1. Introduction
Digital devices are developed by different blocks of digital
logic circuits and the combination of which performs the
desire task. The eficient implementation of logic functions
using minimum number of logic gates is necessary to minimize
production costs, and maximize a device’s performance[1].
All digital systems have two major functional blocks, memory
elements for storing data, and combinational circuits for
transform that information. The three major functions of
any memory elements are to store data i.e. hold data, accept
writing a new data and read the stored data. Minimization of
digital logic circuits are one of the important and well-known
problems in circuit design and testing. Different methodologies
are used for completely speciied Boolean function and
incompletely speciied Boolean function. There are two main
approaches to synthesis in logic design based on formal exact
algorithms and based on informal methods i.e. heuristic
algorithms. The exact algorithms are often unsuitable for the
minimization of Boolean functions and optimization of logic
networks particularly with more number of input variables.
Heuristic algorithm gives acceptable solutions and sometimes
even optimal ones in a short time for large size problems, but
there is no guarantee that they will do so in any particular
case most of them provide quasi-optimal solutions. Heuristic
minimization of Boolean functions are motivated by the need
to reduce the size of two levels. Two-level logic minimization
*Corresponding author.
© Elsevier Publications 2014.
Constraints Analysis for Minimization of Multiple Inputs Logic Programming
Sahadev Roy*, and Chandan Tilak Bhunia
Department of ECE
NIT, Arunachal Pradesh, Yupia, Itanagar, India
Email: sdr.ece@nitap.in
ABSTRACT: Minimization of logic functions by computer programs are considered traditionally to be dificult and tedious as the
incorporation of full logic negation tends to super-exponential time complexity. The paper presents constrains for minimization of logic
circuits. Using these analysis minimized sum of products terms may be generating from any given sum of product terms of multiple
input variables. For a new algorithm for minimization using computer programming must be overcome these problem presented. We also
discuss the scope heuristic minimization technique over the exact minimization technique.
Keywords: Algorithm, Minterms, Minimization, Logic, Boolean function, SOP, POS Weighted sum, Complexity, Constraint.
consists of inding a minimum SOP that covers a given Boolean
function design based on SOP and POS expression [2]. Logic
networks that have more two levels often have fewer gates and
meet lower fan-in and fan-out limits [3]. The design of multi
level networks is more complex that of two level ones [4]. No
practical and exact minimization techniques are known for
general multi level networks[5]. Many heuristic techniques are
present for multi level logic networks optimization[6].
2. Complexity of Minimization
Many heurestic approach minimize the logic circuite quickly.
Using minimization algorithm for multiple input into the two
input variables eassily minimized into two variable [2].
Two main approaches can be used by general tools and
specialized programs. General tools support the declarative
statement of problems but are too ineficient. Specialized
programs require much programming effort and are hard to
maintain. No general and eficient algorithms are exist to
solve minimization problems, which can be viewed as search
problems with mutiple input.
PROLOG provides a powerful language for a logical
formulation of combinational problems. Its relational form and
the logical variables are entirely adequate to solve the problems
in a declarative way, and its nondeterministic computation
liberates the user from tree-search programming. However,
International Conference on Signal and Speech Processing
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