AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

Further Results on Partial Order Equivalences on Infinite Systems

In [26], we investigated decidability issues for standard language equivalence for process description languages with two generalisations based on traditional approachesfor capturing non-interleaving behaviour: pomset equivalence reflecting global causal dependency, and location equivalence reflecting spatial distribution of events. In this paper, we continue by investigating the role played by TCSP-style renaming and hiding combinators with respect to decidability. One result of [26] was that in contrast to pomset equivalence, location equivalence remained decidable for a class of processes consisting of finite sets of BPP processes communicating in a TCSP manner. Here, we show that location equivalence becomes undecidable when either renaming or hiding is added to this class of processes. Furthermore, we investigate the weak versions of location and pomset equivalences.We show that for BPP with prefixing, both weak pomset and weak location equivalence are decidable. Moreover, we show that weak location equivalence is undecidable for BPP semantically extended with CCS communication

Proceedings of the first international workshop on Investigating dataflow in embedded computing architectures (IDEA 2015), January 21, 2015, Amsterdam, The Netherlands

IDEA '15 held at HiPEAC 2015, Amsterdam, The Netherlands on January 21st, 2015 is the rst workshop on Investigating Data ow in Embedded computing Architectures. This technical report comprises of the proceedings of IDEA '15. Over the years, data ow has been gaining popularity among Embedded Systems researchers around Europe and the world. However, research on data ow is limited to small pockets in dierent communities without a common forum for discussion. The goal of the workshop was to provide a platform to researchers and practitioners to present work on modelling and analysis of present and future high performance embedded computing architectures using data ow. Despite being the rst edition of the workshop, it was very pleasant to see a total of 14 submissions, out of which 6 papers were selected following a thorough reviewing process. All the papers were reviewed by at least 5 reviewers. This workshop could not have become a reality without the help of a Technical Program Committee (TPC). The TPC members not only did the hard work to give helpful reviews in time, but also participated in extensive discussion following the reviewing process, leading to an excellent workshop program and very valuable feedback to authors. Likewise, the Organisation Committee also deserves acknowledgment to make this workshop a successful event. We take this opportunity to thank everyone who contributed in making this workshop a success

Proceedings of the first international workshop on Investigating dataflow in embedded computing architectures (IDEA 2015), January 21, 2015, Amsterdam, The Netherlands

IDEA '15 held at HiPEAC 2015, Amsterdam, The Netherlands on January 21st, 2015 is the rst workshop on Investigating Data ow in Embedded computing Architectures. This technical report comprises of the proceedings of IDEA '15. Over the years, data ow has been gaining popularity among Embedded Systems researchers around Europe and the world. However, research on data ow is limited to small pockets in dierent communities without a common forum for discussion. The goal of the workshop was to provide a platform to researchers and practitioners to present work on modelling and analysis of present and future high performance embedded computing architectures using data ow. Despite being the rst edition of the workshop, it was very pleasant to see a total of 14 submissions, out of which 6 papers were selected following a thorough reviewing process. All the papers were reviewed by at least 5 reviewers. This workshop could not have become a reality without the help of a Technical Program Committee (TPC). The TPC members not only did the hard work to give helpful reviews in time, but also participated in extensive discussion following the reviewing process, leading to an excellent workshop program and very valuable feedback to authors. Likewise, the Organisation Committee also deserves acknowledgment to make this workshop a successful event. We take this opportunity to thank everyone who contributed in making this workshop a success

Logische Grundlagen von Datenbanktransformationen für Datenbanken mit komplexen Typen

Database transformations consist of queries and updates which are two fundamental types of computations in any databases - the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. With the rising popularity of web-based applications and service-oriented architectures, the development of database transformations must address new challenges, which frequently call for establishing a theoretical framework that unifies both queries and updates over complex-value databases. This dissertation aims to lay down the foundations for establishing a theoretical framework of database transformations in the context of complex-value databases. We shall use an approach that has successfully been used for the characterisation of sequential algorithms. The sequential Abstract State Machine (ASM) thesis captures semantics and behaviour of sequential algorithms. The thesis uses the similarity of general computations and database transformations for characterisation of the later by five postulates: sequential time postulate, abstract state postulate, bounded exploration postulate, background postulate, and the bounded non-determinism postulate. The last two postulates reflect the specific form of transformations for databases. The five postulates exactly capture database transformations. Furthermore, we provide a logical proof system for database transformations that is sound and complete.Datenbanktransformationen sind Anfragen an ein Datenbanksystem oder Modifikationen der Daten des Datenbanksystemes. Diese beiden grundlegenden Arten von Berechnungen auf Datenbanksystemen erlauben zum einem den Zugriff auf Daten und zum anderen die Pflege der Datenbank. Eine theoretische Fundierung von Datenbanktransformationen muss so flexibel sein, dass auch neue web-basierten Anwendungen und den neuen serviceorientierte Architekturen reflektiert sind, sowie auch die komplexeren Datenstrukturen. Diese Dissertation legt die Grundlagen für eine Theoriefundierung durch Datenbanktransformationen, die auch komplexe Datenstrukturen unterstützen. Wir greifen dabei auf einen Zugang zurück, der eine Theorie der sequentiellen Algorithmen bietet. Die sequentielle ASM-These (abstrakte Zustandsmaschinen) beschreibt die Semantik und das Verhalten sequentieller Algorithmen. Die Dissertation nutzt dabei die Gleichartigkeit von allgemeinen Berechnungen und Datenbanktransformationen zur Charakterisierung durch fünf Postulate bzw. Axiome: das Axiom der sequentiellen Ausführung, das Axiom einer abstrakten Charakterisierbarkeit von Zuständen, das Axiom der Begrenzbarkeit von Zustandsänderungen und Zustandssicht, das Axiom der Strukturierung von Datenbanken und das Axiom der Begrenzbarkeit des Nichtdeterminismus. Die letzten beiden Axiome reflektieren die spezifische Seite der Datenbankberechnungen. Die fünf Axiome beschreiben vollständig das Verhalten von Datenbanktransformationen. Weiterhin wird eine Beweiskalkül für Datenbanktransformationen entwickelt, der vollständig und korrekt ist

Lie algebra actions on module categories for truncated shifted Yangians

We develop a theory of parabolic induction and restriction functors relating modules over Coulomb branch algebras, in the sense of Braverman-Finkelberg-Nakajima. Our functors generalize Bezrukavnikov-Etingof's induction and restriction functors for Cherednik algebras, but their definition uses different tools. After this general definition, we focus on quiver gauge theories attached to a quiver $\Gamma$. The induction and restriction functors allow us to define a categorical action of the corresponding symmetric Kac-Moody algebra $\mathfrak{g}_{\Gamma}$ on category $\mathcal O$ for these Coulomb branch algebras. When $\Gamma$ is of Dynkin type, the Coulomb branch algebras are truncated shifted Yangians and quantize generalized affine Grassmannian slices. Thus, we regard our action as a categorification of the geometric Satake correspondence. To establish this categorical action, we define a new class of "flavoured" KLRW algebras, which are similar to the diagrammatic algebras originally constructed by the second author for the purpose of tensor product categorification. We prove an equivalence between the category of Gelfand-Tsetlin modules over a Coulomb branch algebra and the modules over a flavoured KLRW algebra. This equivalence relates the categorical action by induction and restriction functors to the usual categorical action on modules over a KLRW algebra.Comment: 66 pages, version 2: many corrections, improved treatment of GK dimension, 71 page