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

An exact algorithm for the synthesis of mixed polarity exclusive sum of product (ESOP) expressions for arbitrary size incompletely specified Boolean functions is presented. For more than four input variables, this problem has not been solved yet. A decision function H is constructed for a Boolean function f that describes all possible ESOP solutions to f. The function H plays for the ESOP minimization problem a role analogous to that of the Petrick function for the minimization of the inclusive sum of product expression problem of classical logic. Each product of literals that satisfies the function H corresponds to one ESOP solution of f. The algorithms to create and solve function H are presented. >

/pdf/an-exact-algorithm-to-minimize-mixed-radix-exclusive-sums-of-2kqbu6de1b.pdf

An exact algorithm to minimize mixed-radix exclusive sums of products for incompletely specified Boolean functions

/pdf/multiple-valued-quantum-logic-synthesis-1vk1ji571i.pdf

Multiple-Valued Quantum Logic Synthesis

By investigating some families of elementary order-2 matrices, new transforms of real vectors are introduced. When used for Boolean function transformations these transforms are one-to-one mappings in a binary/ternary vector space. The concept of different polarities of considered arithmetic and adding transforms is introduced. The links of arithmetic and adding transforms with classical logic design are discussed. >

/pdf/a-family-of-all-essential-radix-2-addition-subtraction-multi-128wivt52a.pdf

A family of all essential Radix-2 addition/subtraction multi-polarity transforms: algorithms and interpretations in Boolean domain

Ternary quantum circuits have recently been introduced to help reduce the size of multi-valued logic for multi-level quantum computing systems. However, synthesizing these quantum circuits is not easy. We describe a new genetic algorithm based synthesizer for ternary quantum circuits. Our results show some of the synthesized circuits use fewer gates than previously published methods.

/pdf/genetic-algorithm-based-synthesis-of-multi-output-ternary-53mxrr3jhe.pdf

Genetic algorithm based synthesis of multi-output ternary functions using quantum cascade of generalized ternary gates

The paper presents new logic synthesis methods for single-output incomplete multi-level binary circuits using Memristor-based material implication gates. The first method follows Lehtonen's assumption of using only two working memristors. The algorithm minimizes the number of implication (IMPLY) gates, which corresponds to minimizing the number of pulses or the delay time. This greedy search method uses essential and secondary essential primes, does not require solving the covering problem, is fast, and produces high quality results. We compare it to other synthesis methods, such as the modified SOP and Exclusive-Or Sum of Products (ESOP) with minimum number of working memristors. We analyze the problem of reduction in IMPLY gate count by adding more working memristors and introduce Imply Sequence Diagrams, a new notation, similar to one used in reversible logic.

Marek Perkowski

Papers

An exact algorithm to minimize mixed-radix exclusive sums of products for incompletely specified Boolean functions

Multiple-Valued Quantum Logic Synthesis

A family of all essential Radix-2 addition/subtraction multi-polarity transforms: algorithms and interpretations in Boolean domain

Genetic algorithm based synthesis of multi-output ternary functions using quantum cascade of generalized ternary gates

Logic synthesis and a generalized notation for memristor-realized material implication gates