679 research outputs found

    Complexity of Decision Problems for Mixed and Modal Specifications

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    International audienceWe present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is , where and are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs

    Reachability analysis for timed automata using max-plus algebra

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    International audienceWe show that max-plus polyhedra are usable as a data structure in reachability analysis of timed automata. Drawing inspiration from the extensive work that has been done on difference bound matrices, as well as previous work on max-plus polyhedra in other areas, we develop the algorithms needed to perform forward and backward reachability analysis using max-plus polyhedra. To show that the approach works in practice and theory alike, we have created a proof-of-concept implementation on top of the model checker opaal

    Detection of a Hot Gaseous Halo Around the Giant Spiral Galaxy NGC 1961

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    Hot gaseous halos are predicted around all large galaxies and are critically important for our understanding of galaxy formation, but they have never been detected at distances beyond a few kpc around a spiral galaxy. We used the Chandra ACIS-I instrument to search for diffuse X-ray emission around an ideal candidate galaxy: the isolated giant spiral NGC 1961. We observed four quadrants around the galaxy for 30 ks each, carefully subtracting background and point source emission, and found diffuse emission that appears to extend to 40-50 kpc. We fit β\beta-models to the emission, and estimate a hot halo mass within 50 kpc of 5×109M⊙5\times10^9 M_{\odot}. When this profile is extrapolated to 500 kpc (the approximate virial radius), the implied hot halo mass is 1−3×1011M⊙1-3\times10^{11} M_{\odot}. These mass estimates assume a gas metallicity of Z=0.5Z⊙Z = 0.5 Z_{\odot}. This galaxy's hot halo is a large reservoir of gas, but falls significantly below observational upper limits set by pervious searches, and suggests that NGC 1961 is missing 75% of its baryons relative to the cosmic mean, which would tentatively place it below an extrapolation of the baryon Tully-Fisher relationship of less massive galaxies. The cooling rate of the gas is no more than 0.4 M⊙M_{\odot}/year, more than an order of magnitude below the gas consumption rate through star formation. We discuss the implications of this halo for galaxy formation models.Comment: 26 pages, 5 figures, accepted to ApJ. Updated to include journal ref and small changes added in proof
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