Circuit Satisfiability Using MPI

SATISFY_MPI is a C++ program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem. This version of the program uses MPI to carry out the solution in parallel.

This problem assumes that we are given a logical circuit of AND, OR and NOT gates, with N binary inputs and a single output. We are to determine all inputs which produce a 1 as the output.

The general problem is NP complete, so there is no known polynomial-time algorithm to solve the general case. The natural way to search for solutions then is exhaustive search.

In an interesting way, this is a very extreme and discrete version of the problem of maximizing a scalar function of multiple variables. The difference is that here we know that both the input and output only have the values 0 and 1, rather than a continuous range of real values!

This problem was a natural candidate for parallel computation, since the individual evaluations of the circuit are completely independent.

The latest versions of MPI no longer support the special C++ MPI bindings, so the examples given here have reverted to using the C MPI bindings.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


SATISFY_MPI is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

CNF, a data directory which describes the DIMACS CNF file format for defining instances of the satisfy problem in for boolean formulas in conjunctive normal form.

COMMUNICATOR_MPI, a C++ program which creates new communicators involving a subset of initial set of MPI processes in the default communicator MPI_COMM_WORLD.

HEAT_MPI, a C++ program which solves the 1D Time Dependent Heat Equation using MPI.

HELLO_MPI, a C++ program which prints out "Hello, world!" using the MPI parallel programming environment.

MPI, C++ programs which illustrate the use of the MPI application program interface for carrying out parallel computatioins in a distributed memory environment.

MULTITASK_MPI, a C++ program which demonstrates how to multitask, that is, to execute several unrelated and distinct tasks simultaneously, using MPI for parallel execution.

QUAD_MPI, a C++ program which approximates an integral using a quadrature rule, and carries out the computation in parallel using MPI.

RANDOM_MPI, a C++ program which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.

RING_MPI, a C++ program which uses the MPI parallel programming environment, and measures the time necessary to copy a set of data around a ring of processes.

SATISFY, a C++ program which solves the circuit satisfy problem.

SATISFY_OPENMP, a C++ program which solves the circuit satisfy problem using the OpenMP parallel programming system.

SEARCH_MPI, a C++ program which searches integers between A and B for a value J such that F(J) = C, using MPI for parallel execution.

WAVE_MPI, a C++ program which uses finite differences and MPI to estimate a solution to the wave equation.


  1. Michael Quinn,
    Parallel Programming in C with MPI and OpenMP,
    McGraw-Hill, 2004,
    ISBN13: 978-0071232654,
    LC: QA76.73.C15.Q55.

Source Code:

Examples and Tests:

SATISFY_LOCAL compiles and runs the program on the local machine, which presumably has a version of MPI installed.

SATISFY_FSU compiles and runs the program on the FSU HPC cluster.

SATISFY_SYSX compiles and runs the program on Virginia Tech's System X cluster.

You can go up one level to the C++ source codes.

Last revised on 14 October 2013.