Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

The Parametric Complexity of Lossy Counter Machines

The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove F_d-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < omega. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision

Visual slam in dynamic environments

El problema de localización y construcción visual simultánea de mapas (visual SLAM por sus siglas en inglés Simultaneous Localization and Mapping) consiste en localizar una cámara en un mapa que se construye de manera online. Esta tecnología permite la localización de robots en entornos desconocidos y la creación de un mapa de la zona con los sensores que lleva incorporados, es decir, sin contar con ninguna infraestructura externa. A diferencia de los enfoques de odometría en los cuales el movimiento incremental es integrado en el tiempo, un mapa permite que el sensor se localice continuamente en el mismo entorno sin acumular deriva.Asumir que la escena observada es estática es común en los algoritmos de SLAM visual. Aunque la suposición estática es válida para algunas aplicaciones, limita su utilidad en escenas concurridas del mundo real para la conducción autónoma, los robots de servicio o realidad aumentada y virtual entre otros. La detección y el estudio de objetos dinámicos es un requisito para estimar con precisión la posición del sensor y construir mapas estables, útiles para aplicaciones robóticas que operan a largo plazo.Las contribuciones principales de esta tesis son tres: 1. Somos capaces de detectar objetos dinámicos con la ayuda del uso de la segmentación semántica proveniente del aprendizaje profundo y el uso de enfoques de geometría multivisión. Esto nos permite lograr una precisión en la estimación de la trayectoria de la cámara en escenas altamente dinámicas comparable a la que se logra en entornos estáticos, así como construir mapas en 3D que contienen sólo la estructura del entorno estático y estable. 2. Logramos alucinar con imágenes realistas la estructura estática de la escena detrás de los objetos dinámicos. Esto nos permite ofrecer mapas completos con una representación plausible de la escena sin discontinuidades o vacíos ocasionados por las oclusiones de los objetos dinámicos. El reconocimiento visual de lugares también se ve impulsado por estos avances en el procesamiento de imágenes. 3. Desarrollamos un marco conjunto tanto para resolver el problema de SLAM como el seguimiento de múltiples objetos con el fin de obtener un mapa espacio-temporal con información de la trayectoria del sensor y de los alrededores. La comprensión de los objetos dinámicos circundantes es de crucial importancia para los nuevos requisitos de las aplicaciones emergentes de realidad aumentada/virtual o de la navegación autónoma. Estas tres contribuciones hacen avanzar el estado del arte en SLAM visual. Como un producto secundario de nuestra investigación y para el beneficio de la comunidad científica, hemos liberado el código que implementa las soluciones propuestas.<br /

Incompressible Lagrangian fluid flow with thermal coupling

In this monograph is presented a method for the solution of an incompressible viscous fluid flow with heat transfer and solidification usin a fully Lagrangian description on the motion. The originality of this method consists in assembling various concepts and techniques which appear naturally due to the Lagrangian formulation.Postprint (published version

IST Austria Thesis

The design and verification of concurrent systems remains an open challenge due to the non-determinism that arises from the inter-process communication. In particular, concurrent programs are notoriously difficult both to be written correctly and to be analyzed formally, as complex thread interaction has to be accounted for. The difficulties are further exacerbated when concurrent programs get executed on modern-day hardware, which contains various buffering and caching mechanisms for efficiency reasons. This causes further subtle non-determinism, which can often produce very unintuitive behavior of the concurrent programs. Model checking is at the forefront of tackling the verification problem, where the task is to decide, given as input a concurrent system and a desired property, whether the system satisfies the property. The inherent state-space explosion problem in model checking of concurrent systems causes naïve explicit methods not to scale, thus more inventive methods are required. One such method is stateless model checking (SMC), which explores in memory-efficient manner the program executions rather than the states of the program. State-of-the-art SMC is typically coupled with partial order reduction (POR) techniques, which argue that certain executions provably produce identical system behavior, thus limiting the amount of executions one needs to explore in order to cover all possible behaviors. Another method to tackle the state-space explosion is symbolic model checking, where the considered techniques operate on a succinct implicit representation of the input system rather than explicitly accessing the system. In this thesis we present new techniques for verification of concurrent systems. We present several novel POR methods for SMC of concurrent programs under various models of semantics, some of which account for write-buffering mechanisms. Additionally, we present novel algorithms for symbolic model checking of finite-state concurrent systems, where the desired property of the systems is to ensure a formally defined notion of fairness

Single View Modeling and View Synthesis

This thesis develops new algorithms to produce 3D content from a single camera. Today, amateurs can use hand-held camcorders to capture and display the 3D world in 2D, using mature technologies. However, there is always a strong desire to record and re-explore the 3D world in 3D. To achieve this goal, current approaches usually make use of a camera array, which suffers from tedious setup and calibration processes, as well as lack of portability, limiting its application to lab experiments. In this thesis, I try to produce the 3D contents using a single camera, making it as simple as shooting pictures. It requires a new front end capturing device rather than a regular camcorder, as well as more sophisticated algorithms. First, in order to capture the highly detailed object surfaces, I designed and developed a depth camera based on a novel technique called light fall-off stereo (LFS). The LFS depth camera outputs color+depth image sequences and achieves 30 fps, which is necessary for capturing dynamic scenes. Based on the output color+depth images, I developed a new approach that builds 3D models of dynamic and deformable objects. While the camera can only capture part of a whole object at any instance, partial surfaces are assembled together to form a complete 3D model by a novel warping algorithm. Inspired by the success of single view 3D modeling, I extended my exploration into 2D-3D video conversion that does not utilize a depth camera. I developed a semi-automatic system that converts monocular videos into stereoscopic videos, via view synthesis. It combines motion analysis with user interaction, aiming to transfer as much depth inferring work from the user to the computer. I developed two new methods that analyze the optical flow in order to provide additional qualitative depth constraints. The automatically extracted depth information is presented in the user interface to assist with user labeling work. In this thesis, I developed new algorithms to produce 3D contents from a single camera. Depending on the input data, my algorithm can build high fidelity 3D models for dynamic and deformable objects if depth maps are provided. Otherwise, it can turn the video clips into stereoscopic video

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...