Algebraic model counting

Weighted model counting (WMC) is a well-known inference task on knowledge bases, and the basis for some of the most efficient techniques for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure that provides a unified view on a range of tasks and existing results. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits, which are strictly more succinct, and thus more efficient to evaluate, than direct representations of sets of models. We identify further characteristics of AMC instances that allow for evaluation on even more succinct circuits

Reasoning on Feature Models: Compilation-Based vs. Direct Approaches

Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of the FM have been well resolved by translating the FM into a conjunctive normal form (CNF) formula, and then feeding the CNF to a SAT solver. However, this approach has some limits for other important reasoning issues about the FM, such as counting or enumerating configurations. Two mainstream approaches have been investigated in this direction: (i) direct approaches, using tools based on the CNF representation of the FM at hand, or (ii) compilation-based approaches, where the CNF representation of the FM has first been translated into another representation for which the reasoning queries are easier to address. Our contribution is twofold. First, we evaluate how both approaches compare when dealing with common reasoning operations on FM, namely counting configurations, pointing out one or several configurations, sampling configurations, and finding optimal configurations regarding a utility function. Our experimental results show that the compilation-based is efficient enough to possibly compete with the direct approaches and that the cost of translation (i.e., the compilation time) can be balanced when addressing sufficiently many complex reasoning operations on large configuration spaces. Second, we provide a Java-based automated reasoner that supports these operations for both approaches, thus eliminating the burden of selecting the appropriate tool and approach depending on the operation one wants to perform

Knowledge compilation for online decision-making : application to the control of autonomous systems = Compilation de connaissances pour la décision en ligne : application à la conduite de systèmes autonomes

La conduite de systèmes autonomes nécessite de prendre des décisions en fonction des observations et des objectifs courants : cela implique des tâches à effectuer en ligne, avec les moyens de calcul embarqués. Cependant, il s'agit généralement de tâches combinatoires, gourmandes en temps de calcul et en espace mémoire. Réaliser ces tâches intégralement en ligne dégrade la réactivité du système ; les réaliser intégralement hors ligne, en anticipant toutes les situations possibles, nuit à son embarquabilité. Les techniques de compilation de connaissances sont susceptibles d'apporter un compromis, en déportant au maximum l'effort de calcul avant la mise en situation du système. Ces techniques consistent à traduire un problème dans un certain langage, fournissant une forme compilée de ce problème, dont la résolution est facile et la taille aussi compacte que possible. La traduction peut être très longue, mais n'est effectuée qu'une seule fois, hors ligne. Il existe de nombreux langages-cible de compilation, notamment le langage des diagrammes de décision binaires (BDDs), qui ont été utilisés avec succès dans divers domaines (model-checking, configuration, planification). L'objectif de la thèse était d'étudier l'application de la compilation de connaissances à la conduite de systèmes autonomes. Nous nous sommes intéressés à des problèmes réels de planification, qui impliquent souvent des variables continues ou à grand domaine énuméré (temps ou mémoire par exemple). Nous avons orienté notre travail vers la recherche et l'étude de langages-cible de compilation assez expressifs pour permettre de représenter de tels problèmes.Controlling autonomous systems requires to make decisions depending on current observations and objectives. This involves some tasks that must be executed online-with the embedded computational power only. However, these tasks are generally combinatory; their computation is long and requires a lot of memory space. Entirely executing them online thus compromises the system's reactivity. But entirely executing them offline, by anticipating every possible situation, can lead to a result too large to be embedded. A tradeoff can be provided by knowledge compilation techniques, which shift as much as possible of the computational effort before the system's launching. These techniques consists in a translation of a problem into some language, obtaining a compiled form of the problem, which is both easy to solve and as compact as possible. The translation step can be very long, but it is only executed once, and offline. There are numerous target compilation languages, among which the language of binary decision diagrams (BDDs), which have been successfully used in various domains of artificial intelligence, such as model-checking, configuration, or planning. The objective of the thesis was to study how knowledge compilation could be applied to the control of autonomous systems. We focused on realistic planning problems, which often involve variables with continuous domains or large enumerated domains (such as time or memory space). We oriented our work towards the search for target compilation languages expressive enough to represent such problems

Abstract Compiling Propositional Weighted Bases

In this paper, we investigate the extent to which knowledge compilation can be used to improve model checking and inference from propositional weighted bases. We first focus on the compilability issue for both problems, deriving mainly non-compilability results in the case preferences are subject to change. Then, we present a general notion of ¤-normal weighted base that is parametrized by a tractable class ¤ for the clausal entailment problem. We show how every weighted base can be turned (“compiled”) into a query-equivalent ¤-normal base whenever ¤ is a complete class for propositional logic. Both negative and positive results are presented. On the one hand, complexity results are identified, showing that the inference problem from a ¤-normal weighted base is as difficult as in the general case, when the prime implicates, Horn cover or renamable Horn cover classes are targeted. On the other hand, we show that both the model checking and the (clausal) inference problem become tractable whenever ¥§¦¨¦� ©-normal bases are considered. Moreover, we show that the set of all preferred models of a ¥�¦¨¦� ©-normal weighted base can be computed in time polynomial in the output size, and as a consequence, model checking is also tractable for such bases. Finally, we sketch how our results can be used in model–based diagnosis in order to compute the most likely diagnoses of a system