SATISFY_OPENMP Seek Binary Circuit Inputs that Output 1, Using OpenMP

SATISFY_OPENMP is a FORTRAN90 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:
18,388,6084.38 seconds
28,388,6082.29 seconds
48,388,6082.29 seconds

Usage:

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

```        export OMP_NUM_THREADS=2
./satisfy_openmp
```

Languages:

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

Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN90 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a FORTRAN90 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN90 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

JACOBI_OPENMP, a FORTRAN90 program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

MANDELBROT_OPENMP, a FORTRAN90 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a FORTRAN90 program which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a FORTRAN90 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN90 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

OPENMP_RCC, FORTRAN90 programs which illustrate how a FORTRAN90 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 FORTRAN90 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 FORTRAN90 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a FORTRAN90 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem.

SATISFY_MPI, a FORTRAN90 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.

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

SCHEDULE_OPENMP, a FORTRAN90 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN90 program which solves a linear system by Gaussian elimination, using OpenMP.

ZIGGURAT_OPENMP, a FORTRAN90 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

Reference:

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

List of Routines:

• MAIN is the main program for SATISFY_OPENMP.
• CIRCUIT_VALUE returns the value of a circuit for a given input set.
• I4_TO_BVEC converts an integer into a binary vector.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.

Last revised on 04 September 2009.