Probabilistic Model Checking for Energy Analysis in Software Product Lines

In a software product line (SPL), a collection of software products is defined by their commonalities in terms of features rather than explicitly specifying all products one-by-one. Several verification techniques were adapted to establish temporal properties of SPLs. Symbolic and family-based model checking have been proven to be successful for tackling the combinatorial blow-up arising when reasoning about several feature combinations. However, most formal verification approaches for SPLs presented in the literature focus on the static SPLs, where the features of a product are fixed and cannot be changed during runtime. This is in contrast to dynamic SPLs, allowing to adapt feature combinations of a product dynamically after deployment. The main contribution of the paper is a compositional modeling framework for dynamic SPLs, which supports probabilistic and nondeterministic choices and allows for quantitative analysis. We specify the feature changes during runtime within an automata-based coordination component, enabling to reason over strategies how to trigger dynamic feature changes for optimizing various quantitative objectives, e.g., energy or monetary costs and reliability. For our framework there is a natural and conceptually simple translation into the input language of the prominent probabilistic model checker PRISM. This facilitates the application of PRISM's powerful symbolic engine to the operational behavior of dynamic SPLs and their family-based analysis against various quantitative queries. We demonstrate feasibility of our approach by a case study issuing an energy-aware bonding network device.Comment: 14 pages, 11 figure

System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40A GeV and158A GeV beam energy

Measurements of charged pion and kaon production are presented in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV beam energy as well as in semi-central C+C and Si+Si interactions at 40A GeV. Transverse mass spectra, rapidity spectra and total yields are determined as a function of centrality. The system-size and centrality dependence of relative strangeness production in nucleus-nucleus collisions at 40A GeV and 158A GeV beam energy are derived from the data presented here and published data for C+C and Si+Si collisions at 158A GeV beam energy. At both energies a steep increase with centrality is observed for small systems followed by a weak rise or even saturation for higher centralities. This behavior is compared to calculations using transport models (UrQMD and HSD), a percolation model and the core-corona approach.Comment: 32 pages, 14 figures, 4 tables, typo table II correcte

Search for the QCD critical point in nuclear collisions at the CERN SPS

Pion production in nuclear collisions at the SPS is investigated with the aim to search, in a restricted domain of the phase diagram, for power-laws in the behavior of correlations which are compatible with critical QCD. We have analyzed interactions of nuclei of different size (p+p, C+C, Si+Si, Pb+Pb) at 158$A$ GeV adopting, as appropriate observables, scaled factorial moments in a search for intermittent fluctuations in transverse dimensions. The analysis is performed for $\pi^+\pi^-$ pairs with invariant mass very close to the two-pion threshold. In this sector one may capture critical fluctuations of the sigma component in a hadronic medium, even if the $\sigma$-meson has no well defined vacuum state. It turns out that for the Pb+Pb system the proposed analysis technique cannot be applied without entering the invariant mass region with strong Coulomb correlations. As a result the treatment becomes inconclusive in this case. Our results for the other systems indicate the presence of power-law fluctuations in the freeze-out state of Si+Si approaching in size the prediction of critical QCD.Comment: 31 pages, 11 figure

Results on correlations and fluctuations from NA49

The large acceptance and high momentum resolution as well as the significant particle identification capabilities of the NA49 experiment at the CERN SPS allow for a broad study of fluctuations and correlations in hadronic interactions. In the first part recent results on event-by-event charge and p_t fluctuations are presented. Charge fluctuations in central Pb+Pb reactions are investigated at three different beam energies (40, 80, and 158 AGeV), while for the p_t fluctuations the focus is put on the system size dependence at 158 AGeV. In the second part recent results on Bose Einstein correlations of h-h- pairs in minimum bias Pb+Pb reactions at 40 and 158 AGeV, as well as of K+K+ and K-K- pairs in central Pb+Pb collisions at 158 AGeV are shown. Additionally, other types of two particle correlations, namely pi p, Lambda p, and Lambda Lambda correlations, have been measured by the NA49 experiment. Finally, results on the energy and system size dependence of deuteron coalescence are discussed.Comment: 10 pages, 12 figures, Presented at Quark Matter 2002, Nantes, France, Corrected error in Eq.

