There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The organization of behavior: A neuropsychological theory

The Personal Interview

What is modal logic

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

The design of a high-frequency field-programmable analog array (FPAA) is presented. The FPAA is based on a regular pattern of cells interconnected locally for high frequency performance. No switches of any kind are used in the signal path of a cell: programming of the functions, parameters, and interconnections is achieved solely by modifying cells’ bias conditions digitally. Limited global signal interconnections are also available for those application circuits which cannot be mapped onto locally-only interconnected structure. Key circuits of the FPAA have been fabricated in a CPI transistor-array bipolar technology.

A High-Frequency Field-Programmable Analog Array (FPAA) Part 1: Design

This paper considers minimization of incompletely specified multi-valued functions using functional decomposition. While functional decomposition was originally created for the minimization of logic circuits, this paper uses the decomposition process for both machine learning and logic synthesis of multi-valued functions. As it turns out, the minimization of logic circuits can be used in the concept of "learning" in machine learning, by reducing the complexity of a given data set. A main difference is that machine learning problems normally have a large number of output don't cares. Thus, the decomposition technique presented in this paper is focused on functions with a large number of don't cares. There have been several papers that have discussed the topic of using multi-valued functional decomposition for functions with a large number of don't cares. The novelty brought with this paper is that the proposed method is structured to reduce the resulting "error" of the functional decomposer where "error" is a measure of how well a machine learning algorithm approximates the actual, or true function.

/pdf/an-error-reducing-approach-to-machine-learning-using-multi-4az380youy.pdf

An error reducing approach to machine learning using multi-valued functional decomposition

It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. We describe the experiments that we conducted using GPU programming. Various approaches to fitness function formulation were applied to obtain various realizations of well known universal Boolean reversible quantum gates.

Evolutionary quantum logic synthesis of Boolean reversible logic circuits embedded in ternary quantum space using structural restrictions

A new algorithm is described for calculation of the forward Hadamard-Walsh transform of completely and incompletely specified boolean functions. It makes use of the properties of the disjoint cubes array representation of boolean functions.

One more way to calculate the Hadamard-Walsh spectrum for completely and incompletely specified boolean functions

We advocate an approach to learning hardware based on induction of finite state machines from temporal logic constraints. The method involves training on examples, constraints solving, determinization, state machine minimization, structural mapping, functional decomposition of multi-valued logic functions and relations, and finally, FPGA mapping. In our approach, learning takes place on the level of constraint acquisition and functional decomposition rather than on the lower level of programming binary switches. Our learning strategy is based on the principle of Occam's Razor, facilitating generalization and discovery. We implemented several learning algorithms using DEC-PERLE-1 FPGA board.

/pdf/evolvable-hardware-or-learning-hardware-induction-of-state-1lpfgxybb2.pdf

Marek Perkowski

Papers

A High-Frequency Field-Programmable Analog Array (FPAA) Part 1: Design

An error reducing approach to machine learning using multi-valued functional decomposition

Evolutionary quantum logic synthesis of Boolean reversible logic circuits embedded in ternary quantum space using structural restrictions

One more way to calculate the Hadamard-Walsh spectrum for completely and incompletely specified boolean functions

Evolvable hardware or learning hardware? induction of state machines from temporal logic constraints