A rewriting approach to binary decision diagrams

AbstractBinary decision diagrams (BDDs) provide an established technique for propositional formula manipulation. In this paper, we present the basic BDD theory by means of standard rewriting techniques. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical reduced ordered BDDs (ROBDDs) can be obtained and for which uniqueness of ROBDD representation is proved. Next, an alternative rewriting system is presented, suitable for actually computing ROBDDs from formulas. For this rewriting system a layerwise strategy is defined, and it is proved that when replacing the classical apply-algorithm by layerwise rewriting, roughly the same complexity bound is reached as in the classical algorithm. Moreover, a layerwise innermost strategy is defined and it is proved that the full classical algorithm for computing ROBDDs can be replaced by layerwise innermost rewriting without essentially affecting the complexity. Finally a lazy strategy is proposed sometimes performing much better than the traditional algorithm

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field

Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio lambda=1.5 the system displays paranematic-nematic coexistence. For lambda=2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Increasing the field strength leads to shrinking of the coexistence regions. At high enough field strength a closed loop of immiscibility is induced and phase coexistence vanishes at a double critical point above which the system is homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence, there is nematic-nematic coexistence which persists and hence does not end in a critical point. The partial orientational order parameters along the binodals vary strongly with composition and connect smoothly for each species when closed loops of immiscibility are present in the corresponding phase diagram.Comment: 9 pages, to appear in J.Phys:Condensed Matte

Symbolic Reachability Analysis of B through ProB and LTSmin

We present a symbolic reachability analysis approach for B that can provide a significant speedup over traditional explicit state model checking. The symbolic analysis is implemented by linking ProB to LTSmin, a high-performance language independent model checker. The link is achieved via LTSmin's PINS interface, allowing ProB to benefit from LTSmin's analysis algorithms, while only writing a few hundred lines of glue-code, along with a bridge between ProB and C using ZeroMQ. ProB supports model checking of several formal specification languages such as B, Event-B, Z and TLA. Our experiments are based on a wide variety of B-Method and Event-B models to demonstrate the efficiency of the new link. Among the tested categories are state space generation and deadlock detection; but action detection and invariant checking are also feasible in principle. In many cases we observe speedups of several orders of magnitude. We also compare the results with other approaches for improving model checking, such as partial order reduction or symmetry reduction. We thus provide a new scalable, symbolic analysis algorithm for the B-Method and Event-B, along with a platform to integrate other model checking improvements via LTSmin in the future

Effect of depolarizing concentrations of potassium on calcium uptake and metabolism in rat liver

AbstractExposure of perfused livers of fed rats to 60 mM K+ induces rapid responses in the Ca2+-sensitive metabolic events, glycogenolysis, cytoplasmic and mitochondrial NADH/NAD ratios and octanoate oxidation. All increase within 45 s of K+ addition. Metabolic responses were not observed following K+ addition to livers perfused in the absence of added Ca2+. Movements of Ca2+ into the liver were suggested from experiments in which 45Ca2+ uptake was measured. The Ca2+ antagonists verapamil, diltiazem and Ni2+ essentially abolished changes to tissue metabolism and Ca2+ fluxes induced by K+ addition. K+-induced changes were consistent with Ca2+ channel activiation.LiverPotassium depolarizationGlycogenolysisCalcium antagonis