High p_T Spectra of Identified Particles Produced in Pb+Pb Collisions at 158GeV/nucleon Beam Energy

Transverse momentum spectra of pi^{+/-}, p, pbar, K^{+/-}, K^0_s and Lambda at midrapidity were measured at high p_T in Pb+Pb collisions at 158GeV/nucleon beam energy by the NA49 experiment. Particle yield ratios (p/pi, K/pi and Lambda/K^0_s) show an enhancement of the baryon/meson ratio for p_T>2GeV/c. The nuclear modification factor R_{CP} is extracted and compared to RHIC measurements and pQCD calculations.Comment: Quark Matter 2005 parallel section proceeding

Multiplicity fluctuations in nuclear collisions at 158 A GeV

System size dependence of multiplicity fluctuations of charged particles produced in nuclear collisions at 158 A GeV was studied in the NA49 CERN experiment. Results indicate a non-monotonic dependence of the scaled variance of the multiplicity distribution with a maximum for semi-peripheral Pb+Pb interactions with number of projectile participants of about 35. This effect is not observed in a string-hadronic model of nuclear collision HIJING.Comment: Presented at "Focus on Multiplicity", 17-19 of June, Bari, Ital

Lambda production in central Pb+Pb collisions at CERN-SPS energies

In this paper we present recent results from the NA49 experiment for $\Lambda$ and $\bar{\Lambda}$ hyperons produced in central Pb+Pb collisions at 40, 80 and 158 A$\cdot$GeV. Transverse mass spectra and rapidity distributions for $\Lambda$ are shown for all three energies. The shape of the rapidity distribution becomes flatter with increasing beam energy. The multiplicities at mid-rapidity as well as the total yields are studied as a function of collision energy including AGS measurements. The ratio $\Lambda/\pi$ at mid-rapidity and in 4$\pi$ has a maximum around 40 A$\cdot$GeV. In addition, $\bar{\Lambda}$ rapidity distributions have been measured at 40 and 80 A$\cdot$GeV, which allows to study the $\bar{\Lambda}$/$\Lambda$ ratio.Comment: SQM proceedings. J. Phys. G: Nucl. Part. Phys.: submitte

Bose-Einstein Correlations of Charged Kaons in Central Pb+Pb Collisions at Ebeam=158AGeVE_{beam} = 158 AGeV

Bose-Einstein correlations of charged kaons were measured near mid-rapidity in central Pb+Pb collisions at 158 A$\cdot$GeV by the NA49 experiment at the CERN SPS. Source radii were extracted using the Yano-Koonin-Podgoretsky and Bertsch-Pratt parameterizations. The results are compared to published pion data. The measured $m_\perp$ dependence for kaons and pions is consistent with collective transverse expansion of the source and a freeze-out time of about 9.5 $fm$.Comment: 14 pages with 7 figures, submitted to Phys. Lett.

Pion and kaon production in central Pb+Pb collisions at 20A and 30A GeV: Evidence for the onset of deconfinement

Results on charged pion and kaon production in central Pb+Pb collisions at 20A and 30A GeV are presented and compared to data at lower and higher energies. A rapid change of the energy dependence is observed around 30A GeV for the yields of pions and kaons as well as for the shape of the transverse mass spectra. The change is compatible with the prediction that the threshold for production of a state of deconfined matter at the early stage of the collisions is located at low SPS energies.Comment: 12 pages, 8 figure

Omega and Antiomega production in central Pb+Pb collisions at 40 and 158 AGeV

Results are presented on Omega production in central Pb+Pb collisions at 40 and 158 AGeV beam energy. Given are transverse-mass spectra, rapidity distributions, and total yields for the sum Omega+Antiomega at 40 AGeV and for Omega and Antiomega separately at 158 AGeV. The yields are strongly under-predicted by the string-hadronic UrQMD model and are in better agreement with predictions from a hadron gas models.Comment: 5 papes, 4 figures, 1 table, updated figure 4 and table 1. Final version, including some editorial changes, as published in PR