The Holographic Contractor

In a recent paper, we have described a combinatorial method for proving holographic entropy inequalities based on finding contractions of the hypercube. contractor is an optimized C++ implementation of the greedy algorithm that we sketched in the paper for finding these "proofs by contractions".

Basic Usage

Proving one of the new cyclic inequalities derived in our paper is as simple as in the following example:

#include <contractor/contractor.hpp>

int main() {
    try {
        // Prove ABC + BCD + CDE + DEA + EAB >= AB + BC + CD + DE + EA + ABCDE
        CONTRACTOR_PROVE(5, ("ABC", "BCD", "CDE", "DEA", "EAB"),
                         ("AB", "BC", "CD", "DE", "EA", "ABCDE"));
        std::cout << "Success!" << std::endl;
    } catch(const std::exception &e) {
        std::cerr << "Error: " << e.what() << std::endl;
    }
}

Installation

To compile contractor and run the above example, install cmake and run

cmake -E make_directory build
cmake -E chdir build cmake .. -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release   # to (re)build

cmake -E chdir build ./example         # to run example
cmake -E chdir build make test         # to run unit tests

Attribution

If you find contractor useful for your research, please consider citing our paper:

@article{contractor,
  author  = {Bao, N. and Nezami, S. and Ooguri, H. and Stoica, B. and Sully, J. and Walter, M.},
  title   = {The holographic entropy cone},
  year    = {2015},
  journal = {Journal of High Energy Physics},
  volume  = {09},
  pages   = {130},
  eprint  = {1505.07839},
  doi     = {10.1007/JHEP09(2015)130},
  note    = {Software available at \url{https://github.com/catch22/contractor/}.},
}

Copyright 2015, Michael Walter.