A generic complete dynamic logic for reasoning about purity and effects

For a number of programming languages, among them Eiffel, C, Java, and Ruby, Hoare-style logics and dynamic logics have been developed. In these logics, pre- and postconditions are typically formulated using potentially effectful programs. In order to ensure that these pre- and postconditions behave like logical formulae (that is, enjoy some kind of referential transparency), a notion of purity is needed. Here, we introduce a generic framework for reasoning about purity and effects. Effects are modelled abstractly and axiomatically, using Moggi’s idea of encapsulation of effects as monads. We introduce a dynamic logic (from which, as usual, a Hoare logic can be derived) whose logical formulae are pure programs in a strong sense. We formulate a set of proof rules for this logic, and prove it to be complete with respect to a categorical semantics. Using dynamic logic, we then develop a relaxed notion of purity which allows for observationally neutral effects such writing on newly allocated memory.     

A PTAS for Cutting Out Polygons with Lines

We present a simple O(m+n ⁶/ε ¹²) time (1+ε)-approximation algorithm for finding a minimum-cost sequence of lines to cut a convex n-gon out of a convex m-gon.     

Business process model abstraction: a definition, catalog, and survey

The discipline of business process management aims at capturing, understanding, and improving work in organizations by using process models as central artifacts. Since business-oriented tasks require different information from such models to be highlighted, a range of abstraction techniques has been developed over the past years to manipulate overly detailed models. At this point, a clear understanding of what distinguishes these techniques and how they address real world use cases has not yet been established. In this paper we systematically develop, classify, and consolidate the use cases for business process model abstraction and present a case study to illustrate the value of this technique. The catalog of use cases that we present is based on a thorough evaluation of the state of the art, as well as on our cooperation with end users in the health insurance sector. It has been subsequently validated by experts from the consultancy and tool vendor domains. Based on our findings, we evaluate how the existing business process model abstraction approaches support the discovered use cases and reveal which areas are not adequately covered, as such providing an agenda for further research in this area.     

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input–output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.     

From fine-grained to abstract process models: A semantic approach

Organizations actively managing their business processes face a rapid growth of the number of process models that they maintain. Business process model abstraction has proven to be an effective means to generate readable, high-level views on business process models by showing coarse-grained activities and leaving out irrelevant details. In this way, abstraction facilitates a more efficient management of process models, as a single model can provide for many relevant views. Yet, it is an open question how to perform abstraction in the same skillful way as experienced modelers combine activities into more abstract tasks. This paper presents an approach that uses semantic information of a process model to decide on which activities belong together, which extends beyond existing approaches that merely exploit model structural characteristics. The contribution of this paper is twofold: we propose a novel activity aggregation method and suggest how to discover the activity aggregation habits of human modelers. In an experimental validation, we use an industrial process model repository to compare the developed activity aggregation method with actual modeling decisions, and observe a strong correlation between the two. The presented work is expected to contribute to the development of modeling support for the effective process model abstraction.     

Capability and limitation of max- and sum-type construction of Lyapunov functions for networks of iISS systems

This paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input-to-state stability (iISS). We focus on two ways of constructing a Lyapunov function satisfying a dissipation inequality of a given network. Their difference from one another is elucidated from the viewpoint of formulation, relation, fundamental limitation and capability. One is referred to as the max-type construction resulting in a Lipschitz continuous Lyapunov function. The other is the sum-type construction resulting in a continuously differentiable Lyapunov function. This paper presents geometrical conditions under which the Lyapunov construction is possible for a network comprising $n\ge 2$ subsystems. Although the sum-type construction for general $n>2$ has not yet been reduced to a readily computable condition, we obtain a simple condition of iISS small gain in the case of $n=2$. It is demonstrated that the max-type construction fails to offer a Lyapunov function if the network contains subsystems which are not input-to-state stable (ISS).     

磁控溅射法镀制氮化铝薄膜特性研究

氮化铝薄膜具有高折射率,良好的化学稳定性,耐磨摩、高电阻等特性在微电子器件和光学薄膜中有着广泛地应用.本文研究了反应式磁控溅射方法利用Ar/N2混合气体镀制氮化铝薄膜的工艺过程,实验表明在高真空和高泵浦速率条件下,放电电压直接依赖于反应气体珠浓度.薄膜的折射率,消光系数和薄膜硬度都依赖于氮气浓度的比例.通过工艺研究,找到了氮气在不同浓度下对氮化铝薄膜的折射率,消光系数以及薄膜硬度的影响,找出了镀制氮化镀制氮化铝薄膜的最佳工艺参数.在Ar/N2工作气体中氮气含量保持在40%条件下,用反应式磁控溅射方法,可以精确镀制出良好的氮化铝薄膜,其中折射率范围在2.25~2.4之间,消光系数为10-3,薄膜显微硬度大于20GPa.该薄膜可以广泛应用于微电子器件和光电器件上.     

A Conjecture on Wiener Indices in Combinatorial Chemistry

Drugs and other chemical compounds are often modeled as polygonal shapes, where each vertex represents an atom of the molecule, and covalent bonds between atoms are represented by edges between the corresponding vertices. This polygonal shape derived from a chemical compound is often called its molecular graph, and can be a path, a tree, or in general a graph. An indicator defined over this molecular graph, the Wiener index, has been shown to be strongly correlated to various chemical properties of the compound. The Wiener index conjecture for trees states that for any integer n (except for a finite set), one can find a tree with Wiener index n. This conjecture has been open for quite some time, and many authors have presented incremental progress on this problem. In this paper we present further progress towards proving this conjecture—through the design of efficient algorithms, we show that enumerating all possible trees to verify this conjecture (as done by all the previous approaches) is not necessary, but instead searching in a small special family of trees suffices, thus achieving the first polynomial (in n) time algorithm to verify the conjecture up to integer n. More precisely, we (i) present an infinite family of trees and prove various properties of these trees, (ii) show that a large number of integers, up to at least 10⁸ (compared with the previous best 10⁴) are representable as Wiener indices of trees in this succinct family, (iii) provide several efficient algorithms for computing trees with given Wiener indices, and (iv) implement our algorithms and experimentally show that their performance is asymptotically much better than their theoretical worst-case upper bound.