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Ronald de Haan

Publications and source records attributed to Ronald de Haan.

At least 19 recordsLinked to original sources
arXiv2026

Color Structures and the Monotone Satisfiability Problem with Bounded Variable Occurrence

We study \textsc{Monotone 3-Sat-$(\leq k,1)$}, a restricted variant of the \textsc{Satisfiability} problem where clauses consist of three variables and are monotone (every clause contains either only unnegated or only negated variables) with up to $k$ positive and exactly one negative occurrence per variable in the formula. We resolve a challenge posed by Darmann and Döcker (On simplified NP-complete variants of \textsc{Monotone} 3-\textsc{Sat}, Discrete Applied Mathematics 292:45--58, 2021) by proving that for~$k\in \{3,4\}$, the problem is trivial in the sense that every instance satisfying the given restrictions is satisfiable. This result closes the remaining gap in a dichotomy theorem: Triviality for $k\in \{1,2\}$ follows by a result by Tovey (A simplified NP-complete satisfiability problem, Discrete Applied Mathematics 8(1):85--89, 1984), while NP-completeness for~$k\geq 5$ was shown by Darmann and Döcker. To obtain our result, we introduce the notion of \emph{color structures} and show that a satisfying assignment can always be constructed in $\mathcal{O}(n \cdot m)$ time, where $n$ and $m$ denote the number of negative and positive clauses of the input formula, respectively.

cs.CC↗
arXiv2025

Apportionment with Weighted Seats

Apportionment is the task of assigning resources to entities with different entitlements in a fair manner, and specifically a manner that is as proportional as possible. The best-known application is the assignment of parliamentary seats to political parties based on their share in the popular vote. Here we enrich the standard model of apportionment by associating each seat with a weight representing the (objective) value of that seat. A seat's weight reflects the fact that different seats might come with different roles, such as chair or treasurer. We define several apportionment methods and natural fairness requirements for this new setting, and we study the extent to which our methods satisfy these requirements. Our findings show that full fairness is harder to achieve than in the standard apportionment setting. Yet, for several natural relaxations of those requirements we can achieve stronger results than in the more expressive model of fair division with entitlements, where the values of objects are subjective.

cs.GT↗
arXiv2023

Shortlisting Rules and Incentives in an End-to-End Model for Participatory Budgeting

We introduce an end-to-end model of participatory budgeting grounded in social choice theory. This model accounts for both the first stage, in which participants propose projects to be shortlisted, and the second stage, in which they vote on which of the shortlisted projects should be funded. We introduce several shortlisting rules for the first stage and we analyse them in both normative and algorithmic terms. Our main focus is on the incentives of participants to engage in strategic behaviour, especially in the first stage, in which they need to reason about how their proposals will impact the range of strategies available to everyone in the second stage.

cs.GT↗
arXiv2023

A Belief Model for Conflicting and Uncertain Evidence -- Connecting Dempster-Shafer Theory and the Topology of Evidence

One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent, incomplete, or uncertain, making the problem of evidence fusion highly non-trivial. In this paper, we propose a new model for measuring degrees of beliefs based on possibly inconsistent, incomplete, and uncertain evidence, by combining tools from Dempster-Shafer Theory and Topological Models of Evidence. Our belief model is more general than the aforementioned approaches in two important ways: (1) it can reproduce them when appropriate constraints are imposed, and, more notably, (2) it is flexible enough to compute beliefs according to various standards that represent agents' evidential demands. The latter novelty allows the users of our model to employ it to compute an agent's (possibly) distinct degrees of belief, based on the same evidence, in situations when, e.g, the agent prioritizes avoiding false negatives and when it prioritizes avoiding false positives. Finally, we show that computing degrees of belief with this model is #P-complete in general.

