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

In this paper studied are new concepts of robotic behaviors - determin- istic and quantum probabilistic. In contrast to classical c ircuits, the quantum circuit can realize both of these behaviors. When applied to a robot, a quantum circuit con- troller realizes what we call quantum robot behaviors. We use automated methods to synthesize quantum behaviors (circuits) from the examples (examples are cares of the quantum truth table). The don't knows (minterms not give n as examples) are then converted not only to deterministic cares as in the classica l learning, but also to output values generated with various probabilities. The Occam Razor principle, fundamental to inductive learning, is satisfied in this approach by seeki ng circuits of reduced com- plexity. This is illustrated by the synthesis of single outp ut quantum circuits, as we extended the logic synthesis approach to Inductive Machine Learning for the case of learning quantum circuits from behavioral examples.

/pdf/inductive-learning-of-quantum-behaviors-uy3bavixsx.pdf

Inductive Learning of Quantum Behaviors

For Part 1 see ibid. vol.22, no.3 (2002). A massively parallel reconfigurable processor speeds up the logic operators performed in the learning hardware. The approach uses combinatorial synthesis methods developed within the framework of the logic synthesis approach in digital-circuit-design automation.

Learning hardware using multiple-valued logic - Part 2: Cube calculus and architecture

The classification of Boolean functions plays an underpinning role in logic design and synthesis of VLSI circuits. This paper considers a underpinning question in Boolean function classification: how many distinct classes are there for k-input Boolean functions. We exploit various group algebraic properties to efficiently compute the number of unique equivalent classes. We have reduced the computation complexity from 2mm! to (m + 1)!. We present our analysis for NPN classification of Boolean functions with up to ten variables and compute the number of NP and NPN equivalence classes for 3-10 variables. This is the first time to report the number of NP and NPN classifications for Boolean functions with 9-10 variables. We demonstrate the effectiveness of our method by both theoretical proofs and numeric experiments.

A Group Algebraic Approach to NPN Classification of Boolean Functions

A hierarchical Hough transform (HT) based on pyramidal architecture is described, being a main component of the low-to-medium spatial vision subsystem for a mobile robot. The sequence of processing in the system originally conceived to be essential to the extraction of line features in indoor scenes consisted of: histogram equalization, smoothing with the use of a medial filter, edge detection using the Sobel edge detectors, binarization to extract the edges detected, labeling, rebinarization and thinning to refine the edges to thin lines, and line extraction using a hierarchical approach to the HT method. The task was to establish the importance of each step for the success of the hierarchical HT. It was implemented on a 386-based personal computer with 640 K memory and proved to give results of high quality as compared with the standard HT implementation. >

/pdf/hierarchical-hough-transform-based-on-pyramidal-architecture-4pnao7a5ev.pdf

Hierarchical Hough transform based on pyramidal architecture

In this paper we show how Boolean Ring logic, a group-based logic, leads to a circuit implementation that is highly testable. We develop Boolean Ring based expressions, which we call Generalized-Literal Boolean-Ring Sum-of-Products (GL-BRSOP) and Universal-Literal Boolean-Ring Sum-of-Products (UL-BRSOP) to represent (powers of 2)-valued MVL functions. Our BRSOPs: allow MVL functions to be implemented with vectors of binary AND and EXOR gates; allow the use of a binary logic fault model; and allow a time-multiplexed implementation that is highly testable and uses less redundant circuitry.

Marek Perkowski

Papers

Inductive Learning of Quantum Behaviors

Learning hardware using multiple-valued logic - Part 2: Cube calculus and architecture

A Group Algebraic Approach to NPN Classification of Boolean Functions

Hierarchical Hough transform based on pyramidal architecture

Highly testable Boolean ring logic circuits