Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Abstract

dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

“…The computational complexity of reasoning in ADFs is summarised in Table 2. The results were shown by Brewka et al (2013), Strass and Wallner (2014) and Wallner (2014 …”

“…One way of arriving at adequate encodings for these decision problems is by making use of a characterisation of grounded interpretations given by Strass and Wallner (2014), for the statement of which we make use of the following definition: The above mentioned characterisation of grounded interpretations is expressed in the following proposition by Strass and Wallner (2014) …”

“…the work by Dunne & Bench-Capon, 2002). For ADFs, the complexity of many of the main reasoning tasks with respect to the generalised semantics jump up one level of the polynomial hierarchy (as has been shown by Strass & Wallner, 2014;Wallner, 2014), resulting in some of the reasoning tasks even being on the third level of the polynomial hierarchy. (2) we expanded all proofs, and (3) we present here complexity sensitive encodings also for the grounded and stable semantics.…”

Enhanced hybrid method of divide-and-conquer and RBF neural networks for function approximation of complex problems

“…Other data complexity factors such as noise, atypical patterns, overlap, and bad data distribution usually weaken the quality of the training process, too [5]. The curse of dimensionality problem increases the computational complexity and memory requirements, in some cases exponentially [1,2]. Due to the increased number of input data variables, the number of executing parameters usually increases exponentially.…”

“…Developing multivariate models for industrial or medical applications produces a computational complexity problem [1,2]. The complexity of the input data affects the quality of the neural network training process.…”