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

This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiple-valued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2-qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multi-output Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis

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Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis

An efficient package for construction of and operation on ordered Kronecker Functional Decision Diagrams (OKFDD) is presented. OKFDDs are a generalization of OBDDs and OFDDs and as such provide a more compact representation of the functions than either of the two decision diagrams. In this paper basic properties of OKFDDs and their efficient representation and manipulation are presented. Based on the comparison of the three decision diagrams for several benchmark functions, a 25% improve ment in size over OBDDs is observed for OKFDDs.

Efficient Representation and Manipulation of Switching Functions Based on Ordered Kronecker Functional Decision Diagrams

Logic synthesis for reversible logic differs considerably from standard logic synthesis. The gates are multi-output and the unutilized outputs from these gates are called “garbage”. One of the synthesis tasks is to reduce the number of garbage signals. Previous approaches to reversible logic synthesis minimized either only the garbage or (predominantly) the number of gates. Here we present for the first time a method that minimizes concurrently the number of gates, their total delay and the total garbage. Our method adopts for reversible logic many ideas developed previously for standard logic synthesis (such as Ashenhurst/Curtis Decomposition, Dietmeyer’s Composition, non-linear preprocessing for BDDs), methods created in ReedMuller Logic (such as Pseudo-Kronecker Decision Diagrams with Complemented Edges, Pseudo-Kronecker Lattice Diagrams and their generalizations) and introduces also new methods specific to reversible logic.

/pdf/a-general-decomposition-for-reversible-logic-1v3rbti523.pdf

A General Decomposition for Reversible Logic

There is disclosed a programmable analog or mixed analog/digital circuit. More particularly, this invention provides a circuit architecture that is flexible for a programmable electronic hardware device or for an analog circuit whose input and output signals are analog or multi-valued in nature, and primarily continuous in time. There is further disclosed a design for a current-mode integrator and sample-and-hold circuit, based upon Miller effect.

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Programmable analog array circuit

Exclusive-Sums-Of-Products (ESOPs) play an important role in logic synthesis and design-for-test. This paper presents an improved version of the heuristic ESOP minimization procedure proposed in [1,2]. The improvements concern three aspects of the procedure: (1) computation of the starting ESOP cover; (2) increase of the search space for solutions by applying a larger set of cube transformations; (3) development of specialized datastructures for robust manipulation of ESOP covers. Comparison of the new heuristic ESOP minimizer EXORCISM-4 with other minimizers (EXMIN2 [3], MINT [4], EXORCISM-2 [1] and EXORCISM–3 [2]) show that, in most cases, EXORCISM-4 produces results of comparable or better quality on average ten times faster.

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Marek Perkowski

Papers

Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis

Efficient Representation and Manipulation of Switching Functions Based on Ordered Kronecker Functional Decision Diagrams

A General Decomposition for Reversible Logic

Programmable analog array circuit

Fast Heuristic Minimization of Exclusive-Sums-of-Products