skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Uncertainty, energy, and multiple-valued logics

Abstract

The multiple-valued logics obtained by introducing uncertainty and energy considerations into classical switching theory are studied in this paper. First, the nature of uncertain or unknown signals is examined, and two general uncertainty types called U-values and P-values are identified. It is shown that multiple-valued logics composed of U/P-values can be systematically derived from 2-valued Boolean algebra. These are useful for timing and hazard analysis, and provide a rigorous framework for designing gate-level logic simulation programs. Next, signals of the form (..nu..,S) are considered where ..nu.. and S denote logic level and strength, respectively, and the product vs corresponds to energy flow or power. It is shown that these signals from a type of lattice called a Pseudo-Boolean algebra. Such algebras characterize the behavior of digital circuits at a level (the switch level) intermediate between the conventional analog and logical levels. They provide the mathematical basis for an efficient new class of switch-level simulation programs used in MOS VLSI design.

Authors:
Publication Date:
Research Org.:
Dept. of Electrical Eng. and Computer Science, Univ. of Michigan, Ann Arbor, MI
OSTI Identifier:
5812085
Resource Type:
Journal Article
Journal Name:
IEEE Trans. Comput.; (United States)
Additional Journal Information:
Journal Volume: C-35:2
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; INTEGRATED CIRCUITS; CIRCUIT THEORY; COMPUTER-AIDED DESIGN; SWITCHING CIRCUITS; COMPUTERIZED SIMULATION; ALGEBRA; DATA COVARIANCES; DIGITAL SYSTEMS; MATHEMATICAL LOGIC; MOS TRANSISTORS; PROGRAMMING; SIGNALS; TIME DEPENDENCE; ELECTRONIC CIRCUITS; MATHEMATICS; MICROELECTRONIC CIRCUITS; SEMICONDUCTOR DEVICES; SIMULATION; TRANSISTORS; 420800* - Engineering- Electronic Circuits & Devices- (-1989)

Citation Formats

Hayes, J P. Uncertainty, energy, and multiple-valued logics. United States: N. p., 1986. Web. doi:10.1109/TC.1986.1676728.
Hayes, J P. Uncertainty, energy, and multiple-valued logics. United States. https://doi.org/10.1109/TC.1986.1676728
Hayes, J P. 1986. "Uncertainty, energy, and multiple-valued logics". United States. https://doi.org/10.1109/TC.1986.1676728.
@article{osti_5812085,
title = {Uncertainty, energy, and multiple-valued logics},
author = {Hayes, J P},
abstractNote = {The multiple-valued logics obtained by introducing uncertainty and energy considerations into classical switching theory are studied in this paper. First, the nature of uncertain or unknown signals is examined, and two general uncertainty types called U-values and P-values are identified. It is shown that multiple-valued logics composed of U/P-values can be systematically derived from 2-valued Boolean algebra. These are useful for timing and hazard analysis, and provide a rigorous framework for designing gate-level logic simulation programs. Next, signals of the form (..nu..,S) are considered where ..nu.. and S denote logic level and strength, respectively, and the product vs corresponds to energy flow or power. It is shown that these signals from a type of lattice called a Pseudo-Boolean algebra. Such algebras characterize the behavior of digital circuits at a level (the switch level) intermediate between the conventional analog and logical levels. They provide the mathematical basis for an efficient new class of switch-level simulation programs used in MOS VLSI design.},
doi = {10.1109/TC.1986.1676728},
url = {https://www.osti.gov/biblio/5812085}, journal = {IEEE Trans. Comput.; (United States)},
number = ,
volume = C-35:2,
place = {United States},
year = {Sat Feb 01 00:00:00 EST 1986},
month = {Sat Feb 01 00:00:00 EST 1986}
}