satisfy_mpi, a FORTRAN90 code 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 computer code and data files described and made available on this web page are distributed under the MIT license


satisfy_mpi is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

COMMUNICATOR_MPI, a FORTRAN90 code which creates new communicators involving a subset of initial set of MPI processes in the default communicator MPI_COMM_WORLD.

HEAT_MPI, a FORTRAN90 code which solves the 1D Time Dependent Heat Equation using MPI.

HELLO_MPI, a FORTRAN90 code which prints out "Hello, world!" using the MPI parallel programming environment.

mpi_test, FORTRAN90 examples which illustrate the use of the MPI application code interface for carrying out parallel computations in a distributed memory environment.

PRIME_MPI, a FORTRAN90 code which counts the number of primes between 1 and N, using MPI for parallel execution.

QUAD_MPI, a FORTRAN90 code which approximates an integral using a quadrature rule, and carries out the computation in parallel using MPI.

RANDOM_MPI, a FORTRAN90 code which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.

RING_MPI, a FORTRAN90 code 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 FORTRAN90 code which solves the circuit satisfy problem.


SATISFY_OPENMP, a FORTRAN90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using OpenMP for parallel execution.

SEARCH_MPI, a FORTRAN90 code which searches integers between A and B for a value J such that F(J) = C, using MPI for parallel execution.

WAVE_MPI, a FORTRAN90 code 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:

Last revised on 26 August 2020.