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

A modified Gilbert current gain cell works with a single supply voltage as low as 1.5 V (2V/sub BE/) and reduced power consumption. The circuit inherits most features of the original cell, including the ability to be cascaded without increasing the supply voltage. No special technological features are required to implement the circuit. The design has been verified experimentally using CA 3046 and CA 3096 transistor arrays.

http://ieeexplore.ieee.org/iel3/3834/11195/00539991.pdf

Low-voltage Gilbert current-gain cell

There is a need to convert non-reversible functions to their corresponding reversible functions to be realized as reversible cascades. The original MMD (D.M.Miller, D. Maslov, and G.W.Dueck) algorithm for synthesis of reversible functions using cascades of reversible gates [1] can be modified to allow for the inclusion of “don't cares” within the given function's truth table (reversible or irreversible). This was achieved in the approach presented, by first initializing the “don't cares” to binary values, synthesizing the network using the base MMD algorithm, comparing the cost, and iterating to find an implementation with the smallest possible cost. The “don't care” assignment leading to the circuit with the minimal cost can be determined. This paper discusses this algorithm that is an additional module to the MMD algorithm, the results, the pros and cons of using such an algorithm, and future work to improve the proposed algorithm. A heuristic is also covered, that is superior to the traditional backtracking algorithm and can quickly find an MMD solution with minimum cost for circuits that don’t have large number of “don’t cares”.

/pdf/realization-of-incompletely-specified-f-unctions-in-ph548wzhw1.pdf

Realization of Incompletely Specified F unctions in Minimized Reversible Cascades

In this paper we introduce the new model for Quantum Logic Synthesis. The innovation consists in designing circuits with the measurement process together with the computing circuit. The Measurement is used as a part of the entire computational process. We demonstrate the method to synthesize quantum circuits from examples (examples are cares of the quantum truth table) such that the synthesis process converts the don't knows (minterms not given as examples) to the entangled quantum output values which are measurement dependent. We extended the logic synthesis approach to measurement-based quantum circuits synthesis from incompletely specified or completely specified function specifications.

Projective Measurement-Based Logic Synthesis of Quantum Circuits

Quantum robots, now or never?

We present new experimental Windows 95/98/NT software for investigation of graph properties of boolean (in particular, Reed-Muller) logic with an equal number n of inputs and outputs (called movement functions). Realized at the input of an n-bit register, such functions create autonomous Finite State Machines (FSMs). TRACE software system allows the user to visualize State Transition Graphs (STGs) of the autonomous FSMs. Other features of TRACE help explore graph properties of function families. These families are produced by a generic function, differing from it only in the order of components, one operation, or one literal (this literal is complemented or replaced by another literal). The autonomous FSMs are used to implement economically next-state logic of realtime control units such as CPU controllers. A case study using TRACE to build economical, highly testable reversible counters based on linear Reed-Muller polynomials is given.

http://web.cecs.pdx.edu/~mperkows/=PUBLICATIONS/Perkowski/K1999/RM99trace.pdf

Marek Perkowski

Papers

Low-voltage Gilbert current-gain cell

Realization of Incompletely Specified F unctions in Minimized Reversible Cascades

Projective Measurement-Based Logic Synthesis of Quantum Circuits

Quantum robots, now or never?

TRACE: A Visual Software System to Explore Properties of Reed-Muller Movement Functions