We study model checking problems for pushdown systems and linear time logics. We show that the global model checking problem (computing the set of configurations, reachable or not, that violate the formula) can be solved in O(g P gP 3 gBgB 3 ) time and O(gP gP 2 gBgB 2 ) space, where gP gP and gBgB are the size of the pushdown system and the size of a Büchi automaton for the negation of the formula. The global model checking problem for reachable configurations can be solved in O(gP gP 4 gBgB 3 ) time and O(gP gP 4 gBgB 2 ) space. In the case of pushdown systems with constant number of control states (relevant for our application), the complexity becomes O(gP gP gBgB 3 ) time and O(gP gP gBgB 2 ) space and O(gP gP 2 gBgB 3 ) time and O(gP gP 2 gBgB 2 ) space, respectively. We show applications of these results in the area of program analysis and present some experimental results.
A new method is presented for the calculation of apparent sedimentation coefficient distributions g*(s) for the size‐distribution analysis of polymers in sedimentation velocity experiments. Direct linear least‐squares boundary modeling by a superposition of sedimentation profiles of ideal nondiffusing particles is employed. It can be combined with algebraic noise decomposition techniques for the application to interference optical ultracentrifuge data at low loading concentrations with significant systematic noise components. Because of the use of direct boundary modeling, residuals are available for assessment of the quality of the fits and the consistency of the g*(s) distribution with the experimental data. The method can be combined with regularization techniques based on F statistics, such as used in the program CONTIN, or alternatively, the increment of s values can be adjusted empirically. The method is simple, has advantageous statistical properties, and reveals precise sedimentation coefficients. The new least‐squares ls‐g*(s) exhibits a very high robustness and resolution if data acquired over a large time interval are analyzed. This can result in a high resolution for large particles, and for samples with a high degree of heterogeneity. Because the method does not require a high frequency of scans, it can also be easily used in experiments with the absorbance optical scanning system. Published 2000 John Wiley & Sons, Inc. Biopoly 54: 328–341, 2000
Four amphiphilic block copolymers polyisobutylene-block-poly(methacrylic acid) (IB
m
-MAA
n
;
m = 70−134, n = 52−228) were synthesized and transferred into aqueous medium at pH 10−12. Their
structure in solution was characterized by fluorescence correlation spectroscopy (FCS), static and dynamic
light scattering (SLS, DLS), analytical ultracentrifuge (AUC), and by transmission electron microscopy
(TEM) with freeze-fracturing and staining techniques. DLS data, AUC sedimentation traces, and TEM
images indicate at least two different kinds of particles. TEM shows spherical micelles; however, especially
for polymers with larger hydrophobic blocks, additional particles are observed. FCS shows extremely
low critical micelle concentrations (cmc < 0.3 mg/L). The main part of the particles consists of micelles
with diameters from 15 to 50 nm, built by 130−200 block copolymer molecules. Aggregation numbers
and diameters are consistent with a model recently proposed by Förster et al. (J. Chem. Phys. 1996, 104,
9956−9970). The packing densities are determined from the hydrodynamic diameters and the aggregation
numbers; they vary between 6 and 32%. For large hydrophobic block lengths additional structures are
found, in most cases with a narrow size distribution. The origin of these structures is discussed.
International audienceWe present a linear-time algorithm to compute a decomposition scheme for graphs G that have a set X⊆V(G), called a treewidth-modulator, such that the treewidth of G − X is bounded by a constant. Our decomposition, called a protrusion decomposition, is the cornerstone in obtaining the following two main results. Our first result is that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H. This result partially extends previous meta-theorems on the existence of linear kernels on graphs of bounded genus and H-minor-free graphs. Let F be a fixed finite family of graphs containing at least one planar graph. Given an n-vertex graph G and a non-negative integer k, Planar-F-Deletion asks whether G has a set X⊆V(G) such that |X| ⩽ k and G − X is H-minor-free for every H ε F. As our second application, we present the first single-exponential algorithm to solve Planar-F-Deletion. Namely, our algorithm runs in time 2O(k) · n2, which is asymptotically optimal with respect to k. So far, single-exponential algorithms were only known for special cases of the family F
Abstract.In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(nk 2 3 k ) time and the problem to count the number of perfect matchings in O * (2 k ) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ, σ]-domination problems with finite or cofinite ρ and σ on tree decompositions. These include many well known graph problems. We give additional results on many more graph covering and partitioning problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.