In the paper are described some steps for merger between relativistic quantum theory and theory of computation. The first step is consideration of transformation of qubit state due to rotation of coordinate system. The Lorentz transformation is considered after that. The some new properties of this transformation change usual model of qubit. The system of qbit seems more fundamental relativisti...

We investigate a new research area: we are interested in the ultimate ther-modynamic cost of computing from x to y. Other than its fundamental importance , such research has potential implications in miniaturization of VLSI chips and applications in pattern recognition. It turns out that the theory of thermodynamic cost of computation can be axiomatically developed. Our fundamental theorem conn...

L. M. Adleman launched the field of DNA computing with a demonstration in 1994 that strands of DNA could be used to solve the Hamiltonian path problem for a simple graph. He also identified three broad categories of open questions for the field. First, is DNA capable of universal computation? Second, what kinds of algorithms can DNA implement? Third, can the error rates in the manipulations of ...

Nicholas J. Higham “This superb book is timely and is written with great attention paid to detail, particularly in its referencing of the literature. The book has a wonderful blend of theory and code (MATLAB®) so will be useful both to nonexperts and to experts in the field.” — Alan Laub, Professor, University of California, Los Angeles The only book devoted exclusively to matrix functions, thi...

The information carried by a signal unavoidably decays when the signal is corrupted by random noise. This occurs when a noisy channel transmits a message as well as when a noisy component performs computation. We first study this signal decay in the context of communication and obtain a tight bound on the decay of the information carried by a signal as it crosses a noisy channel. We then use th...