We consider a core language for graph queries. These queries, which may transform graphs to graphs, are seen as formulas to be solved with respect to graph databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of graph homomorphisms are specified. Then, the notion of pattern is introduced to represent a kind of recursively defined formula over graphs. The syntax and formal semantics of patterns are provided. Afterwards, we propose a new sound and complete procedure to solve patterns. This procedure, which is based on a set of rewriting rules, is terminating and develops only one needed derivation per pattern to be solved. Our procedure is generic in the sense that it can be adapted to different kinds of graph queries provided that the notions of graph and graph homomorphism are well defined.

We discuss some issues to the inheritance of crypto assets. We propose a distributed, privacy preserving, protocol to establish a consensus on the death of the owner of crypto assets: the Tales From the Crypt Protocol. Until the actual death of the owner no link can be made between public information and the corresponding crypto assets. This protocol is generic and could be incorparated into any arbitrary crypto platform.

We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of graph homomorphisms are specified. Then, the notion of pattern is introduced to represent a kind of recursively defined formula over graphs. The syntax and formal semantics of patterns are provided. Afterwards, we propose a new sound and complete calculus to solve patterns. This calculus, which is based on a rewriting system, develops only one derivation per pattern to be solved. Our calculus is generic in the sense that it can be adapted to different kinds of graph databases provided that the notions of graph and graph homomorphism (match) are well defined.

Inheritance is the fundamental building block of civilization. This is the addition of wealth, knowledge and properties over time that produce the society in which we are living. Every generation does not have to start from zero and can capitalize on the efforts of previous generations. Blockchain based assets are very efficiently and securely transferred between living entities. Yet the actual way to make heirs inherit crypto-assets is seldom discussed. It appears that the problems linked with the inheritance of crypto-assets raise a lot of technical, societal and legal issues. Part of those issues have to be tackled with at the level of the blockchain infrastructure itself. The aim of this paper is to open a research field, and to discuss some ideas, with regards to this overlooked issue. Inheritance is neither a peripheral question nor one that can be dodged. It comes with its own set of challenges that have to be met if blockchain based finance, and asset management, is to be taken seriously.

We consider the recommendations of the World Wide Web Consortium (W3C) about RDF framework and its associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We define RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and properties associated with the fact that language technology is enumerable. G\"odel's numbering technique is universal for enumerable structures and shows strong limits of the language technology. Computability theory is a particular example: programs can be numbered and all sorts of limits can be studied from there. Computability is also at the heart of science since any experimental validation of a theory supposes that theoretical results have been computed, then checked against concrete experiments. It implies that limitations on what is computable ultimately are also limits of what we understand as "scientific theory", and more generally to all the transmissible knowledge. We argue that it is fruitful to look a epistemology from a computability perspective. We show that it allows to precisely define different kinds of knowledge acquisition techniques, and helps the study of how they are related to one another.

We propose a new algebraic approach to graph transformation, called the Pullback-Pushout ( pbpo ) approach, where we combine smoothly the classical modifications to a host graph specified by a first part of a rule, defined as a span of graph morphisms, with the cloning of structures specified by a second span. The motivation behind this new approach is to support cloning of structures in an elegant and efficient way. After a formal definition of the proposed approach, we demonstrate that pbpo rewriting is a conservative extension of agree and the Sesqui-Pushout approaches. Contrary to agree , we show that the proposed pbpo transformation can easily be extended to cope with attributed graphs. In general, totally attributed graphs are not closed under pbpo transformation. We propose sufficient conditions which guarantee that the attribution of transformed graphs is total. Furthermore, a pbpo transformation can affect all parts of a host graph including non local parts (i.e., parts which are outside the image of the left-hand side of a rule). We propose and discuss some conditions which ensure a form of locality of pbpo transformations.

We consider the recommendations of the World Wide Web Consortium (W3C) about the Resource Description Framework (RDF) and the associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We propose to define the notions of RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

The amount of data produced by individuals and corporations has dramatically increased during the last decades. This generalized gathering of data brings opportunities but also new privacy challenges. Nowadays, data are often organized as graphs with an underlying semantic to allow efficient querying and support inference engines. Such is the case in, for example, linked data and semantic web typically relying on RDF. The SEmantic Networks of Data: Utility and Privacy (SEND UP) project focuses on such databases and will follow two main goals: (1) prevent illegitimate use of private data while querying semantic data graphs and (2) publish useful sensitive semantic data graphs while preserving privacy. Context and goals More and more private information collected: threatening privacy yet useful ⇒ needs for privacy guarantees and utility preservation.

