Speeding up the constraint-based method in difference logic

"The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-40970-2_18"Over the years the constraint-based method has been successfully applied to a wide range of problems in program analysis, from invariant generation to termination and non-termination proving. Quite often the semantics of the program under study as well as the properties to be generated belong to difference logic, i.e., the fragment of linear arithmetic where atoms are inequalities of the form u v = k. However, so far constraint-based techniques have not exploited this fact: in general, Farkas’ Lemma is used to produce the constraints over template unknowns, which leads to non-linear SMT problems. Based on classical results of graph theory, in this paper we propose new encodings for generating these constraints when program semantics and templates belong to difference logic. Thanks to this approach, instead of a heavyweight non-linear arithmetic solver, a much cheaper SMT solver for difference logic or linear integer arithmetic can be employed for solving the resulting constraints. We present encouraging experimental results that show the high impact of the proposed techniques on the performance of the VeryMax verification systemPeer ReviewedPostprint (author's final draft

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Improving the Efficiency of Reasoning Through Structure-Based Reformulation

Abstract. We investigate the possibility of improving the efficiency of reasoning through structure-based partitioning of logical theories, combined with partitionbased logical reasoning strategies. To this end, we provide algorithms for reasoning with partitions of axioms in first-order and propositional logic. We analyze the computational benefit of our algorithms and detect those parameters of a partitioning that influence the efficiency of computation. These parameters are the number of symbols shared by a pair of partitions, the size of each partition, and the topology of the partitioning. Finally, we provide a greedy algorithm that automatically reformulates a given theory into partitions, exploiting the parameters that influence the efficiency of computation.

On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

Multi-robot grasp planning for sequential assembly operations

This paper addresses the problem of finding robot configurations to grasp assembly parts during a sequence of collaborative assembly operations. We formulate the search for such configurations as a constraint satisfaction problem (CSP).Collision constraints in an operation and transfer constraints between operations determine the sets of feasible robot configurations. We show that solving the connected constraint graph with off-the-shelf CSP algorithms can quickly become infeasible even fora few sequential assembly operations. We present an algorithm which, through the assumption of feasible regrasps, divides the CSP into independent smaller problems that can be solved exponentially faster. The algorithm then uses local search techniques to improve this solution by removing a gradually increasing number of regrasps from the plan. The algorithm enables the user to stop the planner anytime and use the current best plan if the cost of removing regrasps from the plan exceeds the cost of executing those regrasps. We present simulation experiments to compare our algorithm’s performance toa naive algorithm which directly solves the connected constraint graph. We also present a physical robot system which uses the output of our planner to grasp and bring parts together in assembly configurations

Developing serious games for cultural heritage: a state-of-the-art review

Although the widespread use of gaming for leisure purposes has been well documented, the use of games to support cultural heritage purposes, such as historical teaching and learning, or for enhancing museum visits, has been less well considered. The state-of-the-art in serious game technology is identical to that of the state-of-the-art in entertainment games technology. As a result, the field of serious heritage games concerns itself with recent advances in computer games, real-time computer graphics, virtual and augmented reality and artificial intelligence. On the other hand, the main strengths of serious gaming applications may be generalised as being in the areas of communication, visual expression of information, collaboration mechanisms, interactivity and entertainment. In this report, we will focus on the state-of-the-art with respect to the theories, methods and technologies used in serious heritage games. We provide an overview of existing literature of relevance to the domain, discuss the strengths and weaknesses of the described methods and point out unsolved problems and challenges. In addition, several case studies illustrating the application of methods and technologies used in cultural heritage are presented

Data consistency: toward a terminological clarification

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21413-9_15Consistency is an inconsistency are ubiquitous term in data engineering. Its relevance to quality is obvious, since consistency is a commonplace dimension of data quality. However, connotations are vague or ambiguous. In this paper, we address semantic consistency, transaction consistency, replication consistency, eventual consistency and the new notion of partial consistency in databases. We characterize their distinguishing properties, and also address their differences, interactions and interdependencies. Partial consistency is an entry door to living with inconsistency, which is an ineludible necessity in the age of big data.Decker and F.D. Muñoz—supported by the Spanish MINECO grant TIN 2012-37719-C03-01.Decker, H.; Muñoz Escoí, FD.; Misra, S. (2015). Data consistency: toward a terminological clarification. 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