Related papers: Where are the hard manipulation problems?
Many electoral bribery, control, and manipulation problems (which we will refer to in general as "manipulative actions" problems) are NP-hard in the general case. It has recently been noted that many of these problems fall into polynomial…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver,…
We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply…
It is a well-known result that bilevel linear optimization is NP-hard. In many publications, reformulations as mixed-integer linear optimization problems are proposed, which suggests that the decision version of the problem belongs to NP.…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
In order to approximate the integral $I(f)=\int_a^b f(x) dx$, where $f$ is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n (n\geq 2)$ equally spaced points. These models arise from…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election's winner? We…
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
We study the query complexity of geodesically convex (g-convex) optimization on a manifold. To isolate the effect of that manifold's curvature, we primarily focus on hyperbolic spaces. In a variety of settings (smooth or not; strongly…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
A recent paper (van Rooij et al. 2024) claims to have proved that achieving human-like intelligence using learning from data is intractable in a complexity-theoretic sense. We point out that the proof relies on an unjustified assumption…
We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…