cs.AI↗
arXiv2022

Viable Algorithmic Options for Creating and Adapting Emergent Software Systems

Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in reliable systems and scales reasonably in required memory and runtime to non-trivial systems. In this paper, we apply computational complexity analysis to evaluate algorithmic options for the reliable creation and adaptation of emergent software systems relative to several popular types of exact and approximate efficient solvability. We show that neither problem is solvable for all inputs when no restrictions are placed on software system structure. This intractability continues to hold relative to all examined types of efficient exact and approximate solvability when software systems are restricted to run (and hence can be verified against system requirements) in polynomial time. Moreover, both of our problems when so restricted remain intractable under a variety of additional restrictions on software system structure, both individually and in many combinations. That being said, we also give sets of additional restrictions that do yield tractability for both problems, as well as circumstantial evidence that emergent software system adaptation is computationally easier than emergent software system creation.

cs.SE↗
arXiv2021

Egalitarian Judgment Aggregation

Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation -- a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.

cs.AI↗
arXiv2020

On the Computational Complexity of Model Checking for Dynamic Epistemic Logic with S5 Models

Dynamic epistemic logic (DEL) is a logical framework for representing and reasoning about knowledge change for multiple agents. An important computational task in this framework is the model checking problem, which has been shown to be PSPACE-hard even for S5 models and two agents---in the presence of other features, such as multi-pointed models. We answer open questions in the literature about the complexity of this problem in more restricted settings. We provide a detailed complexity analysis of the model checking problem for DEL, where we consider various combinations of restrictions, such as the number of agents, whether the models are single-pointed or multi-pointed, and whether postconditions are allowed in the updates. In particular, we show that the problem is already PSPACE-hard in (1) the case of one agent, multi-pointed S5 models, and no postconditions, and (2) the case of two agents, only single-pointed S5 models, and no postconditions. In addition, we study the setting where only semi-private announcements are allowed as updates. We show that for this case the problem is already PSPACE-hard when restricted to two agents and three propositional variables. The results that we obtain in this paper help outline the exact boundaries of the restricted settings for which the model checking problem for DEL is computationally tractable.

cs.CC↗
arXiv2020

Characterizing Polynomial Ramsey Quantifiers

Ramsey quantifiers are a natural object of study not only for logic and computer science, but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey quantifiers are either polynomial-time computable or NP-hard, and whether we can give a natural characterization of the polynomial-time computable quantifiers. In this paper, we first show that there exist intermediate Ramsey quantifiers and then we prove a dichotomy result for a large and natural class of Ramsey quantifiers, based on a reasonable and widely-believed complexity assumption. We show that the polynomial-time computable quantifiers in this class are exactly the constant-log-bounded Ramsey quantifiers.

cs.LO↗
arXiv2019

Decentralization in Open Quorum Systems

Decentralisation is one of the promises introduced by blockchain technologies: fair and secure interaction amongst peers with no dominant positions, single points of failure or censorship. Decentralisation, however, appears difficult to be formally defined, possibly a continuum property of systems that can be more or less decentralised, or can tend to decentralisation in their lifetime. In this paper we focus on decentralisation in quorum-based approaches to open (permissionless) consensus as illustrated in influential protocols such as the Ripple and Stellar protocols. Drawing from game theory and computational complexity, we establish limiting results concerning the decentralisation vs. safety trade-off in Ripple and Stellar, and we propose a novel methodology to formalise and quantitatively analyse decentralisation in this type of blockchains.

cs.DC↗
arXiv2019

Expressing Linear Orders Requires Exponential-Size DNNFs

We show that any DNNF circuit that expresses the set of linear orders over a set of $n$ candidates must be of size $2^{Ω(n)}$. Moreover, we show that there exist DNNF circuits of size $2^{O(n)}$ expressing linear orders over $n$ candidates.

cs.CC↗
arXiv2018

A Parameterized Complexity View on Description Logic Reasoning

Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational problems for these logics have been studied for their computational complexity. However, essentially all complexity analyses of reasoning problems for description logics use the one-dimensional framework of classical complexity theory. The multi-dimensional framework of parameterized complexity theory is able to provide a much more detailed image of the complexity of reasoning problems. In this paper we argue that the framework of parameterized complexity has a lot to offer for the complexity analysis of description logic reasoning problems---when one takes a progressive and forward-looking view on parameterized complexity tools. We substantiate our argument by means of three case studies. The first case study is about the problem of concept satisfiability for the logic ALC with respect to nearly acyclic TBoxes. The second case study concerns concept satisfiability for ALC concepts parameterized by the number of occurrences of union operators and the number of occurrences of full existential quantification. The third case study offers a critical look at data complexity results from a parameterized complexity point of view. These three case studies are representative for the wide range of uses for parameterized complexity methods for description logic problems.

