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BLT - A Library for Lattice Based Integer Linear Programming {#mainpage}


BLT is a C/C++ library for solving certain integer linear programming (ILP) problems using techniques that come from the theory of lattices. It is complementary to many existing, traditional ILP solvers in that there are problems it solves very well and very quickly which traditional solvers do not (and vice-versa).

For a theoretical discussion, see our conference paper from the 2015 SMT Workshop.

This project also provides a higher level set of Haskell bindings to BLT through a Haskell package called "blt". See "Installation and Usage" below for details.

Finally, there is a stand-alone ILP solver included called run_blt. See the "Stand-alone Solver" section.

The current version of BLT is 1.0.0, dated 2016-11-15.


Documentation (HTML) for the C/C++ library and the Haskell binding API can generated from source using doxygen (for the source code documentation of the C/C++ library) and by using cabal haddock to generate the Haskell source documentation.

The C/C++ library API is documented in the file blt.h. For the Haskell API, see the BLT.Bindings module.

Installation and Usage

The C/C++ library may be built using standard Unix build system tools, gcc or clang and make. The Haskell bindings may be built using standard Haskell ecosystems tools such as either cabal or stack.


BLT depends on the following 3rd party software:

  • C++ compiler supporting the c++0x standard
  • GLPK (>= 4.53 && <= 4.55) -- provides real-valued linear programming (note v4.56 & 4.57 are known to be incompatible with BLT)
  • NTL (>= 6.2.1 && <7.0 or 9.x; the 8.x and 10.x series are known not to be compatible with BLT) -- provides lattice reduction algorithms
  • Boost C++ headers (>= 1.55.0) -- provides matrices and vectors, rational numbers, and the unit test framework. Only a subset of the boost headers are needed

and optionally,

  • GHC for Haskell support (>= 7.6)
  • Yices SMT solver (>= 2.3.0, see the section "Sound Mode" for more details).

A bootstrapping script is provided and may be used to automatically download and install most of these (not including the compiler).

Building & Installing 'libblt'

'libblt' is the C/C++ library implementing the core of BLT. The source code and build system for libblt is located in the 'libblt' directory. The library is built using GNU make as follows. First, set the environment variables listed in the file and rename it to The variables should be set so that the dependencies listed above (GLPK, etc..) can be found by the C++ compiler. This can also be done in the shell, at the command line, or in the Makefile itself. Then invoke:

% cd libblt
% make

It is recommended to test your build by running:

% make test
% make longtest

The second command may take from several minutes to several hours depending on how you have chosen to configure the build.

Testing with Yices support enabled is done using:

% make test-yices
% make longteset-yices

You can expect the 'longtest-yices' target to take more than 1 hour.

The optional PREFIX environment variable specifies the installation prefix. BLT may now be installed by invoking:

% make install


% PREFIX=/usr/local make install

or similar.

For example, if the dependency libraries are installed in $HOME/local/lib and the Boost headers are installed in $HOME/local/include, then the following commands will build and install BLT to /usr/local/{lib,bin}.

% export LDFLAGS=-L$HOME/local/lib CPPFLAGS=-I$HOME/local/include
% make
% PREFIX=/usr/local make install


If you have installed GLPK and NTL into a local prefix (as opposed to a system-wide location like /usr/local/lib) it is necessary to tell the Makefile in libblt where to find them. This can be done by explicitly setting the environment variables LDFLAGS and CPPFLAGS.

For example, if your local prefix is $HOME/local, one might use:

% export BLT_LIB_DEST=$HOME/local/lib
% export LDFLAGS=-L$HOME/local/lib
% export CPPFLAGS=-I$HOME/local/include

Sound Mode

Including the Yices SMT solver and enabling it at runtime allows BLT to operate as a sound and complete decision procedure for bounded integer linear programming problems. However, it comes at a large performance cost. In dense, high dimensional problems the cost has been observed as high as a factor of 1000 in total runtime.

Stand-alone Solver

The included program run_blt is a standalone ILP (actually, Bounded ILP) solver using the BLT library. It takes input in the form described below, and returns a SAT or UNSAT decision, optionally a model, and some limited runtime information.


The expected input is a single file, <name>.bilp where <name> is any valid filename prefix. The file is expected to contain a system of two-sided inequalities representing a matrix system

L <= A*x <= U,

where L, U are integer column vectors, A is an integer matrix, and x is a column vector of integer unknowns (variables). run_blt decides the satisfiability of such a system of inequalities. The input .bilp file should be in the form:

l0 <= a11 a12 ... a2n <= u0
.      .                 .
.      .                 .
.      .                 .
lm <= am1 am2 ... amn <= um

with all the a's, l's and u's being integer constants. In this case, 'x' is a vector of 'n' unknowns. In this format, each line represents a single two-sided inequality and excess whitespace is ignored. There are several example .bilp files in the test/data directory for reference.

run_blt supports a few optional flags:

  • -m print out a satisfying model if the problem is SAT
  • -v print out version and compile-time information
  • -h print out program usage


The output consists of a single line on stdout of the form:

PROBLEM <name> RUNTIME <r> niter <i> npru <p> rc <s> check <c>


<name> |  provided on the command line
   <r> |  runtime in seconds
   <i> |  number of search iterations
   <p> |  number of layers pruned during search
   <s> |  return status, e.g. OK, STATUS_INPUT_ERROR, STATUS_LP_ERROR
   <c> |  decision: SAT or UNSAT

If the -m flag is given and the problem is SAT, then an additional line is printed that includes the model:

PROBLEM <name> MODEL <vector>


  <name> |  provided on the command line
<vector> |  vector of integers representing the solution 'x'

Haskell Bindings to BLT

Building the bindings requires the Haskell compiler GHC version 7.6 or greater and the cabal-install tool, preferably version 1.18 or greater, but older versions may also work (untested).

To install the bindings to your user packages:

% cabal install --extra-lib-dirs=<path to deps>

where is a directory containing the dependency libraries libglpk.*, and libntl.*. The flag is not neccesary if GLPK and NTL are installed system wide. See also the sections "Dependencies" and "Troubleshooting"

The cabal configure process automatically builds and installs (locally) the C/C++ library contained in 'libblt', so it's important that the compiler and linker environment flags are set before running cabal install. The BLT library can be used in any Haskell project by adding blt to your build dependencies.

See the Haskell documentation listed in the "Documentation" section for details about the API.