Lex-Partitioning: A New Option for BDD Search

For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs) can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n) ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n). The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611

Theory and applications of hashing: report from Dagstuhl Seminar 17181

This report documents the program and the topics discussed of the 4-day Dagstuhl Seminar 17181 “Theory and Applications of Hashing”, which took place May 1–5, 2017. Four long and eighteen short talks covered a wide and diverse range of topics within the theme of the workshop. The program left sufficient space for informal discussions among the 40 participants

An n log n Algorithm for Online BDD Refinement

Binary Decision Diagrams are in widespread use in verification systemsfor the canonical representation of Boolean functions. A BDD representinga function phi : B^nu -> N can easily be reduced to its canonical form inlinear time.In this paper, we consider a natural online BDD refinement problemand show that it can be solved in O(n log n) if n bounds the size of theBDD and the total size of update operations.We argue that BDDs in an algebraic framework should be understoodas minimal fixed points superimposed on maximal fixed points. We proposea technique of controlled growth of equivalence classes to make theminimal fixed point calculations be carried out efficiently. Our algorithmis based on a new understanding of the interplay between the splittingand growing of classes of nodes.We apply our algorithm to show that automata with exponentiallylarge, but implicitly represented alphabets, can be minimized in timeO(n log n), where n is the total number of BDD nodes representing theautomaton

Star-topology decoupled state-space search in AI planning and model checking

State-space search is a widely employed concept in many areas of computer science. The well-known state explosion problem, however, imposes a severe limitation to the effective implementation of search in state spaces that are exponential in the size of a compact system description, which captures the state-transition semantics. Decoupled state-space search, decoupled search for short, is a novel approach to tackle the state explosion. It decomposes the system such that the dependencies between components take the form of a star topology with a center and several leaf components. Decoupled search exploits that the leaves in that topology are conditionally independent. Such independence naturally arises in many kinds of factored model representations, where the overall state space results from the product of several system components. In this work, we introduce decoupled search in the context of artificial intelligence planning and formal verification using model checking. Building on common formalisms, we develop the concept of the decoupled state space and prove its correctness with respect to capturing reachability of the underlying model exactly. This allows us to connect decoupled search to any search algorithm, and, important for planning, adapt any heuristic function to the decoupled state representation. Such heuristics then guide the search towards states that satisfy a desired goal condition. In model checking, we address the problems of verifying safety properties, which express system states that must never occur, and liveness properties, that must hold in any infinite system execution. Many approaches have been proposed in the past to tackle the state explosion problem. Most prominently partial-order reduction, symmetry breaking, Petri-net unfolding, and symbolic state representations. Like decoupled search, all of these are capable of exponentially reducing the search effort, either by pruning part of the state space (the former two), or by representing large state sets compactly (the latter two). For all these techniques, we prove that decoupled search can be exponentially more efficient, confirming that it is indeed a novel concept that exploits model properties in a unique way. Given such orthogonality, we combine decoupled search with several complementary methods. Empirically, we show that decoupled search favourably compares to state-of-the-art planners in common algorithmic planning problems using standard benchmarks. In model checking, decoupled search outperforms well-established tools, both in the context of the verification of safety and liveness properties.Die Zustandsraumsuche ist ein weit verbreitetes Konzept in vielen Bereichen der Informatik, deren effektive Anwendung jedoch durch das Problem der Zustandsexplosion deutlich erschwert wird. Die Zustandsexplosion ist dadurch charakterisiert dass kompakte Systemmodelle exponentiell große Zustandsräume beschreiben. Entkoppelte Zustandsraumsuche (entkoppelte Suche) beschreibt einen neuartigen Ansatz der Zustandsexplosion entgegenzuwirken indem die Struktur des Modells, insbesondere die bedingte Unabhängigkeit von Systemkomponenten in einer Sterntopologie, ausgenutzt wird. Diese Unabhängigkeit ergibt sich bei vielen faktorisierten Modellen deren Zustandsraum sich aus dem Produkt mehrerer Komponenten zusammensetzt. In dieser Arbeit wird die entkoppelte Suche in der Planung, als Teil der Künstlichen Intelligenz, und der Verifikation mittels Modellprüfung eingeführt. In etablierten Formalismen wird das Konzept des entkoppelten Zustandsraums entwickelt und dessen Korrektheit bezüglich der exakten Erfassung der Erreichbarkeit von Modellzuständen bewiesen. Dies ermöglicht die Kombination der entkoppelten Suche mit beliebigen Suchalgorithmen. Wichtig für die Planung ist zudem die Nutzung von Heuristiken, die die Suche zu Zuständen führen, die eine gewünschte Zielbedingung erfüllen, mit der entkoppelten Zustandsdarstellung. Im Teil zur Modellprüfung wird die Verifikation von Sicherheits- sowie Lebendigkeitseigenschaften betrachtet, die unerwünschte Zustände, bzw. Eigenschaften, die bei unendlicher Systemausführung gelten müssen, beschreiben. Es existieren diverse Ansätze um die Zustandsexplosion anzugehen. Am bekanntesten sind die Reduktion partieller Ordnung, Symmetriereduktion, Entfaltung von Petri-Netzen und symbolische Suche. Diese können, wie die entkoppelte Suche, den Suchaufwand exponentiell reduzieren. Dies geschieht durch Beschneidung eines Teils des Zustandsraums, oder durch die kompakte Darstellung großer Zustandsmengen. Für diese Verfahren wird bewiesen, dass die entkoppelte Suche exponentiell effizienter sein kann. Dies belegt dass es sich um ein neuartiges Konzept handelt, das sich auf eigene Art der Modelleigenschaften bedient. Auf Basis dieser Beobachtung werden, mit Ausnahme der Entfaltung, Kombinationen mit entkoppelter Suche entwickelt. Empirisch kann die entkoppelte Suche im Vergleich zu modernen Planern zu deutlichen Vorteilen führen. In der Modellprüfung werden, sowohl bei der Überprüfung von Sicherheit-, als auch Lebendigkeitseigenschaften, etablierte Programme übertroffen.Deutsche Forschungsgesellschaft; Star-Topology Decoupled State Space Searc

