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.

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Strange attractor in optical logic cells

Optical logic cells, employed in several tasks as optical computing or optically controlled switches for photonic switching, offer a very particular behavior when the working conditions are slightly modified. One of the more striking changes occurs when some delayed feedback is applied between one of the possible output gates and a control input. Some of these new phenomena have been studied by us and reported in previous papers. A chaotic behavior is one of the more characteristic results and its possible applications range from communications to cryptography. But the main problem related with this behavior is the binary character of the resulting signal. Most of the nowadays-employed techniques to analyze chaotic signals concern to analogue signals where algebraic equations are possible to obtain. There are no specific tools to study digital chaotic signals. Some methods have been proposed. One of the more used is equivalent to the phase diagram in analogue chaos. The binary signal is converted to hexadecimal and then analyzed. We represented the fractal characteristics of the signal. It has the characteristics of a strange attractor and gives more information than the obtained from previous methods. A phase diagram, as the one obtained by previous techniques, may fully cover its surface with the trajectories and almost no information may be obtained from it. Now, this new method offers the evolution around just a certain area being this lines the strange attractor.

Logic Based Pattern Recognition - Ontology Content (2)

Logic based Pattern Recognition extends the well known similarity models, where the distance measure is the base instrument for recognition. Initial part (1) of current publication in iTECH-06 reduces the logic based recognition models to the reduced disjunctive normal forms of partially defined Boolean functions. This step appears as a way to alternative pattern recognition instruments through combining metric and logic hypotheses and features, leading to studies of logic forms, hypotheses, hierarchies of hypotheses and effective algorithmic solutions. Current part (2) provides probabilistic conclusions on effective recognition by logic means in a model environment of binary attributes.

On some Properties of Boolean Functions and Their Binary Decision Diagrams

Иво Й. Дамянов - Манипулирането на булеви функции е основнo за теоретичната информатика, в това число логическата оптимизация, валидирането и синтеза на схеми. В тази статия се разглеждат някои първоначални резултати относно връзката между граф-базираното представяне на булевите функции и свойствата на техните променливи.

Extension of bivariate means to weighted means of several arguments by using binary trees

ABSTRACTAveraging aggregation functions are valuable in building decision making and fuzzy logic systems and in handling uncertainty. Some interesting classes of averages are bivariate and not easily extended to the multivariate case. We propose a generic method for extending bivariate symmetric means to n-variate weighted means by recursively applying the specified bivariate mean in a binary tree construction. We prove that the resulting extension inherits many desirable properties of the base mean and design an efficient numerical algorithm by pruning the binary tree. We show that the proposed method is numerically competitive to the explicit analytical formulas and hence can be used in various computational intelligence systems which rely on aggregation functions.

Idempotent weighted aggregation based on binary aggregation trees

We propose weighted aggregation algorithms for creating general idempotent weighted aggregators of n variables derived from related symmetric idempotent aggregators of two variables. This computational method, together with interpolative aggregation, can be used for the development of general idempotent logic aggregators that satisfy a variety of conditions necessary for building decision models in the area of weighted compensative logic.

The logic of ADHD : a brief review of fallacious reasoning

This paper has two central purposes: the first is to survey some of the more important examples of fallacious argument, and the second is to examine the frequent use of these fallacies in support of the psychological construct: Attention Deficit Hyperactivity Disorder (ADHD). The paper divides 12 familiar fallacies into three different categories—material, psychological and logical—and contends that advocates of ADHD often seem to employ these fallacies to support their position. It is suggested that all researchers, whether into ADHD or otherwise, need to pay much closer attention to the construction of their arguments if they are not to make truth claims unsupported by satisfactory evidence, form or logic.