cs.LO↗
arXiv2018

Hunting for Tractable Languages for Judgment Aggregation

Judgment aggregation is a general framework for collective decision making that can be used to model many different settings. Due to its general nature, the worst case complexity of essentially all relevant problems in this framework is very high. However, these intractability results are mainly due to the fact that the language to represent the aggregation domain is overly expressive. We initiate an investigation of representation languages for judgment aggregation that strike a balance between (1) being limited enough to yield computational tractability results and (2) being expressive enough to model relevant applications. In particular, we consider the languages of Krom formulas, (definite) Horn formulas, and Boolean circuits in decomposable negation normal form (DNNF). We illustrate the use of the positive complexity results that we obtain for these languages with a concrete application: voting on how to spend a budget (i.e., participatory budgeting).

cs.AI↗
arXiv2017

Obtaining a Proportional Allocation by Deleting Items

We consider the following control problem on fair allocation of indivisible goods. Given a set $I$ of items and a set of agents, each having strict linear preference over the items, we ask for a minimum subset of the items whose deletion guarantees the existence of a proportional allocation in the remaining instance; we call this problem Proportionality by Item Deletion (PID). Our main result is a polynomial-time algorithm that solves PID for three agents. By contrast, we prove that PID is computationally intractable when the number of agents is unbounded, even if the number $k$ of item deletions allowed is small, since the problem turns out to be W[3]-hard with respect to the parameter $k$. Additionally, we provide some tight lower and upper bounds on the complexity of PID when regarded as a function of $|I|$ and $k$.

cs.MA↗
arXiv2016

Pareto Optimal Allocation under Uncertain Preferences

The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with uncertainty leads to a number of interesting questions including the following ones. How to compute an assignment with the highest probability of being Pareto optimal? What is the complexity of computing the probability that a given assignment is Pareto optimal? Does there exist an assignment that is Pareto optimal with probability one? We consider these problems under two natural uncertainty models: (1) the lottery model in which each agent has an independent probability distribution over linear orders and (2) the joint probability model that involves a joint probability distribution over preference profiles. For both of the models, we present a number of algorithmic and complexity results.

cs.GT↗
arXiv2016

Complexity Results for Manipulation, Bribery and Control of the Kemeny Procedure in Judgment Aggregation

We study the computational complexity of several scenarios of strategic behavior for the Kemeny procedure in the setting of judgment aggregation. In particular, we investigate (1) manipulation, where an individual aims to achieve a better group outcome by reporting an insincere individual opinion, (2) bribery, where an external agent aims to achieve an outcome with certain properties by bribing a number of individuals, and (3) control (by adding or deleting issues), where an external agent aims to achieve an outcome with certain properties by influencing the set of issues in the judgment aggregation situation. We show that determining whether these types of strategic behavior are possible (and if so, computing a policy for successful strategic behavior) is complete for the second level of the Polynomial Hierarchy. That is, we show that these problems are $Σ^p_2$-complete.

cs.AI↗
arXiv2016

Stable Matching with Uncertain Linear Preferences

We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each agent, there is a probability distribution over linear preferences, (2) compact indifference model --- for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model --- there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

cs.GT↗
arXiv2016

The Parameterized Complexity of Reasoning Problems Beyond NP

Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. Recent research shows that in certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. In this paper we develop a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not. This framework is based on several new parameterized complexity classes. As a running example, we use the framework to classify the complexity of the consistency problem for disjunctive answer set programming, with respect to various natural parameters. We underpin the robustness of our theory by providing a characterization of the new complexity classes in terms of weighted QBF satisfiability, alternating Turing machines, and first-order model checking. In addition, we provide a compendium of parameterized problems that are complete for the new complexity classes, including problems related to Knowledge Representation and Reasoning, Logic, and Combinatorics.

cs.CC↗