A new ordering constraint solving method and its applications

We show that it is possible to transform any given LPO ordering constraint $C$ into a finite equivalent set of constraints $S$ for which a special kind of solutions can be obtained. This allows to compute the equalities that follow from ordering constraints, and to decide e.g.\ whether an {\em ordering constrained equation\/} is a tautology. Another application we develop here is a method to check ordered rewrite systems for (ground) confluence

Weakly Equivalent Arrays

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and extensionality axioms originally proposed by McCarthy. Various filters are used to limit the number of axiom instantiations while preserving completeness. We present an algorithm that lazily instantiates lemmas based on weak equivalence classes. These lemmas are easier to interpolate as they only contain existing terms. We formally define weak equivalence and show correctness of the resulting decision procedure

A Comparison between Relativistic and Semi-Relativistic Treatment in the Diquark-Quark Model

In the diquark-quark model of the nucleon including scalar and axialvector diquarks we compare solutions of the ladder Bethe-Salpeter equation in the instantaneous Salpeter approximation and in the fully covariant (i.e. four-dimensional) treatment. We obtain that the binding energy is severly underestimated in the Salpeter approximation. For the electromagnetic form factors of the nucleon we find that in both approaches the overall shapes of the respective form factors are reasonably similar up to $Q^2 \approx 0.4$ GeV^2. However, the magnetic moments differ substantially as well as results for the pion-nucleon and the axial coupling of the nucleon.Comment: 12 pages,4 figures, 3 tables; minor modifications in text and tables, references added, version to be published in Physics Letters

Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

Burstiness predictions based on rough network traffic measurements

To dimension network links, such that they will not become QoS bottle- necks, the peak rate on these links should be known. To measure these peaks on sufficiently small time scales, special measurement tools are needed. Such tools can be quite expensive and complex. Therefore network operators often rely on more cheap, standard tools, like MRTG, which were designed to measure average traffic rates (m) on time scales such as 5 minutes. For estimating the peak traffic rate (p), operators often use simple rules, such as p = α · m. In this paper we describe measurements that we have performed to investigate how well this rule describes the relation between peak and average traffic rate. In addition, we pro- pose some more advanced rules, and compare these to the simple rule mentioned above. The analyses of our measurements, which have been performed on differ- ent kinds of networks, show that our advanced rules more adequately describe the relation between peak and average traffic rate

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, produce significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.Comment: 25 pags, 19 figures, prepared for the volume celebrating the 70th birthday of Yuri Simono

Nonperturbative study of generalized ladder graphs in a \phi^2\chi theory

The Feynman-Schwinger representation is used to construct scalar-scalar bound states for the set of all ladder and crossed-ladder graphs in a \phi^2\chi theory in (3+1) dimensions. The results are compared to those of the usual Bethe-Salpeter equation in the ladder approximation and of several quasi-potential equations. Particularly for large couplings, the ladder predictions are seen to underestimate the binding energy significantly as compared to the generalized ladder case, whereas the solutions of the quasi-potential equations provide a better correspondence. Results for the calculated bound state wave functions are also presented.Comment: 5 pages revtex, 3 Postscripts figures, uses epsf.sty, accepted for publication in Physical Review Letter