Sparsity-Sensitive Finite Abstraction

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network

Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation

Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. The abstraction theory therefore provides a mechanism for coping with the state space explosion problem and supports the analysis and comparison of multi-valued networks. We take as our starting point the abstraction theory for synchronous multi-valued networks which is based on the finite set of traces that represent the behaviour of such a model. The problem with extending this approach to the asynchronous case is that we can now have an infinite set of traces associated with a model making a simple trace inclusion test infeasible. To address this we develop a decision procedure for checking asynchronous abstractions based on using the finite state graph of an asynchronous multi-valued network to reason about its trace semantics. We illustrate the abstraction techniques developed by considering a detailed case study based on a multi-valued network model of the regulation of tryptophan biosynthesis in Escherichia coli.Comment: Presented at MeCBIC 201

An Abstraction Theory for Qualitative Models of Biological Systems

Multi-valued network models are an important qualitative modelling approach used widely by the biological community. In this paper we consider developing an abstraction theory for multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. This is important as it aids the analysis and comparison of multi-valued networks and in particular, helps address the well-known problem of state space explosion associated with such analysis. We also consider developing techniques for efficiently identifying abstractions and so provide a basis for the automation of this task. We illustrate the theory and techniques developed by investigating the identification of abstractions for two published MVN models of the lysis-lysogeny switch in the bacteriophage lambda.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Dynamic Model-based Management of Service-Oriented Infrastructure.

Models are an effective tool for systems and software design. They allow software architects to abstract from the non-relevant details. Those qualities are also useful for the technical management of networks, systems and software, such as those that compose service oriented architectures. Models can provide a set of well-defined abstractions over the distributed heterogeneous service infrastructure that enable its automated management. We propose to use the managed system as a source of dynamically generated runtime models, and decompose management processes into a composition of model transformations. We have created an autonomic service deployment and configuration architecture that obtains, analyzes, and transforms system models to apply the required actions, while being oblivious to the low-level details. An instrumentation layer automatically builds these models and interprets the planned management actions to the system. We illustrate these concepts with a distributed service update operation

Abstract Interpretation of Stateful Networks

Modern networks achieve robustness and scalability by maintaining states on their nodes. These nodes are referred to as middleboxes and are essential for network functionality. However, the presence of middleboxes drastically complicates the task of network verification. Previous work showed that the problem is undecidable in general and EXPSPACE-complete when abstracting away the order of packet arrival. We describe a new algorithm for conservatively checking isolation properties of stateful networks. The asymptotic complexity of the algorithm is polynomial in the size of the network, albeit being exponential in the maximal number of queries of the local state that a middlebox can do, which is often small. Our algorithm is sound, i.e., it can never miss a violation of safety but may fail to verify some properties. The algorithm performs on-the fly abstract interpretation by (1) abstracting away the order of packet processing and the number of times each packet arrives, (2) abstracting away correlations between states of different middleboxes and channel contents, and (3) representing middlebox states by their effect on each packet separately, rather than taking into account the entire state space. We show that the abstractions do not lose precision when middleboxes may reset in any state. This is encouraging since many real middleboxes reset, e.g., after some session timeout is reached or due to hardware failure