arXiv subjects

Andreas Jakoby

Publications and source records attributed to Andreas Jakoby.

6 recordsLinked to original sources

arXiv2026

The 2D Ray Tracing Problem using ABCD Lenses and Mirrors is Turing Complete

We establish that the two-dimensional ray tracing problem with thin lenses and plane mirrors is Turing-complete, thereby resolving an open question posed by Reif et al. in 1994 as to whether three-dimensional space is necessary for computational universality in optical systems. To this end, we consider the standard approximation of reflection and refraction, namely the ABCD model for paraxial optics, which describes ray propagation through lenses (refraction) via a 2 x 2 matrix, combined with the geometric reflection model for plane mirrors. In the absence of mirrors, two-dimensional ray tracing using any combination of lenses in this ABCD matrix model can be described by a single 2 x 2 matrix-vector product, where the matrix has real entries and determinant 1. Conversely, we show that any such matrix with determinant 1 can be represented as a composition of exactly three appropriately spaced thin lenses. When mirrors are combined with lenses, the ray tracing problem can be described by a flowchart using only two variables, which establishes Turing computability for rational-valued inputs, spaces and matrix entries. Building on this observation, we present a construction of ray tracing that simulates a reversible Turing machine. We begin with a restricted version of the reversible flowchart problem, in which only two variables and certain linear functions are permitted. We prove that this restricted variant is Turing-complete. We then show that such a flowchart admits a geometric realization using lenses and mirrors in our model, thereby establishing the main result: Turing-completeness of the two-dimensional ray tracing problem with ABCD-model lenses and mirrors.

cs.CC↗

arXiv2026

Overview of PAN 2026: Voight-Kampff Generative AI Detection, Text Watermarking, Multi-Author Writing Style Analysis, Generative Plagiarism Detection, and Reasoning Trajectory Detection

The goal of the PAN workshop is to advance computational stylometry and text forensics via objective and reproducible evaluation. In 2026, we run the following five tasks: (1) Voight-Kampff Generative AI Detection, particularly in mixed and obfuscated authorship scenarios, (2) Text Watermarking, a new task that aims to find new and benchmark the robustness of existing text watermarking schemes, (3) Multi-author Writing Style Analysis, a continued task that aims to find positions of authorship change, (4) Generative Plagiarism Detection, a continued task that targets source retrieval and text alignment between generated text and source documents, and (5) Reasoning Trajectory Detection, a new task that deals with source detection and safety detection of LLM-generated or human-written reasoning trajectories. As in previous years, PAN invites software submissions as easy-to-reproduce Docker containers for most of the tasks. Since PAN 2012, more than 1,100 submissions have been made this way via the TIRA experimentation platform.

cs.CL↗

arXiv2025

How Pinball Wizards Simulate a Turing Machine

We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls, parabolic walls, moving plane walls, and bumpers that cause acceleration or deceleration. Given the initial position and velocity of the pinball, the task is to decide whether it will hit a specified target point. By simulating a two-stack pushdown automaton, we show that the problem is Turing-complete -- even in two-dimensional space. In our construction, each step of the automaton corresponds to a constant number of reflections. Thus, deciding the Pinball Wizard problem is at least as hard as the Halting problem. Furthermore, our construction allows bumpers to be replaced with moving walls. In this case, even a ball moving at constant speed -- a so-called ray particle -- can be used, demonstrating that the Ray Particle Tracing problem is also Turing-complete.

cs.CC↗

arXiv2017

Critical Graphs for Minimum Vertex Cover

In the context of the chromatic-number problem, a critical graph is an instance where the deletion of any element would decrease the graph's chromatic number. Such instances have shown to be interesting objects of study for deepen the understanding of the optimization problem. This work introduces critical graphs in context of Minimum Vertex Cover. We demonstrate their potential for the generation of larger graphs with hidden a priori known solutions. Firstly, we propose a parametrized graph-generation process which preserves the knowledge of the minimum cover. Secondly, we conduct a systematic search for small critical graphs. Thirdly, we illustrate the applicability for benchmarking purposes by reporting on a series of experiments using the state-of-the-art heuristic solver NuMVC.

cs.DM↗

arXiv2016

Cyclone Codes

We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The number of data symbols is chosen according to the Robust Soliton distribution. XOR and cyclic shift operations establish a unitary commutative ring if data symbols have a length of $p-1$ bits, for some prime number $p$. We consider the graph given by code symbols combining two data symbols. If $n/2$ such random pairs are given for $n$ data symbols, then a giant component appears, which can be resolved in linear time. We can extend Cyclone codes to data symbols of arbitrary even length, provided the Goldbach conjecture holds. Applying results for this giant component, it follows that Cyclone codes have the same encoding and decoding time complexity as LT codes, while the overhead is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes significantly decreases the overhead of extra coding symbols.

cs.IT↗

arXiv2006

Using quantum oblivious transfer to cheat sensitive quantum bit commitment

It is well known that unconditionally secure bit commitment is impossible even in the quantum world. In this paper a weak variant of quantum bit commitment, introduced independently by Aharonov et al. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] is investigated. In this variant, the parties require some nonzero probability of detecting a cheating, i.e. if Bob, who commits a bit b to Alice, changes his mind during the revealing phase then Alice detects the cheating with a positive probability (we call this property binding); and if Alice gains information about the committed bit before the revealing phase then Bob discovers this with positive probability (sealing). In our paper we give quantum bit commitment scheme that is simultaneously binding and sealing and we show that if a cheating gives epsilon advantage to a malicious Alice then Bob can detect the cheating with a probability Omega(epsilon^2). If Bob cheats then Alice's probability of detecting the cheating is greater than some fixed constant lambda>0. This improves the probabilities of cheating detections shown by Hardy and Kent and the scheme by Aharonov et al. who presented a protocol that is either binding or sealing, but not simultaneously both. To construct a cheat sensitive quantum bit commitment scheme we use a protocol for a weak quantum one-out-of-two oblivious transfer.

quant-ph↗