A Reformulation of Matrix Graph Grammars with Boolean Complexes

Prior publication in the Electronic Journal of Combinatorics.Graph transformation is concerned with the manipulation of graphs by means of rules. Graph grammars have been traditionally studied using techniques from category theory. In previous works, we introduced Matrix Graph Grammars (MGG) as a purely algebraic approach for the study of graph dynamics, based on the representation of simple graphs by means of their adjacency matrices. The observation that, in addition to positive information, a rule implicitly defines negative conditions for its application (edges cannot become dangling, and cannot be added twice as we work with simple digraphs) has led to a representation of graphs as two matrices encoding positive and negative information. Using this representation, we have reformulated the main concepts in MGGs, while we have introduced other new ideas. In particular, we present (i) a new formulation of productions together with an abstraction of them (so called swaps), (ii) the notion of coherence, which checks whether a production sequence can be potentially applied, (iii) the minimal graph enabling the applicability of a sequence, and (iv) the conditions for compatibility of sequences (lack of dangling edges) and G-congruence (whether two sequences have the same minimal initial graph).This work has been partially sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN)

Crisis y complejidad socioeconómica

Una nueva variable socioeconómica -que denominamos “complejidad”-, que es representativa de la hipertrofia de las estructuras socioeconómicas y del gigantismo de los mecanismos de control de estas, se demuestra como característica estrechamente vinculada a la productividad de los recursos, y es explicativa de las dinámicas asociadas al crecimiento económico y las crisis subsecuentes. Y es que la detracción de recursos productivos originada por un entorno socioeconómico excesivamente “complejo” se conforma como causa mayor en el establecimiento de límites para el crecimiento. El entendimiento profundo de esta variable omnipresente, es imprescindible para establecer políticas de incremento de la productividad que no introduzcan costes adicionales de control y con ello riesgos de colapso del sistema

Dotación de una semántica formal a Solidity que permita su verificación

Trabajo de Fin de Grado en Ingeniería Informática, Facultad de Informática UCM, Departamento de Sistemas Informáticos y Computación, Curso 2019/2020Whilst the number of programming languages continuously increases, along with their multiple applications, the need of guaranteeing correction or predicting the outcome of a certain program arises. Due to the lack of information that is often available in the official documentation of the languages, formal methods seem a powerful tool in this sense. Thanks to program verification using formal semantics we can abstract the behaviour of an instruction using mathematical notation. In this work we will study Solidity, a language used to create the so-called smart contracts in the Ethereum platform. Our goal is to study the state-of-the-art semantics in this topic, to ultimately suggest our own, with the aim of covering what we believe has not been covered yet, and to propose modifications to the rules that we have found rather imprecise. We have decided to pay special attention to how values are updated and retrieved from the storage, which is one on the four data locations Solidity makes use of. Lastly, it has been our goal to propose semantics that are executable in languages like K or Maude. For this reason, we have also coded several Maude modules which can be helpful when verifying a contract using this language.En un contexto en el cual el número de lenguajes de programación cada vez es más elevado, y su uso se extiende a un mayor número de ámbitos, aparece la necesidad de asegurar la corrección o de determinar el resultado de ciertos programas. Debido a la falta de información concreta que muchas veces encontramos en la documentación oficial de los lenguajes, surgen técnicas como la verificación de programas a través de semánticas formales, que permiten modelizar mediante abstracciones matemáticas el funcionamiento de las instrucciones. En este trabajo estudiaremos el lenguaje Solidity, utilizado para crear los llamados smart contracts en la plataforma Ethereum. Nuestro objetivo es estudiar qué propuestas de semánticas se han hecho, para posteriormente aportar la nuestra, que tratará de rellenar y corregir ciertos huecos e imprecisiones que hayamos podido encontrar en la literatura consultada. En nuestro caso, presentamos una semántica centrada sobre todo en la obtención y actualización de valores en storage, una de las cuatro memorias que utiliza Ethereum. Por último, el objetivo último de este trabajo es el ofrecer una semántica que sea implementable en lenguajes como K o Maude. En nuestro caso, hemos desarrollado diferentes módulos en Maude que pueden servir como base a la hora de realizar una verificación de un contrato en este lenguaje.Depto. de Sistemas Informáticos y ComputaciónFac. de InformáticaTRUEunpu

Suavidad, convexidad, dualidad y renormamientos

The goal of this Bachelor thesis is to study some specifical geometric properties, which are related to the convexity and smoothness of Banach spaces. More precisely we will go over the definitions of strict convexity, uniform convexity, smoothness and uniform smoothness. We will study some duality relationships between strict convexity and smoothness, namely that the strict convexity (smoothness) of the dual norm implies the smoothness (strict convexity) of the norm. We show an example proving that the converse of this duality results do not hold. However, we will prove that there is a complete duality relationship between uniform convexity and uniform smoothness through Lindenstrauss’ formula. With regard to renorming theory, it will be also showed that every separable space can be renormed in order to be strictly convex. We will go also over Enflo’s Theorem: a space is superreflexive if and only if it admits an uniform convex renorming. In the last chapter we improve the above results. In fact, almost all renormings of a separable space are strictly convex and almost all renomings of a superreflexive space are uniformly convex.Universidad de Sevilla. Grado en Matemática

"The authority of the steam" : power dynamics of digital production in the Bitcoin blockchain

This thesis offers a critical investigation of the Bitcoin currency and the operation of its technical structure, i.e. blockchain technology. The main objective of the research is to identify and describe the specific power dynamics performed by and through this digital phenomenon. “Power dynamics” are framed in this work largely in terms of authority and sovereignty. To structure an exploration of such dynamics, the narrative is overarched by four different notions of “utopia” —as paradox, ideal, no-place, and imagined governance— that address the following main questions always underpinned by the general inquiry on power: What is the Bitcoin Blockchain? Where is it located? How are power relations performed in it? And how are power relations modified in relation with previous institutional systems? The thesis addresses distinct notions of authority in Bitcoin through the observation of its historical, spatial, and organizational characteristics. It maps the techno-political emergence of the blockchain system, the geographical distribution of Bitcoin’s infrastructural network, and the strategies for governance involved in its development as software. Based on the observation of these settings, this thesis argues that Bitcoin posits a restructuration of power dynamics through the automation of code, in particular, through its process of production. In order to develop this restructuration, the power dynamics of the Bitcoin blockchain are weighted against authority models of the state’s institutions. The thesis builds upon existing political theories of Empire (Hardt and Negri), protocol (Galloway), and the Stack (Bratton) to develop a critical account of Bitcoin’s power dynamics. The work sits in between the disciplines of Media Theory, Software Studies, Political Theory, and Digital Methods, and makes use of qualitative and quantitative methods to empirically support the former argument