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 discovers an emerging area of application of the advanced Multivalued Logic (MVL), – a collaboration between humans and autonomous machines in the first responder teams (firefighters, search-and-rescue operators, disaster response personnel, and military special operations forces). We developed an approach to formalization of the collaboration protocols (also known as contagion protocols) that model the human-machine teaming in emergency missions. MVL techniques satisfy the requirements of encoding the states of stress and trust, and their propagation between the teammates. Advanced MVL techniques are also useful for other applications, such as modeling the contagion of infection, or the spread of rumors, ideas, panic, and fear.

Discovering Emerging Applications of Multi-Valued Logic: Protocols for Human-Autonomy Teaming

Quantum Machine Learning, Logic Minimization, and Circuit Design by Optimizing Ternary-Input Binary-Output Kronecker Reed-Muller Forms

Test pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found that quantum mechanics allows one to execute multiple test vectors concurrently, making each gate realized in the process act on a complete set of characteristic states in space/time complexity that breaks classical testability lower bounds.

Fault testing quantum switching circuits

An efficient computer implementation of an originally developed spectral representation of multiple-valued input binary functions is presented. In such a representation, the spectrum for each multiple-valued input binary function is composed of a vector of Walsh transforms, each of them denned for one pair of input variables of the function. By that approach, the number of spectral coefficients describing a given multiple-valued input binary function is a minimal one. The implementation of the algorithm allows for the calculation of the spectra of binary functions having an arbitrary number of literals; each of them can have up to 32 different logical values. The algorithm is interactive so users can manually determine the generation of a partial or whole spectrum.

An efficient computer algorithm for the calculation of the Walsh transform for incompletely specified multiple-valued binary functions†

Maximum frequent pattern generation from a large database of transactions and items for association rule mining is an important research topic in data mining. Association rule mining aims to discover interesting correlations, frequent patterns, associations, or causal structures between items hidden in a large database. By exploiting quantum computing, we propose an efficient quantum search algorithm design to discover the maximum frequent patterns. We modified Grover’s search algorithm so that a subspace of arbitrary symmetric states is used instead of the whole search space. We presented a novel quantum oracle design that employs a quantum counter to count the maximum frequent items and a quantum comparator to check with a minimum support threshold. The proposed derived algorithm increases the rate of the correct solutions since the search is only in a subspace. Furthermore, our algorithm significantly scales and optimizes the required number of qubits in design, which directly reflected positively on the performance. Our proposed design can accommodate more transactions and items and still have a good performance with a small number of qubits. 

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Marek Perkowski

Papers

Discovering Emerging Applications of Multi-Valued Logic: Protocols for Human-Autonomy Teaming

Quantum Machine Learning, Logic Minimization, and Circuit Design by Optimizing Ternary-Input Binary-Output Kronecker Reed-Muller Forms

Fault testing quantum switching circuits

An efficient computer algorithm for the calculation of the Walsh transform for incompletely specified multiple-valued binary functions†

Quantum Algorithm for Mining Frequent Patterns for Association Rule Mining