In this paper, the authors continue the researches described in [1],
that consists in a comparative study of two methods to eliminate the static hazard
from logical functions, by using the form of Product of Sums (POS), static hazard
“0”. In the first method, it used the consensus theorem to determine the cover term
that is equal with the product of the two residual implicants, and in the second
method it resolved a Boolean equation system. The authors observed that in the second
method the digital hazard can be earlier detected. If the Boolean equation system
is incompatible (doesn’t have solutions), the considered logical function doesn’t
have the static 1 hazard regarding the coupled variable. Using the logical computations,
this method permits to determine the needed transitions to eliminate the digital
hazard.

The paper consists in the use of some logical functions
decomposition algorithms with application in the implementation of classical
circuits like SSI, MSI and PLD. The decomposition methods use the Boolean
matrix calculation. It is calculated the implementation costs emphasizing the
most economical solutions. One
important aspect of serial decomposition is the task of selecting “best candidate” variables for the G
function. Decomposition is essentially a process of substituting two or more input variables
with a lesser number of new variables. This substitutes results in the
reduction of the number of rows in the truth table. Hence, we look for
variables which are most likely to reduce the number of rows in the truth table as a result of
decomposition. Let us consider an input variable purposely avoiding all inter-relationships among the input
variables. The only available parameter to evaluate its activity is the number
of “l”s or “O”s that it has in the
truth table. If the variable has only “1” s or “0” s, it is the “best candidate” for decomposition, as it is practically
redundant.

Abstract:
We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as the function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10fm^4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices.

Abstract:
We performed dynamical simulations with HYP smeared staggered fermions using the recently proposed partial-global stochastic Metropolis algorithm with fermion matrix reduction and determinant breakup improvements. In this paper we discuss our choice of the action parameters and study the autocorrelation time both with four and two fermionic flavors at different quark mass values on approximately 10 fm^4 lattices. We find that the update is especially efficient with two flavors making simulations on larger volumes feasible.

Abstract:
We discuss several methods that improve the partial-global stochastic Metropolis (PGSM) algorithm for smeared link staggered fermions. We present autocorrelation time measurements and argue that this update is feasible even on reasonably large lattices.

Abstract:
Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a break-up can be achieved using polynomial approximations for the fermionic matrix. In this paper we will focus on methods of determining the optimum polynomials.

Abstract:
We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.

Abstract:
We investigate the phase diagram in the temperature, imaginary chemical potential plane for QCD with three degenerate quark flavors using Wilson type fermions. While more expensive than the staggered fermions used in past studies in this area, Wilson fermions can be used safely to simulate systems with three quark flavors. In this talk, we focus on the (pseudo)critical line that extends from $\mu=0$ in the imaginary chemical potential plane, trace it to the Roberge-Weiss line, and determine its location relative to the Roberge-Weiss transition point. In order to smoothly follow the (pseudo)critical line in this plane we perform a multi-histogram reweighting in both temperature and chemical potential. To perform reweighting in the chemical potential we use the compression formula to compute the determinants exactly. Our results are compatible with the standard scenario.

Abstract:
We use the background field method to extract the polarizability for the neutral "pion". In our previous study we found that the polarizability for this system is negative which is believed to be a finite volume artifact. To address this issue, we carry out simulations for different lattice sizes and we also look at the influence of the boundary conditions on these results. We find that for pion masses lower than 400 MeV the polarizability remains negative even on larger lattices. An infinite volume extrapolation is attempted, but the results are not conclusive due mainly to a lack of an analytical form for the finite volume corrections for this system.

Abstract:
Vacuum characteristics quantifying dynamical tendency toward self-duality in gauge theories could be used to judge the relevance of classical solutions or the viability of classically motivated vacuum models. Here we decompose the field strength of equilibrium gauge configurations into self-dual and anti-self-dual parts, and apply absolute X-distribution method to the resulting polarization dynamics in order to construct such characteristics. Using lattice regularization and focusing on pure-glue SU(3) gauge theory at zero temperature, we find evidence for positive but very small dynamical tendency for self-duality of vacuum in the continuum limit.