3CAM - A NOVEL TERNARY CONTENT ADDRESSABLE MEMORY USING THREE-VALUED LOGIC

Content Addressable Memory (CAM) is a special type of Complementary Metal-Oxide-Semiconductor (CMOS) storage element that allows for a parallel search operation on a memory stack in addition to the read and write operations yielded by a conventional SRAM storage array. In practice, it is often desirable to be able to store a “don’t care” state for faster searching operation. However, commercially available CAM chips are forced to accomplish this functionality by having to include two binary memory storage elements per CAM cell,which is a waste of precious area and power resources. This research presents a novel CAM circuit that achieves the “don’t care” functionality with a single ternary memory storage element. Using the recent development of multiple-voltage-threshold (MVT) CMOS transistors, the functionality of the proposed circuit is validated and characteristics for performance, power consumption, noise immunity, and silicon area are presented. This workpresents the following contributions to the field of CAM and ternary-valued logic:• We present a novel Simple Ternary Inverter (STI) transistor geometry scheme for achieving ternary-valued functionality in existing SOI-CMOS 0.18µm processes.• We present a novel Ternary Content Addressable Memory based on Three-Valued Logic (3CAM) as a single-storage-element CAM cell with “don’t care” functionality.• We explore the application of macro partitioning schemes to our proposed 3CAM array to observe the benefits and tradeoffs of architecture design in the context of power, delay, and area.

Many-Valued Logic and Qualitative Modelling of Electrical Circuits

Lee M.H., Many-Valued Logic and Qualitative Modelling of Electrical Circuits, in Proc. QR?2000, 14th Int. Workshop on Qualitative Reasoning, Morelia, Mexico June 3rd - 7th 2000.

Smart universal multiple-valued logic gates by transferring single electrons

This paper proposes smart universal multiple-valued (MV) logic gates by transferring single electrons (SEs). The logic gates are based on MOSFET based SE turnstiles that can accurately transfer SEs with high speed at high temperature. The number of electrons transferred per cycle by the SE turnstile is a quantized function of its gate voltage, and this characteristic is fully exploited to compactly finish MV logic operations. First, we build arbitrary MV literal gates by using pairs of SE turnstiles. Then, we propose universal MV logic-to-value conversion gates and MV analog-digital conversion circuits. We propose a SPICE model to describe the behavior of the MOSFET based SE turnstile. We simulate the performances of the proposed gates. The MV logic gates have small number of transistors and low power dissipations.

SYM-1, a program that detects symmetry of variable-valued logic functions /

Mode of access: Internet.

A comparative discussion of variable-valued logic and grammatical inference /

Bibliography: p. 45-46.

Selected problems of minimization of variable-valued logic formulas /

"UIUCDCS-R-75-726"

A planar geometrical model for representing multidimensional discrete spaces and multiple-valued logic functions /

Bibliography: p. 37-38.

Learning without negative examples via variable-valued logic characterizations : the uniclass inductive program AQ7UNI /

"July 1979."

An Avron rule for fragments of R-mingle

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a ‘modus-ponens-like’ rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication–fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set of rules. Indeed, this latter case provides an example of a three-valued logic with a finitely axiomatizable consequence relation that has no finite basis for its admissible rules.

Multiplication and comultiplication of beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the analytical product and coproduct of beta probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions. (C) 2004 Elsevier Inc. All rights reserved.

Truth Values in t-norm based Systems Many-valued FUZZY Logic

In t-norm based systems many-valued logic, valuations of propositions form a non-countable set: interval [0,1]. In addition, we are given a set E of truth values p, subject to certain conditions, the valuation v is v=V(p), V reciprocal application of E on [0,1]. The general propositional algebra of t-norm based many-valued logic is then constructed from seven axioms. It contains classical logic (not many-valued) as a special case. It is first applied to the case where E=[0,1] and V is the identity. The result is a t-norm based many-valued logic in which contradiction can have a nonzero degree of truth but cannot be true; for this reason, this logic is called quasi-paraconsistent.

Reed-Muller Canonical Forms in Multivalued Logic

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Compact voltage-mode multi-valued literal gate using nanoscale ballistic MOSFETs

A CMOS voltage-mode multi-valued literal gate is presented. The ballistic electron transport characteristic of nanoscale MOSFETs is smartly used to compactly achieve universal radix-4 literal operations. The proposed literal gates have small numbers of transistors and low power dissipations, which makes them promising for future nanoscale multi-valued circuits. The gates are simulated by HSPICE.