Short course

Representations and Classifications of Logic Signals - Trends and Challenges (Tentatively 2 cr)

Instructors: Prof.  R. Stankovic, Prof. J. Astola

Requirements:

Attendance + Homework

Contents

Historical Perspective (1)

Demands of Future Computing Technologies (1)

Binary, Multiple-Valued, and Quantum Logic Signals and Circuits (1)

Spectral Representations (1)

Classification of Switching Functions in Boolean Domain (2)

Classification of Switching Functions in Spectral Domain (Walsh, Autocorrelation, WDD) (2)

SD-classification, Majority and Threshold Logic (1)

Implementation of Threshold Logic by Quantum Circuits (1)

Schedule

Five meetings with two lectures each

Wed 11.11. 16-18, TB215

Fri 13.11. 15-17, TB222

Mon 16.11. 15-17, TB110

Tue 17.11. 16-18, TB215

Wed 18.11. 16-18, TB215

Short description of topics per lectures

Historical Perspective

We briefly present development of Switching Theory and Logic Design and discuss design objectives in different periods pointing out that compact representations were the main goal at the beginning of the area and they are again the main goal in the era of System-on-Chip and Network-on-Chip.

Demands from Future Computing Technologies

We review and discuss what are main characteristics expected to be satisfied from future computing technologies, as regularity, programmability and re-programmability, delay constrains, deep-submicron effects, logic span, reusability. These demands support need for compact representations and extensions to multiple-valued and quantum logic.

Binary, Multiple-Valued, and Quantum Logic Signals and Circuits

Brief review of the definitions and the main characteristics with examples (resonant tunneling diodes (RTD), quantum cellular automata (QCA)).

Spectral Representations

Definitions of Walsh and Reed-Muller representations that are needed for further discussions of different classifications.

Classification of Switching Functions in Boolean Domain

Classification operations and equivalence classes in Boolean domain (NPN, RM, LD).

Classification of Switching Functions in Spectral Domain

Classification operations and equivalence classes in classification by Walsh coefficients and autocorrelation coefficients. Applications of Binary decision diagrams in classification by autocorrelation coefficients and Walsh decision diagrams in classification by Walsh coefficients.

SD-classification, Majority and Threshold Logic

Definition of SD-classification rules and classes. Relationships of self-dual functions majority functions and threshold functions.

Implementation of Threshold Logic by Quantum Circuits

Discussion of realizations of threshold logic by quantum circuits as resonant tunneling diodes and quantum cellular automata. Applications of these methods in synthesis arbitrary multi-output switching functions.