Compilation for QCSP

We propose in this article a framework for compilation of quantified constraint satisfaction problems (QCSP). We establish the semantics of this formalism by an interpretation to a QCSP. We specify an algorithm to compile a QCSP embedded into a search algorithm and based on the inductive semantics of QCSP. We introduce an optimality property and demonstrate the optimality of the interpretation of the compiled QCSP.Comment: Proceedings of the 13th International Colloquium on Implementation of Constraint LOgic Programming Systems (CICLOPS 2013), Istanbul, Turkey, August 25, 201

Structurally Tractable Uncertain Data

Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query possibility, certainty, or probability: these problems are hard on arbitrary uncertain input instances. We thus ask whether we could restrict the structure of uncertain data so as to guarantee the tractability of exact query evaluation. We present our tractability results for tree and tree-like uncertain data, and a vision for probabilistic rule reasoning. We also study uncertainty about order, proposing a suitable representation, and study uncertain data conditioned by additional observations.Comment: 11 pages, 1 figure, 1 table. To appear in SIGMOD/PODS PhD Symposium 201

Compiling CSPs: A Complexity Map of (Non-Deterministic) Multivalued Decision Diagrams

International audienceConstraint Satisfaction Problems (CSPs) offer a powerful framework for representing a great variety of problems. The difficulty is that most of the requests associated with CSPs are NP-hard. When these requests have to be addressed online, Multivalued Decision Diagrams (MDDs) have been proposed as a way to compile CSPs. In the present paper, we draw a compilation map of MDDs, in the spirit of the NNF compilation map, analyzing MDDs according to their succinctness and to their tractable transformations and queries. Deterministic ordered MDDs are a generalization of ordered binary decision diagrams to non-Boolean domains: unsurprisingly, they have similar capabilities. More interestingly, our study puts forward the interest of non-deterministic ordered MDDs: when restricted to Boolean domains, they capture OBDDs and DNFs as proper subsets and have performances close to those of DNNFs. The comparison to classical, deterministic MDDs shows that relaxing the determinism requirement leads to an increase in succinctness and allows more transformations to be satisfied in polynomial time (typically, the disjunctive ones). Experiments on random problems confirm the gain in succinctness

Preprints of Proceedings of GWAI-92

This is a preprint of the proceedings of the German Workshop on Artificial Intelligence (GWAI) 1992. The final version will appear in the Lecture Notes in Artificial Intelligence

The Language of Search

This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, and a search algorithm then defines a propositional language consisting of circuits that are generated across all possible executions of the algorithm. In particular, we show that several versions of exhaustive DPLL search correspond to such well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF. By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various languages of interest, and a new methodology whereby the power and limitations of search algorithms can be understood by looking up the tractability and succinctness of the corresponding propositional languages

Small Resolution Proofs for QBF using Dependency Treewidth

In spite of the close connection between the evaluation of quantified Boolean formulas (QBF) and propositional satisfiability (SAT), tools and techniques which exploit structural properties of SAT instances are known to fail for QBF. This is especially true for the structural parameter treewidth, which has allowed the design of successful algorithms for SAT but cannot be straightforwardly applied to QBF since it does not take into account the interdependencies between quantified variables. In this work we introduce and develop dependency treewidth, a new structural parameter based on treewidth which allows the efficient solution of QBF instances. Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF. We augment our results by developing algorithms for computing the decompositions that are required to use the parameter

Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog

We propose a novel, type-elimination-based method for reasoning in the description logic SHIQbs including DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst case optimal w.r.t. combined and data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for publication in Logical Methods in Computer Scienc

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

A Quantitative Flavour of Robust Reachability

Many software analysis techniques attempt to determine whether bugs are reachable, but for security purpose this is only part of the story as it does not indicate whether the bugs found could be easily triggered by an attacker. The recently introduced notion of robust reachability aims at filling this gap by distinguishing the input controlled by the attacker from those that are not. Yet, this qualitative notion may be too strong in practice, leaving apart bugs which are mostly but not fully replicable. We aim here at proposing a quantitative version of robust reachability, more flexible and still amenable to automation. We propose quantitative robustness, a metric expressing how easily an attacker can trigger a bug while taking into account that he can only influence part of the program input, together with a dedicated quantitative symbolic execution technique (QRSE). Interestingly, QRSE relies on a variant of model counting (namely, functional E-MAJSAT) unseen so far in formal verification, but which has been studied in AI domains such as Bayesian network, knowledge representation and probabilistic planning. Yet, the existing solving methods from these fields turn out to be unsatisfactory for formal verification purpose, leading us to propose a novel parametric method. These results have been implemented and evaluated over two security-relevant case studies, allowing to demonstrate the feasibility and relevance of our ideas