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The Parameterized Complexity of Reasoning Problems

Final Report Summary - COMPLEX REASON (The Parameterized Complexity of Reasoning Problems)

Reasoning, to derive conclusions from facts, is a fundamental task in Artificial Intelligence that arises in a wide range of applications from Robotics to Expert Systems. Different applications require different forms of reasoning such as Nonmonotonic Reasoning (e.g. reasoning under the presence of default as- sumptions), Constraint-Based Reasoning(reasoning with forbidden configurations), and Bayesian Reasoning (reasoning with uncertain data). All these forms of reasoning give rise to computational problems that can be solved algorithmically.

Within the project we devised new efficient algorithms for reasoning problems and gained new theoretical insights into the question of what makes a reasoning problem hard, and what makes it easy. Our general approach was to study reasoning problems within the framework of Parameterized Complexity, a new and rapidly emerging field of Algorithms and Complexity. Parameterized Complexity takes structural aspects of problem instances into account which are most significant for empirically observed problem hardness. Most of the considered reasoning problems are intractable in general, but the real-world context of their origin provides structural information that can be made accessible to algorithms in form of parameters. This makes Parameterized Complexity an ideal setting for the analysis and efficient solution of these problems that we want to explore.

This general approach showed to be very useful within the many case studies we carried out on specific hard reasoning problems arising in Planning, Constraint Satisfaction, Satisfiability, Argumentation, Answer-Set Programming, Combinatorial Optimisation, Abductive Reasoning, Model Counting, and Probabilistic Network Structure Learning. Our results and findings established that Parameterized Complexity provides the means for redrawing the complexity landscape of important reasoning problems. By utilizing the additional power of fixed-parameter tractability over polynomial-time tractability we could often break through barriers of classical complexity.

We complemented our technical work by organising workshops and symposia to foster the connections between relevant research communities and to further disseminate our results and findings.