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The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Contemporary large language models are powerful problem-solving tools, but they exhibit weaknesses in their reasoning abilities which ongoing research seeks to mitigate. We investigate graph coloring as a means of evaluating an LLM's…
In the paper where he first defined Communication Complexity, Yao asks: \emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \le k$, when given the…
We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this…
We define a metric on $\mathbb{F}_q^n$ using the linear complexity of finite sequences. We will then develop a coding theory for this metric. We will give a Singleton-like bound and we will give constructions of subspaces of…
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
As one of the three main pillars of fine-grained complexity theory, the 3SUM problem explains the hardness of many diverse polynomial-time problems via fine-grained reductions. Many of these reductions are either directly based on or…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…
In this paper, we consider the minimal doubly resolving set problem in Hamming graphs, hypercubes and folded hypercubes. We prove that the minimal doubly resolving set problem in hypercubes is equivalent to the coin weighing problem. Then…
This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
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…
Neural machine translation has achieved remarkable empirical performance over standard benchmark datasets, yet recent evidence suggests that the models can still fail easily dealing with substandard inputs such as misspelled words, To…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural…