Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

Applications of Finite Model Theory: Optimisation Problems, Hybrid Modal Logics and Games.

There exists an interesting relationships between two seemingly distinct fields: logic from the field of Model Theory, which deals with the truth of statements about discrete structures; and Computational Complexity, which deals with the classification of problems by how much of a particular computer resource is required in order to compute a solution. This relationship is known as Descriptive Complexity and it is the primary application of the tools from Model Theory when they are restricted to the finite; this restriction is commonly called Finite Model Theory. In this thesis, we investigate the extension of the results of Descriptive Complexity from classes of decision problems to classes of optimisation problems. When dealing with decision problems the natural mapping from true and false in logic to yes and no instances of a problem is used but when dealing with optimisation problems, other features of a logic need to be used. We investigate what these features are and provide results in the form of logical frameworks that can be used for describing optimisation problems in particular classes, building on the existing research into this area. Another application of Finite Model Theory that this thesis investigates is the relative expressiveness of various fragments of an extension of modal logic called hybrid modal logic. This is achieved through taking the Ehrenfeucht-Fraïssé game from Model Theory and modifying it so that it can be applied to hybrid modal logic. Then, by developing winning strategies for the players in the game, results are obtained that show strict hierarchies of expressiveness for fragments of hybrid modal logic that are generated by varying the quantifier depth and the number of proposition and nominal symbols available

On the landscape of combinatorial optimization problems

This paper carries out a comparison of the fitness landscape for four classic optimization problems: Max-Sat, graph-coloring, traveling salesman, and quadratic assignment. We have focused on two types of properties, local average properties of the landscape, and properties of the local optima. For the local optima we give a fairly comprehensive description of the properties, including the expected time to reach a local optimum, the number of local optima at different cost levels, the distance between optima, and the expected probability of reaching the optima. Principle component analysis is used to understand the correlations between the local optima. Most of the properties that we examine have not been studied previously, particularly those concerned with properties of the local optima. We compare and contrast the behavior of the four different problems. Although the problems are very different at the low level, many of the long-range properties exhibit a remarkable degree of similarity

Propagators and Violation Functions for Geometric and Workload Constraints Arising in Airspace Sectorisation

Airspace sectorisation provides a partition of a given airspace into sectors, subject to geometric constraints and workload constraints, so that some cost metric is minimised. We make a study of the constraints that arise in airspace sectorisation. For each constraint, we give an analysis of what algorithms and properties are required under systematic search and stochastic local search

On Improving Local Search for Unsatisfiability

Stochastic local search (SLS) has been an active field of research in the last few years, with new techniques and procedures being developed at an astonishing rate. SLS has been traditionally associated with satisfiability solving, that is, finding a solution for a given problem instance, as its intrinsic nature does not address unsatisfiable problems. Unsatisfiable instances were therefore commonly solved using backtrack search solvers. For this reason, in the late 90s Selman, Kautz and McAllester proposed a challenge to use local search instead to prove unsatisfiability. More recently, two SLS solvers - Ranger and Gunsat - have been developed, which are able to prove unsatisfiability albeit being SLS solvers. In this paper, we first compare Ranger with Gunsat and then propose to improve Ranger performance using some of Gunsat's techniques, namely unit propagation look-ahead and extended resolution

Deconstructing Reo

AbstractCoordination in Reo emerges from the composition of the behavioural constraints of the primitives, such as channels, in a component connector. Understanding and implementing Reo, however, has been challenging due to interaction of the channel metaphor, which is an inherently local notion, and the non-local nature of constraint propagation imposed by composition. In this paper, the channel metaphor takes a back seat, and we focus on the behavioural constraints imposed by the composition of primitives, and phrase the semantics of Reo as a constraint satisfaction problem. Not only does this provide a clear intensional description of the behaviour of Reo connectors in terms of synchronisation and data flow constraints, it also paves the way for new implementation techniques based on constraint propagation and satisfaction. In fact, decomposing Reo into constraints provides a new computational model for connectors, which we extend to model interaction with an unknown external world beyond what is currently possible in Reo