Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes

We present recent results of the Landau gauge gluon and ghost propagators in SU(3) pure gauge theory at Wilson \beta=5.7 for lattice sizes up to 80^4 corresponding to physical volumes up to (13.2 fm)^4. In particular, we focus on finite-volume and Gribov copy effects. We employ a gauge fixing method that combines a simulated annealing algorithm with finalizing overrelaxation. We find the gluon propagator for the largest volumes and at q^2 ~ 0.01 GeV^2 to become flat. Although not excluded by our data, there is still no clear indication of a gluon propagator tending towards zero in the zero-momentum limit. New data for the ghost propagator are reported, too.Comment: 7 pages, 3 figures, poster presented at Lattice-2007, Regensburg, July 30 - August 4, 2007, 1 figure replace

Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited

The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma_corr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Gamma_corr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances

An FPGA based approach for Černý conjecture falsification

A synchronizing sequence for an automaton is a special input sequence that sends all states of the automaton to the same state. J. Černý conjectured that the length of the shortest synchronizing sequence of an automaton with n states cannot be greater than (n-1)2, which is known today as the Černý conjecture. This half-a-century old conjecture is still open and it is considered to be the most long-standing open problem in the combinatorial theory of finite state automata. One research line that has been pursued in the literature is to check if the conjecture holds for a fixed number of states n, by considering all automata with n states and checking if any of these automata falsifies the conjecture. This is a computationally intensive task, even for automata up to a dozen of states and only two input symbols. To accelerate the search parallel computation approaches using multicore CPUs have been tried before. In this thesis, we study the use of FPGAs to accelerate the search for an automaton falsifying the Černý conjecture. We present a design to calculate iii the minimum length synchronizing sequence of a finite state automaton. The proposed design is implemented with the parallel computing capability of hardware designs while optimizing the time performance

Dual Superconductor Scenario of Confinement: A Systematic Study of Gribov Copy Effects

We perform a study of the effects from maximal abelian gauge Gribov copies in the context of the dual superconductor scenario of confinement, on the basis of a novel approach for estimation of systematic uncertainties from incomplete gauge fixing. We present numerical results, in SU(2) lattice gauge theory, using the overrelaxed simulated annealing gauge fixing algorithm. We find abelian and non-abelian string tensions to differ significantly, their ratio being 0.92(4) at BETA = 2.5115. An approximate factorization of the abelian potential into monopole and photon contributions has been confirmed, the former giving rise to the abelian string tension.Comment: 35 pages uucompressed LaTeX with 10 encapsuled postscript figure

Quantum Chaotic Scattering in Microwave Resonators

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both, a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data