Seek Binary Circuit Inputs that Output 1, Using OpenMP

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

This problem assumes that we are given a logical circuit of AND, OR and NOT gates, with N=23 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 of all 2^N possible inputs.

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

On an Apple PowerPC G5 with two processors, the following results were observed:
18,388,6084.24 seconds
28,388,6082.15 seconds
48,388,6082.28 seconds


In the BASH shell, the program could be run with 2 threads using the commands:

        export OMP_NUM_THREADS=2


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


SATISFY_OPENMP 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.

COMBO, a C library which includes many combinatorial routines.

DIJKSTRA_OPENMP, a C program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a C program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a C program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a C program which prints out "Hello, world!" using the OpenMP parallel programming environment.

LAU_NP, a FORTRAN90 library which implements heuristic algorithms for various NP-hard combinatorial problems.

MD_OPENMP, a C program which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a C program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a C program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

OPENMP, C programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

OPENMP_RCC, C programs which illustrate how a C program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).

POISSON_OPENMP, a C program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_OPENMP, a C program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a C program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a C program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY, a C program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem.

SATISFY_MPI, a C program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using MPI to carry out the calculation in parallel.

SCHEDULE_OPENMP, a C program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a C program which solves a linear system by Gaussian elimination, using OpenMP.

SATISFY_PARFOR, a MATLAB program which is intended to be run in parallel using MATLAB's "PARFOR" feature.

SUBSET, a C++ library which enumerates combinations, partitions, subsets, index sets, and other combinatorial objects.

ZIGGURAT_OPENMP, a C program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.


  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_ITHACA runs SATISFY_OPENMP through the batch system.

List of Routines:

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

Last revised on 20 May 2010.