Vlad - Boolean functions: topics in asynchronicity

1. Chapter 1
2. Chapter 2
3. Chapter 3
4. Chapter 4
5. Chapter 5
6. Chapter 6
7. Chapter 7
8. Chapter 8
9. Chapter 9
10. Chapter 10
11. Chapter 11
12. Chapter 13
13. Chapter 14
14. Chapter 15

First Edition

Serban E. Vlad

Oradea, Romania

This edition first published 2019

2019 John Wiley & Sons, inc

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Library of Congress CataloginginPublication Data

Names: Vlad, Serban E., 1959- author.

Title: Boolean functions : topics in asynchronicity / Serban E. Vlad.

Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2018. |

Includes bibliographical references and index. |

Identifiers: LCCN 2018034871 (print) | LCCN 2018057135 (ebook) | ISBN

9781119517498 (Adobe PDF) | ISBN 9781119517511 (ePub) | ISBN 9781119517474

(hardcover) | ISBN 9781119517498 (ePDF)

Subjects: LCSH: Algebra, Boolean.

Classification: LCC QA10.3 (ebook) | LCC QA10.3 .V533 2018 (print) | DDC

511.3/24--dc23

LC record available at https://lccn.loc.gov/2018034871

ISBN 9781119517474 (Hardback)

ISBN 9781119517498 (ePDF)

ISBN 9781119517511 (epub)

Cover Design: Wiley

Cover Image: Courtesy of Serban E. Vlad

To Ciupi and Puiu Mic

In this framework, by asynchronicity we mean that the coordinate functions of a function are computed independently on each other, asynchronously. Synchronicity is that special case of asynchronicity when are computed at the same time, synchronously. It is of special interest to study the iterations of which can be asynchronous or synchronous.

Our project Topics in asynchronicity has been thought of having two parts, part I: Boolean functions and part II: Boolean systems. While working we took the decision to split it in two books.

The source of inspiration is represented by the asynchronous circuits from electronics that can be modeled by Boolean functions iterating their coordinates in arbitrary time, independently on each other, i.e. asynchronously. The uncertainties related with the behavior of the circuits and their models are generated by technology and also by temperature variations and voltage supply variations.

In order to understand the dynamics of these systems, we give the example of the function from (we have adopted the terminology of state portrait, by analogy with the phase portraits of the dynamical systems theory; such drawings might be called in engineering and elsewhere state transition graphs or state transition diagrams).

An example.