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Reed-Muller Expressions, Development, generalizations, and some applications

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Reed-Muller expressions are representations for switching functions that can be interpreted as both polynomial and spectral expressions. That allows different possibilities for their applications, development of efficient calculation algorithms, and various extensions and generalizations to the representation of different classes of discrete and digital signals.

The renewed considerable research interest in theory and applications of Reed-Muller expressions is probably the best confirmed by the organization of regular international Workshops on Applications of Reed-Muller Expression in Circuit Design, every second year from 1993.

In this talk, different interpretations and approaches to Reed-Muller expressions will be discussed. Extensions and generalizations to the representation of multiple-valued functions are achieved in different algebraic structures. The arithmetic transform, can be considered as the word-level counterparts of the Reed-Muller expressions closely related to the discrete Walsh transform.

The applications of this theory will be illustrated by the example of optimization of both bit-level and word-level polynomial expressions and decision diagram representations for n-bit adders.

Prof. Radomir S. Stanković
Dept. of Computer Science
Faculty of Electronics
Niš
Serbia

and

Jaakko Astola
Institute of Signal Processing
Tampere University of Technology
Tampere
Finland


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