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

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

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

Rapidity and energy dependence of the electric charge correlations in A+A collisions at the SPS energies

Results from electric charge correlations studied with the Balance Function method in A+A collisions from 20\emph{A} to 158\emph{A} GeV are presented in two different rapidity intervals: In the mid-rapidity region we observe a decrease of the width of the Balance Function distribution with increasing centrality of the collision, whereas this effect vanishes in the forward rapidity region. Results from the energy dependence study in central Pb+Pb collisions show that the narrowing of the Balance Function expressed by the normalised width parameter \textit{W} increases with energy towards the highest SPS and RHIC energies. Finally we compare our experimental data points with predictions of several models. The hadronic string models UrQMD and HIJING do not reproduce the observed narrowing of the Balance Function. However, AMPT which contains a quark-parton transport phase before hadronization can reproduce the narrowing of the BF's width with centrality. This confirms the proposed sensitivity of the Balance Function analysis to the time of hadronization.Comment: Submitted in Phys. Rev.

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

Results of the NA49 collaboration on the production of hadrons with large transverse momentum in Pb+Pb collisions at 158A GeV beam energy are presented. A range up to p_T = 4 GeV/c is covered. The nuclear modification factor R_CP is extracted for pions, kaons and protons, and the baryon to meson ratios p/pi+, pbar/pi- and Lambda/K^0_s are studied. All results are compared to other measurements at SPS and RHIC and to theoretical calculations.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 5 pages, 3 figure

Strangeness production at SPS energies

We present a summary of measurements of strange particles performed by the experiment NA49 in central and minimum bias Pb+Pb collisions in the beam energy range 20A - 158A GeV. New results on Xi production in central Pb+Pb collisions and on Lambda, Xi production in minimum bias collisions are shown. Transverse mass spectra and rapidity distributions of strange particles at different energies are compared. The energy dependence of the particle yields and ratios is discussed. NA49 measurements of the Lambda and Xi enhancement factors are shown for the first time.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 9 pages, 9 figure

System-size dependence of strangeness production in nucleus-nucleus collisions at sqrt{s_{NN}}=17.3 GeV

Emission of pi, K, phi and Lambda was measured in near-central C+C and Si+Si collisions at 158 AGeV beam energy. Together with earlier data for p+p, S+S and Pb+Pb, the system-size dependence of relative strangeness production in nucleus-nucleus collisions is obtained. Its fast rise and the saturation observed at about 60 participating nucleons can be understood as onset of the formation of coherent partonic subsystems of increasing size.Comment: Phys.Rev.Lett in print; version2: changes made according to the request of the referee

Event-by-Event Fluctuations of Particle Ratios in Central Pb+Pb Collisions at 20 to 158 AGeV

In the vicinity of the QCD phase transition, critical fluctuations have been predicted to lead to non-statistical fluctuations of particle ratios, depending on the nature of the phase transition. Recent results of the NA49 energy scan program show a sharp maximum of the ratio of K+ to Pi+ yields in central Pb+Pb collisions at beam energies of 20-30 AGeV. This observation has been interpreted as an indication of a phase transition at low SPS energies. We present first results on event-by-event fluctuations of the kaon to pion and proton to pion ratios at beam energies close to this maximum.Comment: 4 pages, 4 figures, Quark Matter 2004 proceeding

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