Vandermonde and resultant matrices: An abstract approach

We propose an abstract approach to the problems of common divisors and common multiples of rational matrix functions which (in the case of matrix polynomials) have been studied before using Vandermonde and resultant matrices.Supported in part by the Office of Naval Research, Air Force Office of Scientific Research, and the National Science Foundation.The work of this author was partially supported by an NSF grant and was carried out while visiting the University of California, San Diego.     

Inversion of confluent Vandermonde matrices

This paper is concerned with the inversion of confluent Vandermonde matrices. A novel and simple recursive algorithm for inverting confluent Vandermonde matrices is presented. The algorithm is suitable for classroom use in both numerical as well as symbolic computation. Examples are included to illustrate the proposed algorithm.     

A relation between the Hilbert and Vandermonde matrices

A relation is established between two famous matrices and two simple applications are proposed. We first study the asymptotic behaviour of the spectral condition number of a Vandermonde matrix with a particular configuration of points. We then apply our relation to the problem of the computation of the Christoffel number starting from the moments of the weight function; we show that the relative asymptotic condition number of the problem is essentially the Turing condition number of the Hilbert matrix as observed numerically by other authors in the past.     

An abstract architecture for virtual organizations: The THOMAS approach

Today, the need for architectures and computational models for large-scale open multi-agent systems is considered to be a key issue for the success of agent technology in real-world scenarios. This paper analyzes the significant unsolved problems that must be taken into account in order to develop real, open multi-agent systems. It identifies requirements and related open issues, discusses how some of these requirements have been tackled by current technologies, and explains how the THOMAS architecture is able to give support to these open issues. This paper also describes the THOMAS abstract architecture and computational model for large-scale open multi-agent systems based on a service-oriented approach that specifically addresses the design of virtual organizations. An application example for the management of a travel agency system, which demonstrates the new features of the proposal, is also presented.     

An inversion procedure of the generalized Vandermonde matrix

Using the interpolation method à la Hermite, an efficient procedure to invert the generalized Vandermonde matrix is presented.     

An abstract pretty printer

The author has distilled the basic operations of the pretty printer into an abstract pretty printer that uses procedural parameters to perform low-level printing actions. By encapsulating the algorithm in one place, all the pretty-printing utilities will use the same algorithm, and the algorithm itself can be changed easily. The author describes how the abstract pretty printer can be used for basic design, printing to files and screens, setting the cursor, identifying a node, formatting text, and lexical changes     

An abstract knowledge based approach to diagnosis and recovery of plan failure in multi-agent systems

Open multi-agent systems (MAS) are decentralised and distributed systems that consist of a large number of loosely coupled autonomous agents. In the absence of centralised control they tend to be difficult to manage, especially in an open environment, which is dynamic, complex, distributed and unpredictable. This dynamism and uncertainty in an open environment gives rise to unexpected plan failures. In this paper we present an abstract knowledge based approach for the diagnosis and recovery of plan action failures. Our approach associates a sentinel agent with each problem solving agent in order to monitor the problem solving agent’s interactions. The proposed approach also requires the problem solving agents to be able to report on the status of a plan’s actions.Once an exception is detected the sentinel agents start an investigation of the suspected agents. The sentinel agents collect information about the status of failed plan abstract actions and knowledge about agents’ mental attitudes regarding any failed plan. The sentinel agent then uses this abstract knowledge and the agents’ mental attitudes, to diagnose the underlying cause of the plan failure. The sentinel agent may ask the problem solving agent to retry their failed plan based on the diagnostic result.     

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.     

Bulking I: An abstract theory of bulking

This paper is the first part of a series of two papers dealing with bulking: a quasi-order on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we discuss the proper components of grouping and study the most general extensions. We identify the most general space-time transforms and give an axiomatization of bulking quasi-order. Finally, we study some properties of intrinsically universal cellular automata obtained by comparing grouping to bulking.     

An abstract programming language and correctness proofs

The realization of an abstract programming language is a good approach for automating the software production process and facilitating the correctness proof of a software system.

This paper introduces a formal language for programming at the abstract level by combining Pascal with VDM (Vienna Development Method). The notation provided by the language obliges programmers to consider the correctness of programs throughout the whole process of programming, and the proof axiom and rules presented in this paper may be used to prove the correctness of programs. A complete example is given to illustrate how to program using APL and how to prove the correctness of programs using the given axiom and rules.     

