The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument. - The Center problem asks whether, given two extensions of distance k, whether there is a "center" extension that is a distance at most (k-1) from both given extensions. We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results covers several different semantics, including admissible, complete, preferred, semi-stable and stable semantics

Cliquewidth and knowledge compilation

In this paper we study the role of cliquewidth in succinct representation of Boolean functions. Our main statement is the following: Let Z be a Boolean circuit having cliquewidth k. Then there is another circuit Z * computing the same function as Z having treewidth at most 18k + 2 and which has at most 4|Z| gates where |Z| is the number of gates of Z. In this sense, cliquewidth is not more ‘powerful’ than treewidth for the purpose of representation of Boolean functions. We believe this is quite a surprising fact because it contrasts the situation with graphs where an upper bound on the treewidth implies an upper bound on the cliquewidth but not vice versa. We demonstrate the usefulness of the new theorem for knowledge compilation. In particular, we show that a circuit Z of cliquewidth k can be compiled into a Decomposable Negation Normal Form (dnnf) of size O(918k k 2|Z|) and the same runtime. To the best of our knowledge, this is the first result on efficient knowledge compilation parameterized by cliquewidth of a Boolean circuit