Toward Autonomous Verification Systems

Design verification has been a challenging problem due to the increasing complexity of modern system-on-chip (SoC) designs and it is considered one of the costliest processes in hardware design flow. This dissertation investigates a major labor-intensive task, generating tests to hit a given coverage point, in simulation-based verification, and proposes an autonomous software system capable of completing the task. A key feature of the proposed system is its learning capability -- it can learn from examples provided by human engineers to improve itself. There are three major components in the proposed system: test generation, a knowledge database, and rule learning algorithms. The proposed system is able to retrieve information from the database, use the information to analyze simulation results, and generate new tests based on the analysis. Several machine learning techniques are used in the proposed system. For test generation, a novel method, constrained process discovery, is used to learn a test case generation model from manually developed tests. The test case generation model can create new tests and increase its test generation capability by learning from tests developed by humans. For creating a knowledge database, text mining methods are used to extract important design features from design documents. Experiments showed that the extracted signals can be utilized as observation points to infer important hardware events. Last, a novel rule learning method, VeSC-CoL, is proposed to analyze simulation results. VeSC-CoL can handle extremely imbalanced data, which is common in verification, while traditional rule learning methods cannot

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

Featured Anomaly Detection Methods and Applications

Anomaly detection is a fundamental research topic that has been widely investigated. From critical industrial systems, e.g., network intrusion detection systems, to people’s daily activities, e.g., mobile fraud detection, anomaly detection has become the very first vital resort to protect and secure public and personal properties. Although anomaly detection methods have been under consistent development over the years, the explosive growth of data volume and the continued dramatic variation of data patterns pose great challenges on the anomaly detection systems and are fuelling the great demand of introducing more intelligent anomaly detection methods with distinct characteristics to cope with various needs. To this end, this thesis starts with presenting a thorough review of existing anomaly detection strategies and methods. The advantageous and disadvantageous of the strategies and methods are elaborated. Afterward, four distinctive anomaly detection methods, especially for time series, are proposed in this work aiming at resolving specific needs of anomaly detection under different scenarios, e.g., enhanced accuracy, interpretable results, and self-evolving models. Experiments are presented and analysed to offer a better understanding of the performance of the methods and their distinct features. To be more specific, the abstracts of the key contents in this thesis are listed as follows: 1) Support Vector Data Description (SVDD) is investigated as a primary method to fulfill accurate anomaly detection. The applicability of SVDD over noisy time series datasets is carefully examined and it is demonstrated that relaxing the decision boundary of SVDD always results in better accuracy in network time series anomaly detection. Theoretical analysis of the parameter utilised in the model is also presented to ensure the validity of the relaxation of the decision boundary. 2) To support a clear explanation of the detected time series anomalies, i.e., anomaly interpretation, the periodic pattern of time series data is considered as the contextual information to be integrated into SVDD for anomaly detection. The formulation of SVDD with contextual information maintains multiple discriminants which help in distinguishing the root causes of the anomalies. 3) In an attempt to further analyse a dataset for anomaly detection and interpretation, Convex Hull Data Description (CHDD) is developed for realising one-class classification together with data clustering. CHDD approximates the convex hull of a given dataset with the extreme points which constitute a dictionary of data representatives. According to the dictionary, CHDD is capable of representing and clustering all the normal data instances so that anomaly detection is realised with certain interpretation. 4) Besides better anomaly detection accuracy and interpretability, better solutions for anomaly detection over streaming data with evolving patterns are also researched. Under the framework of Reinforcement Learning (RL), a time series anomaly detector that is consistently trained to cope with the evolving patterns is designed. Due to the fact that the anomaly detector is trained with labeled time series, it avoids the cumbersome work of threshold setting and the uncertain definitions of anomalies in time series anomaly detection tasks