Finite domain constraint programming systems

Tutorial at CP'2002, Principles and Practice of Constraint Programming. Powerpoint slides.</p

A geometric constraint over k-dimensional objects and shapes subject to business rules

This report presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering. The business rules allow to express a great variety of packing and placement constraints, while admitting efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem

Adding Logical Operators to Tree Pattern Queries on Graph-Structured Data

As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery and SPARQL, support logical expressions using logical-AND/OR/NOT operators to define structural constraints of tree patterns. In this paper, (1) we propose generalized tree pattern queries (GTPQs) over graph-structured data, which fully support propositional logic of structural constraints. (2) We make a thorough study of fundamental problems including satisfiability, containment and minimization, and analyze the computational complexity and the decision procedures of these problems. (3) We propose a compact graph representation of intermediate results and a pruning approach to reduce the size of intermediate results and the number of join operations -- two factors that often impair the efficiency of traditional algorithms for evaluating tree pattern queries. (4) We present an efficient algorithm for evaluating GTPQs using 3-hop as the underlying reachability index. (5) Experiments on both real-life and synthetic data sets demonstrate the effectiveness and efficiency of our algorithm, from several times to orders of magnitude faster than state-of-the-art algorithms in terms of evaluation time, even for traditional tree pattern queries with only conjunctive operations.Comment: 16 page

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Interaction Grammars

Interaction Grammar (IG) is a grammatical formalism based on the notion of polarity. Polarities express the resource sensitivity of natural languages by modelling the distinction between saturated and unsaturated syntactic structures. Syntactic composition is represented as a chemical reaction guided by the saturation of polarities. It is expressed in a model-theoretic framework where grammars are constraint systems using the notion of tree description and parsing appears as a process of building tree description models satisfying criteria of saturation and minimality

On the Benefits of Non-Canonical Filtering in Publish/Subscribe Systems

Current matching approaches in pub/sub systems only allow conjunctive subscriptions. Arbitrary subscriptions have to be transformed into canonical expressions, e.g., DNFs, and need to be treated as several conjunctive subscriptions. This technique is known from database systems and allows us to apply more efficient filtering algorithms. Since pub/sub systems are the contrary to traditional database systems, it is questionable if filtering several canonical subscriptions is the most efficient and scalable way of dealing with arbitrary subscriptions. In this paper we show that our filtering approach supporting arbitrary Boolean subscriptions is more scalable and efficient than current matching algorithms requiring transformations of subscriptions into DNFs