A new approach for diagnosability analysis of Petri nets using Verifier Nets

In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented

High statistics calculations of quenched QCD spectrum using various quark sources

We present the results for the hadron spectrum calculated on 400 configurations using point source, wall source and 8-cubic sources, in quenched QCD with Wilson fermions at $\beta=6.0$ and $K=0.155$ on a $24^3 \times 54$ lattice. The results for the ground state masses obtained with three types of quark sources agree well with each other. Masses of the first excited states appear consistent with experimental values within large errors.Comment: 3 pages, 2 postscript figures, to appear in the Proceedings of LATTICE 93, Dallas, USA; preprint UTHEP-26

Extremal Optimization for Sherrington-Kirkpatrick Spin Glasses

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using $\pm J$ bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of $\omega=2/3$ for the finite-size correction exponent, and of $\rho=3/4$ for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent.Comment: Substantially revised, several new results, 5 pages, 6 eps figures included, (see http://www.physics.emory.edu/faculty/boettcher/ for related information

Finite-Size Effect of Hadron Masses with Kogut-Susskind Quarks

We present numerical results and their analyses of finite-size effects of hadron masses for both quenched and full QCD calculations. We show that they are much larger for full QCD due to dynamical sea quarks and the associated breaking of $Z(3)$ symmetry. We also argue that finite-size effects are non-negligible even for the largest lattice size simulation currently being made for a very small quark mass. (talk at lattice93)Comment: 4 pages, compressed, uuencoded PostScript file(name:lat93.ps.Z

Phenomenology with Wilson fermions using smeared sources

We investigate the use of two types of non-local (``smeared'') sources for quark propagators in quenched lattice QCD at $\beta=6.0$ using Wilson fermions at $\kappa=0.154$ and $0.155$. We present results for the hadron mass spectrum, meson decay constants, quark masses, the chiral condensate and the quark distribution amplitude of the pion. The use of smeared sources leads to a considerable improvement over previous results. We find a disturbing discrepancy between the baryon spectra obtained using Wuppertal and wall sources. We find good signals in the ratio of correlators used to calculate the quark mass and the chiral condensate and show that the extrapolation to the chiral limit is smooth.Comment: (revised), 57 pages (29 pages of PostScript in landscape mode, 765924 bytes

APE Results of Hadron Masses in Full QCD Simulations

We present numerical results obtained in full QCD with 2 flavors of Wilson fermions. We discuss the relation between the phase of Polyakov loops and the {\bf sea} quarks boundary conditions. We report preliminary results about the HMC autocorrelation of the hadronic masses, on a $16^3 \times 32$ lattice volume, at $\beta=5.55$ with $k_{sea}=0.1570$.Comment: 3 pages, compressed ps-file (uufiles), Contribution to Lattice 9

Pion-Nucleon Sigma Term in Lattice QCD

We calculate both connected and disconnected contribution to the $\pi$-$N$ $\sigma$-term in quenched lattice QCD with Wilson quark action on a $12^3\times 20$ lattice at $\beta=5.7$. The latter is evaluated with the aid of the variant wall source method, which was previously applied successfully for extraction of $\pi$-$\pi$ scattering lengths and $\eta^\prime$ meson mass. We found that the disconnected contribution is about twice larger than the connected one. The value for the full $\pi$-$N$ $\sigma$ term $\sigma=40-60$ MeV is consistent with the experimental estimates. The nucleon matrix element of the strange quark density $\bar s s$ is fairly large in our result.Comment: 11 pages. Latex file. Figures are also included as ps file

Progress and status of APEmille

We report on the progress and status of the APEmille project: a SIMD parallel computer with a peak performance in the TeraFlops range which is now in an advanced development phase. We discuss the hardware and software architecture, and present some performance estimates for Lattice Gauge Theory (LGT) applications.Comment: Talk presented at LATTICE97, 3 pages, Late

Light Quark Masses from Lattice QCD

We present estimates of the masses of light quarks using lattice data. Our main results are based on a global analysis of all the published data for Wilson, Sheikholeslami-Wohlert (clover), and staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. We find that the values of masses with the various formulations agree after extrapolation to the continuum limit for the $n_f=0$ theory. Our best estimates, in the MSbar scheme at $\mu=2 GeV$, are \mbar=3.4 +- 0.4 +- 0.3 MeV and $m_s = 100 +- 21 +- 10 MeV$ in the quenched approximation. The $n_f=2$ results, \mbar = 2.7 +- 0.3 +- 0.3 MeV and $m_s = 68 +- 12 +- 7 MeV$, are preliminary. (A linear extrapolation in $n_f$ would further reduce these estimates for the physical case of three dynamical flavors.) These estimates are smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. The new results have a significant impact on the extraction of $\epsilon'/\epsilon$ from the Standard Model. Using the same lattice data we estimate the quark condensate using the Gell-Mann-Oakes-Renner relation. Again the three formulations give consistent results after extrapolation to $a=0$, and the value turns out to be correspondingly larger, roughly preserving m_s \vev{\bar \psi \psi}.Comment: 32 pages. Package submitted in uufiles format: unpack and tex paper.tex. Modified "axis" source for figures also included. Latex2e document. Uncomment hyperref if available. This is the final published versio

Decay Constants of Heavy-Light Mesons

The decay constants of the heavy-light pseudoscalar mesons are studied in a high statistics run using the Wilson action at $\beta=6.0$ and $\beta=6.2$, and the clover action at $\beta=6.0$. The systematics of $O(a)$ discretisation errors are discussed. Our best estimates of the decay constants are: $f_D$ = 218(9) MeV, $f_D/f_{Ds}$ = 1.11(1) and we obtain preliminary values for $f_B$.Comment: at the Dallas Lattice Conference, October 1993. 3 pages in a single postscript file, uuencoded form. Rome Preprint 93/98