10,085 research outputs found
Minimization via duality
We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object
Physics as Quantum Information Processing: Quantum Fields as Quantum Automata
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can
physics be simulated by a quantum computer? Do we believe that a quantum field
is ultimately made of a numerable set of quantum systems that are unitarily
interacting? A positive answer to these questions corresponds to substituting
QFT with a theory of quantum cellular automata (QCA), and the present work is
examining this hypothesis. These investigations are part of a large research
program on a "quantum-digitalization" of physics, with Quantum Theory as a
special theory of information, and Physics as emergent from the same
quantum-information processing. A QCA-based QFT has tremendous potential
advantages compared to QFT, being quantum "ab-initio" and free from the
problems plaguing QFT due to the continuum hypothesis. Here I will show how
dynamics emerges from the quantum processing, how the QCA can reproduce the
Dirac-field phenomenology at large scales, and the kind of departures from QFT
that that should be expected at a Planck-scale discreteness. I will introduce
the notions of linear field quantum automaton and local-matrix quantum
automaton, in terms of which I will provide the solution to the Feynman's
problem about the possibility of simulating a Fermi field with a quantum
computer.Comment: This version: further improvements in notation. Added reference. Work
presented at the conference "Foundations of Probability and Physics-6" (FPP6)
held on 12-15 June 2011 at the Linnaeus University, Vaaxjo, Sweden. Many new
results, e.g. Feynman problem of qubit-ization of Fermi fields solved
On Damage Spreading Transitions
We study the damage spreading transition in a generic one-dimensional
stochastic cellular automata with two inputs (Domany-Kinzel model) Using an
original formalism for the description of the microscopic dynamics of the
model, we are able to show analitically that the evolution of the damage
between two systems driven by the same noise has the same structure of a
directed percolation problem. By means of a mean field approximation, we map
the density phase transition into the damage phase transition, obtaining a
reliable phase diagram. We extend this analysis to all symmetric cellular
automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u
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