Proceedings ArticleDOI
An efficient program for logic synthesis of mod-2 sum expressions
P.W. Besslich,M.W. Riege +1 more
- pp 136-141
TLDR
The authors report on a program based on new algorithms: Quasi-minimum covering is obtained in a polarized Reed-Muller domain using a modified disjoint sharp operator that performs about an order of magnitude faster than other algorithms.Abstract:
Resurrected interest in mod-2 sum logic requires efficient algorithms for synthesis of incompletely specified multiple-output functions. The authors report on a program based on new algorithms: Quasi-minimum covering is obtained in a polarized Reed-Muller domain using a modified disjoint sharp operator. Since a new algorithm for cubewise RMT is applied, and since no iterative procedures are employed, the program performs about an order of magnitude faster than other algorithms. The new program can handle functions of hundreds of variables on a personal computer. Solutions are (on average) superior to those of other methods. >read more
Citations
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Journal ArticleDOI
EXMIN2: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued-input two-valued-output functions
TL;DR: A simplification algorithm that iteratively reduces the number of the products in ESOPs and then reduces theNumber of the literals is presented, used to replace a pair of products with another one.
Journal ArticleDOI
Minimization of exclusive sum-of-products expressions for multiple-valued input, incompletely specified functions
N. Song,Marek Perkowski +1 more
TL;DR: Evaluation on benchmark functions is given and it proves the superiority of the program to those known from the literature on the basis of power and efficiency.
Proceedings ArticleDOI
Fast exact and quasi-minimal minimization of highly testable fixed-polarity AND/XOR canonical networks
Andisheh Sarabi,Marek Perkowski +1 more
TL;DR: Fast exact and quasi-minimal algorithms for minimal fixed polarity AND/XOR canonical representation of Boolean functions and features of arrays of disjoint cubes representations of functions to identify the minimal networks are introduced.
Proceedings ArticleDOI
Efficient graph-based computation and manipulation of functional decision diagrams
TL;DR: An efficient canonical representation for arbitrary Boolean functions, the functional decision diagrams (FDDs), are presented and show that FDDs are applicable for new approaches to Reed-Muller logic synthesis.
Proceedings ArticleDOI
Logic synthesis for arithmetic circuits using the Reed-Muller representation
TL;DR: A procedure for multi-level Reed-Muller minimization has been developed which introduces a Reed-muller factored form, and uses algebraic algorithms for factorization, decomposition, resubstitution, collapsing, and extraction of common cubes and subexpressions.
References
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Journal ArticleDOI
On the complexity of mod-2l sum PLA's
Tsutomu Sasao,P. Besslich +1 more
TL;DR: Upper bounds on the number of products of this type of PLA are derived that are useful for estimating the size of a PLA as well as for assessing the minimality of the solutions obtained by heuristic ESOP minimization algorithms.
Proceedings ArticleDOI
A fast algorithm to minimize multi-output mixed-polarity generalized Reed-Muller forms
Martin Helliwell,Marek Perkowski +1 more
TL;DR: A very fast computer program that accepts a Boolean function as an array of multi-output disjoint cubes and returns a mixed-polarity Generalized Reed-Muller Form is presented.
Journal ArticleDOI
Minimization of Exclusive or and Logical Equivalence Switching Circuits
A. Mukhopadhyay,G. Schmitz +1 more
TL;DR: This paper is an attempt to develop minimization algorithms for switching circuits based on Reed-Muller canonic forms for obtaining minimal modulo 2 or complement modulo2 sum-of- products expressions of any arbitrary single-output or multiple-output switching function with fixed polarities of the input variables.
Journal ArticleDOI
On Minimal Modulo 2 Sums of Products for Switching Functions
Shimon Even,I. Kohavi,A. Paz +2 more
TL;DR: Every symmetric function of 2m+1 variables has a modulo 2 sum of products realization with at most 3m terms; but there are functions of n variables which require at least 2n/n log 2 3 terms for sufficiently large n.
Journal ArticleDOI
Efficient computer method for ExOR logic design
TL;DR: An efficient computer method is developed for the generation of all 2n sets of GRM coefficients of an n-variable Boolean function and a metric is calculated from which the minimum cost set according to some criterion may be selected.