22. Workshop Komplexitätstheorie und effiziente Algorithmen

his publication contains abstracts of the 22nd workshop on complexity theory and efficient algorithms. The workshop was held on February 8, 1994, at the Max-Planck-Institut für Informatik, Saarbrücken, Germany

Learning understandable classifier models.

The topic of this dissertation is the automation of the process of extracting understandable patterns and rules from data. An unprecedented amount of data is available to anyone with a computer connected to the Internet. The disciplines of Data Mining and Machine Learning have emerged over the last two decades to face this challenge. This has led to the development of many tools and methods. These tools often produce models that make very accurate predictions about previously unseen data. However, models built by the most accurate methods are usually hard to understand or interpret by humans. In consequence, they deliver only decisions, and are short of any explanations. Hence they do not directly lead to the acquisition of new knowledge. This dissertation contributes to bridging the gap between the accurate opaque models and those less accurate but more transparent for humans. This dissertation first defines the problem of learning from data. It surveys the state-of-the-art methods for supervised learning of both understandable and opaque models from data, as well as unsupervised methods that detect features present in the data. It describes popular methods of rule extraction from unintelligible models which rewrite them into an understandable form. Limitations of rule extraction are described. A novel definition of understandability which ties computational complexity and learning is provided to show that rule extraction is an NP-hard problem. Next, a discussion whether one can expect that even an accurate classifier has learned new knowledge. The survey ends with a presentation of two approaches to building of understandable classifiers. On the one hand, understandable models must be able to accurately describe relations in the data. On the other hand, often a description of the output of a system in terms of its input requires the introduction of intermediate concepts, called features. Therefore it is crucial to develop methods that describe the data with understandable features and are able to use those features to present the relation that describes the data. Novel contributions of this thesis follow the survey. Two families of rule extraction algorithms are considered. First, a method that can work with any opaque classifier is introduced. Artificial training patterns are generated in a mathematically sound way and used to train more accurate understandable models. Subsequently, two novel algorithms that require that the opaque model is a Neural Network are presented. They rely on access to the network\u27s weights and biases to induce rules encoded as Decision Diagrams. Finally, the topic of feature extraction is considered. The impact on imposing non-negativity constraints on the weights of a neural network is considered. It is proved that a three layer network with non-negative weights can shatter any given set of points and experiments are conducted to assess the accuracy and interpretability of such networks. Then, a novel path-following algorithm that finds robust sparse encodings of data is presented. In summary, this dissertation contributes to improved understandability of classifiers in several tangible and original ways. It introduces three distinct aspects of achieving this goal: infusion of additional patterns from the underlying pattern distribution into rule learners, the derivation of decision diagrams from neural networks, and achieving sparse coding with neural networks with non-negative weights

Formal modelling and analysis of broadcasting embedded control systems

PhD ThesisEmbedded systems are real-time, communicating systems, and the effective modelling and analysis of these aspects of their behaviour is regarded as essential for acquiring confidence in their correct operation. In practice, it is important to minimise the burden of model construction and to automate the analysis, if possible. Among the most promising techniques for real-time systems are reachability analysis and model-checking of networks of timed automata. We identify two obstacles to the application of these techniques to a large class of distributed embedded systems: firstly, the language of timed automata is too low-level for straightforward model construction, and secondly, the synchronous, handshake communication mechanism of the timed automata model does not fit well with the asynchronous, broadcast mechanism employed in many distributed embedded systems. As a result, the task of model construction can be unduly onerous. This dissertation proposes an expressive language for the construction of models of real-time, broadcasting control systems, and demonstrates how effi- cient analysis techniques can be applied to them. The dissertation is concerned in particular with the Controller Area Network (CAN) protocol which is emerging as a de facto standard in the automotive industry. An abstract formal model of CAN is developed. This model is adopted as the communication primitive in a new language, bCANDLE, which includes value passing, broadcast communication, message priorities and explicit time. A high-level language, CANDLE, is introduced and its semantics defined by translation to bCANDLE. We show how realistic CAN systems can be described in CANDLE and how a timed transition model of a system can be extracted for analysis. Finally, it is shown how efficient methods of analysis, such as 'on-the- fly' and symbolic techniques, can be applied to these models. The dissertation contributes to the practical application of formal methods within the domain of broadcasting, embedded control systemsSchool of Computing and Mathematics at the University of Northumbri

Formal Verification based on Boolean Expression Diagrams

AbstractThis dissertation examines the use of a new data structure called Boolean Expression Diagrams (BEDs) in the area of formal verification. The recently developed data structure allows fast and efficient manipulation of Boolean formulae. Many problems in formal verification can be cast as problems on Boolean formulae. We chose a number of such problems and show how to solve them using BEDs.Equivalence checking of combinational circuits is a formal verification problem which translates into tautology checking of Boolean formulae. Using BEDs we are able to preserve much of the structure of the circuits within the Boolean formulae. We show how to exploit the structural information in the verification process.Sometimes combinational circuits are specified in a hierarchical or modular way. We present a method for verifying equivalence between two such circuits. The method builds on cut propagation. Assuming that the two circuits are given identical inputs, we propagate this knowledge through the circuits from the inputs to the outputs. The result is the knowledge of how the outputs of the two circuits correspond, e.g., are the outputs of the two circuits pairwise equivalent? The circuits and the movements of cuts can be described using Boolean formulae.Symbolic model checking is a technique for verifying temporal specifications of finite state machines. It is well known how finite state machines and the evaluation of the temporal specifications can be expressed using Boolean formulae. We show how to do these manipulations using BEDs. We concentrate on examples which are hard for standard symbolic model checking methods.Determining whether a formula is satisfiability is a problem which occurs in verification of combinational circuits and in symbolic model checking. Often satisfiability checking is associated with detecting errors. We examine how satisfiability checking can be done using the BED data structure.Finally, we take a look at how it is possible to extend the BED data structure. Among other operations, we introduce an operator for computing minimal p-cuts in fault trees. A fault tree is a Boolean formula expressing whether a system fails based on the condition (“failure” or “working”) of each of the components. A minimal p-cut is a representation of the most likely reasons for system failure. This method can be used to calculate approximately the probability of system failure given the failure probabilities of each of the components.As part of this research, we have developed a BED package. The appendix describes the package from a user's point of view