DyNetKAT: An Algebra of Dynamic Networks

We introduce a formal language for specifying dynamic updates for Software Defined Networks. Our language builds upon Network Kleene Algebra with Tests (NetKAT) and adds constructs for synchronisations and multi-packet behaviour to capture the interaction between the control- and data-plane in dynamic updates. We provide a sound and ground-complete axiomatisation of our language. We exploit the equational theory to provide an efficient reasoning method about safety properties for dynamic networks. We implement our equational theory in DyNetiKAT -- a tool prototype, based on the Maude Rewriting Logic and the NetKAT tool, and apply it to a case study. We show that we can analyse the case study for networks with hundreds of switches using our initial tool prototype

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors

A Logic for Non-Deterministic Parallel Abstract State Machines

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748

Hybrid Information Flow Analysis for Programs with Arrays

Information flow analysis checks whether certain pieces of (confidential) data may affect the results of computations in unwanted ways and thus leak information. Dynamic information flow analysis adds instrumentation code to the target software to track flows at run time and raise alarms if a flow policy is violated; hybrid analyses combine this with preliminary static analysis. Using a subset of C as the target language, we extend previous work on hybrid information flow analysis that handled pointers to scalars. Our extended formulation handles arrays, pointers to array elements, and pointer arithmetic. Information flow through arrays of pointers is tracked precisely while arrays of non-pointer types are summarized efficiently. A prototype of our approach is implemented using the Frama-C program analysis and transformation framework. Work on a full machine-checked proof of the correctness of our approach using Isabelle/HOL is well underway; we present the existing parts and sketch the rest of the correctness argument.Comment: In Proceedings VPT 2016, arXiv:1607.0183

Introducing Dynamic Behavior in Amalgamated Knowledge Bases

The problem of integrating knowledge from multiple and heterogeneous sources is a fundamental issue in current information systems. In order to cope with this problem, the concept of mediator has been introduced as a software component providing intermediate services, linking data resources and application programs, and making transparent the heterogeneity of the underlying systems. In designing a mediator architecture, we believe that an important aspect is the definition of a formal framework by which one is able to model integration according to a declarative style. To this purpose, the use of a logical approach seems very promising. Another important aspect is the ability to model both static integration aspects, concerning query execution, and dynamic ones, concerning data updates and their propagation among the various data sources. Unfortunately, as far as we know, no formal proposals for logically modeling mediator architectures both from a static and dynamic point of view have already been developed. In this paper, we extend the framework for amalgamated knowledge bases, presented by Subrahmanian, to deal with dynamic aspects. The language we propose is based on the Active U-Datalog language, and extends it with annotated logic and amalgamation concepts. We model the sources of information and the mediator (also called supervisor) as Active U-Datalog deductive databases, thus modeling queries, transactions, and active rules, interpreted according to the PARK semantics. By using active rules, the system can efficiently perform update propagation among different databases. The result is a logical environment, integrating active and deductive rules, to perform queries and update propagation in an heterogeneous mediated framework.Comment: Other Keywords: Deductive databases; Heterogeneous databases; Active rules; Update