The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a successful parameter. A well-known result by Chen in parameterized complexity is that QSAT when parameterized by the treewidth of the primal graph of the input formula together with the quantifier depth of the formula is fixed-parameter tractable. More precisely, the runtime of such an algorithm is polynomial in the formula size and exponential in the treewidth, where the exponential function in the treewidth is a tower, whose height is the quantifier depth. A natural question is whether one can significantly improve these results and decrease the tower while assuming the Exponential Time Hypothesis (ETH). In the last years, there has been a growing interest in the quest of establishing lower bounds under ETH, showing mostly problem-specific lower bounds up to the third level of the polynomial hierarchy. Still, an important question is to settle this as general as possible and to cover the whole polynomial hierarchy. In this work, we show lower bounds based on the ETH for arbitrary QBFs parameterized by treewidth (and quantifier depth). More formally, we establish lower bounds for QSAT and treewidth, namely, that under ETH there cannot be an algorithm that solves QSAT of quantifier depth i in runtime significantly better than i-fold exponential in the treewidth and polynomial in the input size. In doing so, we provide a versatile reduction technique to compress treewidth that encodes the essence of dynamic programming on arbitrary tree decompositions. Further, we describe a general methodology for a more fine-grained analysis of problems parameterized by treewidth that are at higher levels of the polynomial hierarchy.

We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of incrementally constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase and in the solving phase. Experimental results show that incremental QBF solving outperforms non-incremental QBF solving. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.

Backdoors are a powerful tool to obtain efficient algorithms for hard problems. Recently, two new notions of backdoors to planning were introduced. However, for one of the new notions (i.e., variable-deletion) only hardness results are known so far. In this work we improve the situation by defining a new type of variable-deletion backdoors based on the extended causal graph of a planning instance. For this notion of backdoors several fixed-parameter tractable algorithms are identified. Furthermore, we explore the capabilities of polynomial time preprocessing, i.e., we check whether there exists a polynomial kernel. Our results also show the close connection between planning and verification problems such as Vector Addition System with States (VASS).

Backdoors measure the distance to tractable fragments and have become an important tool to find fixed-parameter tractable (fpt) algorithms. Despite their success, backdoors have not been used for planning, a central problem in AI that has a high computational complexity. In this work, we introduce two notions of backdoors building upon the causal graph. We analyze the complexity of finding a small backdoor (detection) and using the backdoor to solve the problem (evaluation) in the light of planning with (un)bounded plan length/domain of the variables. For each setting we present either an fpt-result or rule out the existence thereof by showing parameterized intractability. In three cases we achieve the most desirable outcome: detection and evaluation are fpt.

Generalized CP-nets (GCP-nets) allow a succinct representation of preferences over multi-attribute domains. As a consequence of their succinct representation, many GCP-net related tasks are computationally hard. Even finding the more preferable of two outcomes is PSPACE-complete. In this work, we employ the framework of parameterized complexity to achieve two goals: First, we want to gain a deeper understanding of the complexity of GCP-nets. Second, we search for efficient fixed-parameter tractable algorithms.

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these systems suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra studied the complexity of dishonest behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. Furthermore, we explore the relations between several notions of nearly single-peakedness.

Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logic-based abduction, where knowledge is represented by propositional formulas. The computational complexity of this problem is highly intractable in many interesting settings. In this work we therefore present an extensive parameterized complexity analysis of abduction within various fragments of propositional logic together with (combinations of) natural parameters.