JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis

Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

08381 Abstracts Collection -- Computational Complexity of Discrete Problems

From the 14th of September to the 19th of September, the Dagstuhl Seminar 08381 ``Computational Complexity of Discrete Problems\u27\u27 was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work as well as open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this report. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Symmetry and complexity in propositional reasoning

We establish computational complexity results for a number of simple problem formulations connecting group action and prepositional formulas. The results are discussed in the context of complexity results arising from established work in the area of automated reasoning techniques which exploit symmetry

Artificial evolution with Binary Decision Diagrams: a study in evolvability in neutral spaces

This thesis develops a new approach to evolving Binary Decision Diagrams, and uses it to study evolvability issues. For reasons that are not yet fully understood, current approaches to artificial evolution fail to exhibit the evolvability so readily exhibited in nature. To be able to apply evolvability to artificial evolution the field must first understand and characterise it; this will then lead to systems which are much more capable than they are currently. An experimental approach is taken. Carefully crafted, controlled experiments elucidate the mechanisms and properties that facilitate evolvability, focusing on the roles and interplay between neutrality, modularity, gradualism, robustness and diversity. Evolvability is found to emerge under gradual evolution as a biased distribution of functionality within the genotype-phenotype map, which serves to direct phenotypic variation. Neutrality facilitates fitness-conserving exploration, completely alleviating local optima. Population diversity, in conjunction with neutrality, is shown to facilitate the evolution of evolvability. The search is robust, scalable, and insensitive to the absence of initial diversity. The thesis concludes that gradual evolution in a search space that is free of local optima by way of neutrality can be a viable alternative to problematic evolution on multi-modal landscapes

On Computing Probabilistic Abductive Explanations

The most widely studied explainable AI (XAI) approaches are unsound. This is the case with well-known model-agnostic explanation approaches, and it is also the case with approaches based on saliency maps. One solution is to consider intrinsic interpretability, which does not exhibit the drawback of unsoundness. Unfortunately, intrinsic interpretability can display unwieldy explanation redundancy. Formal explainability represents the alternative to these non-rigorous approaches, with one example being PI-explanations. Unfortunately, PI-explanations also exhibit important drawbacks, the most visible of which is arguably their size. Recently, it has been observed that the (absolute) rigor of PI-explanations can be traded off for a smaller explanation size, by computing the so-called relevant sets. Given some positive {\delta}, a set S of features is {\delta}-relevant if, when the features in S are fixed, the probability of getting the target class exceeds {\delta}. However, even for very simple classifiers, the complexity of computing relevant sets of features is prohibitive, with the decision problem being NPPP-complete for circuit-based classifiers. In contrast with earlier negative results, this paper investigates practical approaches for computing relevant sets for a number of widely used classifiers that include Decision Trees (DTs), Naive Bayes Classifiers (NBCs), and several families of classifiers obtained from propositional languages. Moreover, the paper shows that, in practice, and for these families of classifiers, relevant sets are easy to compute. Furthermore, the experiments confirm that succinct sets of relevant features can be obtained for the families of classifiers considered.Comment: arXiv admin note: text overlap with arXiv:2207.04748, arXiv:2205.0956

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.