Some recent algebraic approaches to graph transformation include a pullback construction involving the match, that allows one to specify the cloning of items of the host graph. We pursue further this trend by proposing the Pullback-Pushout (pb-po) Approach, where we combine smoothly the classical modifications to a host graph specified by a rule (a span of graph morphisms) with the cloning of structures specified by another rule. The approach is shown to be a conservative extension of agree (and thus of the sqpo approach), and we show that it can be extended with standard techniques to attributed graphs. We discuss conditions to ensure a form of locality of transformations, and conditions to ensure that the attribution of transformed graphs is total.

Graph clustering is widely used in many data analysis applications. In this paper we propose several parallel graph clustering algorithms based on Monte Carlo simulations and expectation maximization in the context of stochastic block models. We apply those algorithms to the specific problems of recommender systems and social network anonymization. We compare the experimental results to previous propositions.

Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly)copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way.

A 5x5 board is the smallest board on which one can set up all kind of chess pieces as a start position. We consider Gardner's minichess variant in which all pieces are set as in a standard chessboard (from Rook to King). This game has roughly 9x10^{18} legal positions and is comparable in this respect with checkers. We weakly solve this game, that is we prove its game-theoretic value and give a strategy to draw against best play for White and Black sides. Our approach requires surprisingly small computing power. We give a human readable proof. The way the result is obtained is generic and could be generalized to bigger chess settings or to other games.

We tackle the problem of graph transformation with particular focus on node cloning. We propose a new approach to graph rewriting, called polarized node cloning, where a node may be cloned together with either all its incident edges or with only its outgoing edges or with only its incoming edges or with none of its incident edges. We thus subsume previous works such as the sesqui-pushout, the heterogeneous pushout and the adaptive star grammars approaches. We first define polarized node cloning algorithmically, then we propose an algebraic definition. We use polarization annotations to declare how a node must be cloned. For this purpose, we introduce the notion of polarized graphs as graphs endowed with some annotations on nodes and we define graph transformations with polarized node cloning by means of sesqui-pushouts in the category of polarized graphs.

Noninterference is the mathematical basis for confidentiality analyses. The idea is to ensure that private data will not be observable at a public level. Understood in a strict way noninterference is a too strong property. Standard every day life examples like password checks or message encryption formally break the noninterference property. In this paper we propose a framework in which it is possible to define an interference policy allowing to define safe data declassification. Moreover this policy is dynamic, i.e. the confidentiality level of data may evolve during computation: think at policies in which you want to express that a user has a limited number of guesses or to the sending of a pay-per-view information. We develop a notion of program safety with relation to a dynamic interference policy and give an algorithm (in the form of an abstract evaluation of the program) to check that a program is safe with relation to a dynamic interference policy.

This document presents the LIG in two parts. The first part (Volume 1) presents three aspects of the LIG: (1) organisation, (2) results obtained in the first four-year period, and (3) the scientific projects for the next five years. The second part (Volume 2) presents the 23 teams of the laboratory.

Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a new notion of abstract rewriting in the framework of categories. Then, we define the functoriality property of rewriting systems. This property is sometimes called vertical composition. We show that most of graph transformation systems are functorial and provide a counter-example of graph transformation systems which is not functorial.

We tackle the problem of graph transformation with a particular focus on node cloning. We propose a new approach to graph rewriting where nodes can be cloned zero, one or more times. A node can be cloned together with all its incident edges, with only its outgoing edges, with only its incoming edges or with none of its incident edges. We thus subsume previous works such as the sesqui-pushout, the heterogeneous pushout and the adaptive star grammars approaches. A rewrite rule is defined as a span where the right-hand and left-hand sides are graphs while the interface is a polarized graph. A polarized graph is a graph endowed with some annotations on nodes. The way a node is cloned is indicated by its polarization annotation. We use these annotations for designing graph transformation with polarized cloning. We show how a clone of a node can be built according to the different possible polarizations and define a rewrite step as a final pullback complement followed by a pushout. This is called the polarized sesqui-pushout approach. We also provide an algorithmic presentation of the proposed graph transformation with polarized cloning.

We present a logical approach to the separability analysis issue for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably because they are highly non-compositional. Nevertheless, the intrisic non determinism of quantum computation has a large impact on the definitions of the semantics and the validity of logical assertions. To the knowledge of the authors, it is the first proposal of an entanglement/separability analysis for a functional quantum programming language with higher-order functions.