORSATFilterBuilderAlloc(0, 0);

Here, the first argument 0 is the number of expected elements the filter will encode. It is safe to leave this number as 0, but will decrease calls to malloc if the number is given ahead of time. The second argument is the number of bytes of metatdata to store with each element. To use the data structure as a filter, enter 0. To use the data structure as a dictionary, enter the number of bytes to store in the dictionary.

Elements are added to the builder, like so:

  XORSATFilterBuilderAddElement(xsfb, pElement, nElementBytes, pMetaData);

Here, pElement is a pointer to at least nElementBytes number of bytes. This element will be copied into the builder. pMetaData is a pointer to an array of bytes that will be stored into the data structure and can be retrieved after construction. If the data structure is used as a filter, this last argument may be NULL.

It is also possible to add the absence of an element to the filter. This will cause the filter to return False when queried against the element.

  XORSATFilterBuilderAddAbsence(xsfb, pElement, nElementBytes);

After all elements have been stored, the querier is ready to be created:

  XORSATFilterQuerier *xsfq = XORSATFilterBuilderFinalize(xsfb, XORSATFilterFastParameters, nThreads);

The second argument is a structure consisting of four parameters: the number of literals per row, the number of solutions, the number of elements per block, and the desired efficiency of the filter. Three samples are provided by the package,

  1. XORSATFilterEfficientParameters creates small filters but has longer build time.

  2. XORSATFilterPaperParameters creates filters according to parameters used in a recent paper on XORSAT filters.

  3. XORSATFilterFastParameters creates filters quickly but the filters are larger.

More information can be found near the tops of include/xorsat_filter.h and src/xorsat_blocks.c. Feel free to define your own parameters to meet the needs of your application.

The third nThreads argument corresponds to the number of pthreads used when building the querier. The returned querier (xsfq) will be NULL on error.

When finalizing, you will notice that the progress is printed to stderr. These print statements can be turned off by commenting out the following line in xorsat_filter.h and recompiling the package.


After creating the querier, it is suggested that the builder be free'd, like so:


The filter can be queried, like so:

  uint8_t ret = XORSATFilterQuery(xsfq, pElement, nElementBytes);

Here, pElement is a pointer to nElementBytes number of bytes. If this element might be in the filter (depending on the false positive rate), ret will return 1. Otherwise, ret will return 0, indicating that this element is definitely not in the filter.

Stored metadata can be retrived like so:

  uint8_t *pMetaData_retrieved = XORSATFilterRetrieveMetadata(xsfq, pElement, nElementBytes);

If pElement was not added to the data structure, the metadata returned will appear random. Otherwise, the stored metadata will be returned via a newly allocated pointer.

Queriers can be serialized (written to a file) in the following way:

  uint8_t ret = XORSATFilterSerialize(fout, xsfq);

Here, fout is of type FILE *. ret will be 0 on failure and 1 on success.

A querier can be deserialized (read from a file) in the following way:

  xsfq = XORSATFilterDeserialize(fout);

Here, fout is of type FILE *. xsfq will be NULL on error.

When querying is done, the filter can be freed, like so:


To use, simply link against lib/libxorsatfilter.a and include include/xorsat_filter.h.

This interface is demonstrated in a test provided with this library.


A sample interface is given in the test directory. The test builds a k-XORSAT dictionary for 1000000 random 10-byte elements each with 10-bytes of metadata, writes the dictionary to a file, reads the file back, then queries the filter against the original elements (for a consistency check) and prints statistics. To run the test type:

$ make test/test && test/test


A paper about SAT Filters is published in JSAT, available here: Satisfiability-based Set Membership Filters

A paper about XORSAT Filters is published in SAT'18, available here: XOR-Satisfiability Set Membership Filters


This work was prepared by U.S. Government employees and, therefore, is excluded from copyright by Section 105 of the Copyright Act of 1976.

Copyright and Related Rights in the Work worldwide are waived through the CC0 1.0 Universal license.


This Work is provided "as is." Any express or implied warranties, including but not limited to, the implied warranties of merchantability and fitness for a particular purpose are disclaimed. In no event shall the United States Government be liable for any direct, indirect, incidental, special, exemplary or consequential damages (including, but not limited to, procurement of substitute goods or services, loss of use, data or profits, or business interruption) however caused and on any theory of liability, whether in contract, strict liability, or tort (including negligence or otherwise) arising in any way out of the use of this Guidance, even if advised of the possibility of such damage.

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A library for building efficient set-membership filters and dictionaries based on the Satisfiability problem.




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