Finite-energy infinite clusters without anchored expansion

Hermon and Hutchcroft have recently proved the long-standing conjecture that in Bernoulli(p) bond percolation on any nonamenable transitive graph G, at any p > p_c(G), the probability that the cluster of the origin is finite but has a large volume n decays exponentially in n. A corollary is that all infinite clusters have anchored expansion almost surely. They have asked if these results could hold more generally, for any finite energy ergodic invariant percolation. We give a counterexample, an invariant percolation on the 4-regular tree.Comment: 9 pages, 1 figure. Small changes throughout. To appear in Bernoull

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Learning automata with help.

Analitzem i proposem diverses versions millorades d’algorismes existents d'aprenentatge d’autòmats finits deterministes. Les nostres millores pertanyen a la categoria d'aprenentatge amb ajuda, amb l'objectiu d'accelerar o influir en la qualitat del procés d'aprenentatge. Una part considerable del nostre treball es basa en un enfocament pràctic; per a cada algorisme que tractem, hi ha resultats comparatius obtinguts després de la implementació i posada a prova dels processos d'aprenentatge en conjunts d'autòmats generats aleatòriament. Després de fer un gran nombre d’experiments, presentem gràfics i dades numèriques amb els resultats comparats que hem obtingut. Estudiem algorismes pertanyents a dos models diferents d'aprenentatge: actiu i passiu. Un augment del nombre de símbols de sortida permet un nombre reduït de preguntes; una orientació al llarg del procés d'aprenentatge dóna una única resposta per a diverses preguntes; la millora de l'estructura d'aprenentatge permet una millor exploració de l'entorn d'aprenentatge. En el marc de l'aprenentatge actiu, un algorisme d'aprenentatge amb preguntes modificades i amb un etiquetatge útil no trivial és capaç d'aprendre autòmats sense contraexemples. Es revisen les preguntes de correcció definint-les com un tipus particular d'etiquetatge. Introduïm correccions minimals, maximals i a l'atzar. Un algorisme clàssic aprèn autòmats típics amb recorreguts aleatòries dins del marc d'aprenentatge passiu en línia. Per l'algorisme original, no podem estimar el nombre d'assaigs necessaris per aprendre completament un autòmat per alguns casos. Afegint transicions inverses al graf subjacent de l'autòmat, el recorregut aleatori actúa com un recorregut aleatori en un graf no dirigit. L'avantatge és que, per a aquests grafs, hi ha un límit superior polinòmic per al temps de cobertura. El nou algorisme és encara un algorisme eficient amb un límit superior polinòmic pel nombre d'errors per defecte i el nombre d'assaigs.Analizamos y proponemos varias versiones mejoradas de los algoritmos de aprendizaje existentes para autómatas finitos deterministas. Nuestras mejoras pertenecen a la categoría de aprendizaje com ayuda, con el objetivo de acelerar, o influir sobre la calidad del proceso de aprendizaje. Una parte considerable de nuestro trabajo se basa en un enfoque práctico; para cada algoritmo que se presenta, existen resultados comparativos obtenidos después de la implementación y puesta a prueba de los procesos de aprendizaje en conjuntos de autómatas generados aleatoriamente. Después de muchos experimentos, presentamos gráficos y datos numéricos con los resultados comparados que hemos obtenido . Estudiamos algoritmos pertenecientes a dos modelos diferentes de aprendizaje: activo y pasivo. Un aumento del número de símbolos de salida permite un número reducido de consultas; una orientación parcial a lo largo del camino de aprendizaje da los resultados de varias consultas como uno solo; la mejora de la estructura de aprendizaje permite una mejor exploración del entorno de aprendizaje. En el marco del aprendizaje activo, un algoritmo de aprendizaje com consulta modificada y dotado de un etiquetado de ayuda no trivial es capaz de aprender autómatas sin contraejemplos. Se revisan las consultas de corrección definiéndolas como tipos particulares de etiquetado. Introducimos correcciones minimales, maximales y al azar. Un algoritmo clásico aprende autómatas típicos de recorridos aleatorios en el marco del aprendizaje pasivo en línea. Para el algoritmo original, no podemos estimar el número de intentos necesarios para aprender completamente el autómata para algunos casos. Añadiendo transiciones inversas al grafo subyacente del autómata, el recorrido aleatorio actúa como un recorrido aleatorio en un grafo no dirigido. La ventaja es que, para estos grafos, existe un límite superior polinómico para el tiempo de cobertura. El nuevo algoritmo es todavía un algoritmo eficiente con límites superiores polinómicos para el número de errores por defecto y el número de intentos.We analyze and propose several enhanced versions of existing learning algorithms for deterministic finite automata. Our improvements belong to the category of helpful learning, aiming to speed up, or to influence the quality of the learning process. A considerable part of our work is based on a practical approach; for each algorithm we discuss, there are comparative results, obtained after the implementation and testing of the learning processes on sets of randomly generated automata. After extended experiments, we present graphs and numerical data with the comparative results that we obtained. We study algorithms belonging to two different learning models: active and passive. An increased number of output symbols allows a reduced number of queries; some partial guidance along the learning path gives the results of several queries as a single one; enhancing the learning structure permits a better exploration of the learning environment. In the active learning framework, a modified query learning algorithm benefiting by a nontrivial helpful labeling is able to learn automata without counterexamples. We review the correction queries defining them as particular types of labeling. We introduce minimal corrections, maximal corrections, and random corrections. A classic algorithm learns typical automata from random walks in the online passive learning framework. For the original algorithm, we cannot estimate the number of trials needed to learn completely a target automaton for some cases. Adding inverse transitions to the underlying graph of the target automaton, the random walk acts as a random walk on an undirected graph. The advantage is, that for such graphs, there exists a polynomial upper bound for the cover time. The new algorithm is still an efficient algorithm with a polynomial upper bound for the number of default mistakes and the number of trials