An abstract model of service discovery and binding

We propose a formal operational semantics for service discovery and binding. This semantics is based on a graph-based representation of the configuration of global computers typed by business activities. Business activities execute distributed workflows that can trigger, at run time, the discovery, ranking and selection of services to which they bind, thus reconfiguring the workflows that they execute. Discovery, ranking and selection are based on compliance with required business and interaction protocols and optimisation of quality-of-service constraints. Binding and reconfiguration are captured as algebraic operations on configuration graphs. We also discuss the methodological implications that this model framework has on software engineering using a typical travel-booking scenario. To the best of our knowledge, our approach is the first to provide a clear separation between service computation and discovery/instantiation/binding, and to offer a formal framework that is independent of the SOA middleware components that act as service registries or brokers, and the protocols through which bindings and invocations are performed.     

Normative requirements for regulatory compliance: An abstract formal framework

By definition, regulatory rules (in legal context called norms) intend to achieve specific behaviour from business processes, and might be relevant to the whole or part of a business process. They can impose conditions on different aspects of process models, e.g., control-flow, data and resources etc. Based on the rules sets, norms can be classified into various classes and sub-classes according to their effects. This paper presents an abstract framework consisting of a list of norms and a generic compliance checking approach on the idea of (possible) execution of processes. The proposed framework is independent of any existing formalism, and provides a conceptually rich and exhaustive ontology and semantics of norms needed for business process compliance checking. Apart from the other uses, the proposed framework can be used to compare different compliance management frameworks (CMFs).     

An experience in implementing abstract data types

The abstract data type concept appears to be a useful software structuring tool. A project, called ‘Système d'Objets Conservés’, which was developed at the University of Rennes, (France), gave some experience in implementing this concept. The possibility of including abstract data type into a pre-existing compiler is demonstrated, and desirable properties of the host language are exhibited. Provision of external procedures and data makes some type checking extensions necessary: these features increase software reliability.     

An abstract formal basis for digital crowds

Distributed and Parallel Databases - Crowdsourcing, together with its related approaches, has become very popular in recent years. All crowdsourcing processes involve the participation of a digital...     

An abstract data type for name analysis

This paper defines an abstract data type on which a solution to the name analysis subproblem of a compiler can be based. (Name analysis uses the scope rules of a language to associate uses of identifiers with their definitions.) We give a state model for the ADT, and show how to implement that model efficiently. The implementation is independent of any particular name analysis, so it is possible to create a library module that can be used in any compiler. Such a library module has been incorporated into the Eli compiler construction system.     

An abstract framework for globalising interactive systems

We present an abstract framework for designing and developing globalised interactive systems from simple components viewed as games [1] (K. Stathis, M.J. Sergot, Games as a Metaphor for Interactive Systems, in: M.A. Sasse, R.J. Cunningham, R.L. Winder (Eds.), People and Computers XI (Proceedings of HCI′96), August 1996, London, UK, BCS Conference Series, Springer-Varlag, pp. 19–33). We identify a set of concepts required to specify and implement interactions, in such a way whereby instantiating the specifications and implementations of games we obtain components that correspond to localised instances of an interactive system. Localisation is also obtained by either customising the specification or the implementation of the interactive system, or both. The framework also caters for complex interactive systems which are interpreted as compound games built-up from sub-games. In this case, coordination of sub-games is the main issue that we must address at the global level. This is resolved by specifying and implementing sub-games as active components of the more complex games, and, as a result, we localise the coordination of components in the interactive system. The framework lends itself towards a methodology that is suitable for globalising the development of interactive systems.     

An efficient abstract machine for Safe Ambients

Safe Ambients (SA) are a variant of the Ambient Calculus (AC) in which types can be used to avoid certain forms of interferences among processes called grave interferences.An abstract machine, called GcPan, for a distributed implementation of typed SA is presented and studied. Our machine improves over previous proposals for executing AC, or variants of it, mainly through a better management of special agents (the forwarders), created upon code migration to transmit messages to the target location of the migration. Well-known methods (such as reference counting and union-find) are applied in order to garbage collect forwarders, thus avoiding long – possibly distributed – chains of forwarders, as well as avoiding useless persistent forwarders.We present the proof of correctness of GcPan w.r.t. typed SA processes. We describe a distributed implementation of the abstract machine in OCaml.More broadly, this study is a contribution towards understanding issues of correctness and optimisations in implementations of distributed languages encompassing mobility.     

An abstract interpretation toolkit for μCRL

This paper describes a toolkit that assists in the task of generating abstract approximations of process algebraic specifications written in the language μCRL. Abstractions are represented by Modal Labelled Transition Systems, which are mixed transition systems with may and must modalities. The approach permits to infer the satisfaction or refutation of safety and liveness properties expressed in the (action-based) μ-calculus. The tool supports the abstraction of states and action labels, which allows to deal with infinitely branching systems.     

An algorithm for generating abstract syntax trees

In this paper, we discuss the notion of an abstract syntax. An algorithm is presented for automatically deriving an abstract syntax directly from a BNF grammar. The implementation of this algorithm and its application to the grammar for Modula are discussed.