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

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

Inclusive production of charged pions in p+C collisions at 158 GeV/c beam momentum

The production of charged pions in minimum bias p+C interactions is studied using a sample of 377000 inelastic events obtained with the NA49 detector at the CERN SPS at 158 GeV/c beam momentum. The data cover a phase space area ranging from 0 to 1.8 GeV/c in transverse momentum and from -0.1 to 0.5 in Feynman x. Inclusive invariant cross sections are given on a grid of 270 bins per charge thus offering for the first time a dense coverage of the projectile hemisphere and of the cross-over region into the target fragmentation zone.Comment: 31 pages, 30 figures, submitted to European Journal of Physic

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

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

Energy dependence of particle ratio fluctuations in central Pb+Pb collisions from sNN=\sqrt{s_{_{NN}}} =~6.3 to 17.3 GeV

We present measurements of the energy dependence of event-by-event fluctuations in the K/pi and (p + \bar{p})/pi multiplicity ratios in heavy ion collisions at the CERN SPS. The particle ratio fluctuations were obtained for central Pb+Pb collisions at five collision energies, \sqrt{s_{_{NN}}}, between 6.3 and 17.3 GeV. After accounting for the effects of finite-number statistics and detector resolution, we extract the strength of non-statistical fluctuations at each energy. For the K/pi ratio, larger fluctuations than expected for independent particle production are found at all collision energies. The fluctuations in the (p + \bar{p})/pi ratio are smaller than expectations from independent particle production, indicating correlated pion and proton production from resonance decays. For both ratios, the deviation from purely statistical fluctuations shows an increase towards lower collision energies. The results are compared to transport model calculations, which fail to describe the energy dependence of the K/pi ratio fluctuations.Comment: 11 pages, 10 figures, update to published versio

Upper Limit of D0 Production in Central Pb-Pb Collisions at 158A GeV

Results are presented from a search for the decays D0 -> Kmin piplus and D0bar -> Kplus pimin in a sample of 3.8x10^6 central Pb-Pb events collected with a beam energy of 158A GeV by NA49 at the CERN SPS. No signal is observed. An upper limit on D0 production is derived and compared to predictions from several models.Comment: REVTEX 5 pages, 4 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

Report from NA49

The most recent data of NA49 on hadron production in nuclear collisions at CERN SPS energies are presented. Anomalies in the energy dependence of pion and kaon production in central Pb+Pb collisions are observed. They suggest that the onset of deconfinement is located at about 30 AGeV. Large multiplicity and transverse momentum fluctuations are measured for collisions of intermediate mass systems at 158 AGeV. The need for a new experimental programme at the CERN SPS is underlined.Comment: invited talk presented at Quark Matter 2004, 10 page