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Parallel cryptanalysis

Most of today’s cryptographic primitives are based on computations that are hard to perform for a potential attacker but easy to perform for somebody who is in possession of some secret information, the key, that opens a back door in these hard computations and allows them to be solved in a small amount of time. To estimate the strength of a cryptographic primitive it is important to know how hard it is to perform the computation without knowledge of the secret back door and to get an understanding of how much money or time the attacker has to spend. Usually a cryptographic primitive allows the cryptographer to choose parameters that make an attack harder at the cost of making the computations using the secret key harder as well. Therefore designing a cryptographic primitive imposes the dilemma of choosing the parameters strong enough to resist an attack up to a certain cost while choosing them small enough to allow usage of the primitive in the real world, e.g. on small computing devices like smart phones. This thesis investigates three different attacks on particular cryptographic systems: Wagner’s generalized birthday attack is applied to the compression function of the hash function FSB. Pollard’s rho algorithm is used for attacking Certicom’s ECC Challenge ECC2K-130. The implementation of the XL algorithm has not been specialized for an attack on a specific cryptographic primitive but can be used for attacking some cryptographic primitives by solving multivariate quadratic systems. All three attacks are general attacks, i.e. they apply to various cryptographic systems; the implementations of Wagner’s generalized birthday attack and Pollard’s rho algorithm can be adapted for attacking other primitives than those given in this thesis. The three attacks have been implemented on different parallel architectures. XL has been parallelized using the Block Wiedemann algorithm on a NUMA system using OpenMP and on an Infiniband cluster using MPI. Wagner’s attack was performed on a distributed system of 8 multi-core nodes connected by an Ethernet network. The work on Pollard’s Rho algorithm is part of a large research collaboration with several research groups; the computations are embarrassingly parallel and are executed in a distributed fashion in several facilities with almost negligible communication cost. This dissertation presents implementations of the iteration function of Pollard’s Rho algorithm on Graphics Processing Units and on the Cell Broadband Engine