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<html>
<head>
<title>
SATISFY - Seek Binary Circuit Inputs that Output 1
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SATISFY <br> Seek Binary Circuit Inputs that Output 1
</h1>
<hr>
<p>
<b>SATISFY</b>
is a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfy problem.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
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!
</p>
<p>
This problem is a natural candidate for parallel computation, since
the individual evaluations of the circuit are completely independent.
</p>
<p>
The example circuit considered here has been described in conjunctive
normal form ("CNF"). This is a standard format for logical formulas.
At the highest level, the formula consists of <i>clauses</i> joined
by the <b>AND</b> (conjunction) operator. Each clause consists of
<i>signed literals</i> joined by the <b>OR</b> (disjunction) operator.
Each signed literal is either the name of a variable (positive literal),
or the name of a variable preceded by the <b>NOT</b> (negation) operator
(a negative literal). There is a CNF file format that can be used to
store logical formulas that have been cast into conjunctive normal form.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SATISFY</b> is available in
<a href = "../../c_src/satisfy/satisfy.html">a C version</a> and
<a href = "../../cpp_src/satisfy/satisfy.html">a C++ version</a> and
<a href = "../../f77_src/satisfy/satisfy.html">a FORTRAN77 version</a> and
<a href = "../../f_src/satisfy/satisfy.html">a FORTRAN90 version</a> and
<a href = "../../m_src/satisfy/satisfy.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/change_making/change_making.html">
CHANGE_MAKING</a>,
a MATLAB library which
considers the change making problem,
in which a given sum is to be formed using coins of various denominations.
</p>
<p>
<a href = "../../data/cnf/cnf.html">
CNF</a>,
a data directory which
describes the DIMACS CNF file format for defining instances of the
satisfy problem for boolean formulas in conjunctive normal form.
</p>
<p>
<a href = "../../m_src/combination_lock/combination_lock.html">
COMBINATION_LOCK</a>,
a MATLAB program which
simulates the process of determining the secret combination of a lock.
</p>
<p>
<a href = "../../m_src/combo/combo.html">
COMBO</a>,
a MATLAB library which
includes many combinatorial routines.
</p>
<p>
<a href = "../../m_src/partition_problem/partition_problem.html">
PARTITION_PROBLEM</a>,
a MATLAB library which
seeks solutions of the partition problem, splitting a set of integers into
two subsets with equal sum.
</p>
<p>
<a href = "../../m_src/satisfy_parfor/satisfy_parfor.html">
SATISFY_PARFOR</a>,
a MATLAB program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
running in parallel using MATLAB's parfor feature.
</p>
<p>
<a href = "../../m_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
a MATLAB program which
searches the integers from A to B for a value J such that F(J) = C.
this version of the program is intended as a starting point for
a parallel approach.
</p>
<p>
<a href = "../../m_src/subset/subset.html">
SUBSET</a>,
a MATLAB library which
enumerates combinations, partitions, subsets, index sets,
and other combinatorial objects.
</p>
<p>
<a href = "../../m_src/subset_sum/subset_sum.html">
SUBSET_SUM</a>,
a MATLAB library which
seeks solutions of the subset sum problem.
</p>
<p>
<a href = "../../m_src/tsp_brute/tsp_brute.html">
TSP_BRUTE</a>,
a MATLAB program which
reads a file of city-to-city distances and solves the
traveling salesperson problem, using brute force.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Rina Dechter,<br>
Enhancement Schemes for constraint processing:
Backjumping, learning, and cutset decomposition,<br>
Artificial Intelligence,<br>
Volume 41, Number 3, January 1990, pages 273-312.
</li>
<li>
Michael Quinn,<br>
Parallel Programming in C with MPI and OpenMP,<br>
McGraw-Hill, 2004,<br>
ISBN13: 978-0071232654,<br>
LC: QA76.73.C15.Q55.
</li>
<li>
Steven Skiena,<br>
The Algorithm Design Manual,<br>
Springer, 1997,<br>
ISBN: 0-387-94860-0,<br>
LC: QA76.9.A43S55.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "satisfy.m">satisfy.m</a>,
the program.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "satisfy_output.txt">satisfy_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for SATISFY.
</li>
<li>
<b>CIRCUIT_VALUE</b> returns the value of a circuit for a given input set.
</li>
<li>
<b>I4_TO_BVEC</b> converts an integer into a binary vector.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 20 March 2009.
</i>
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