This thesis presents three works on different aspects of efficiency of algorithm design for large scale graph computations.

In the first work, we consider a setting of classical centralized computing, and we consider the question of generalizing modular decompositions and designing time-efficient algorithm for this problem. Modular decomposition, and more broadly module detection, are ways to reveal and analyze modular properties in structured data. As the classical modular decomposition is well studied and have an optimal linear-time algorithm, we firstly study the generalizations of these concepts to hypergraphs and present here positive results obtained for three definitions of modular decomposition in hypergraphs from the literature. We also consider the generalization of allowing errors in classical graph modules and present negative results for two this kind of definitions.

The second work focuses on graph data query scenarios. Here the model differs from classical computing scenarios in that we are not designing algorithms to solve an original problem, but we assume that there is an oracle which provides partial information about the solution to the original problem, where oracle queries have time or resource consumption, which we model as costs, and we need to have an algorithm deciding how to efficiently query the oracle to get the exact solution to the original problem, thus here the efficiency is addressing to the query costs. We study the generalized binary search problem for which we compute an efficient query strategy to find a hidden target in graphs. We present the results of our work on approximating the optimal strategy of generalized binary search on weighted trees.

Our third work draws attention to the question of memory efficiency. The setup in which we perform our computations is distributed and memory-restricted. Specif- ically, every node stores its local data, exchanging data by message passing, and is able to proceed local computations. This is similar to the LOCAL/CONGEST model in distributed computing, but our model additionally requires that every node can only store a constant number of variables w.r.t. its degree. This model can also describe natural algorithms. We implement an existing procedure of multiplicative reweighting for approximating the maximum s–t flow problem on this model, this type of methodology may potentially provide new opportunities for the field of local or natural algorithms.

From a methodological point of view, the three types of efficiency concerns cor respond to the following types of scenarios: the first one is the most classical one – given the problem, we try to design by hand the more efficient algorithm; the second one, the efficiency is regarded as an objective function – where we model query costs as an objective function, and using approximation algorithm techniques to get a good design of efficient strategy; the third one, the efficiency is in fact posed as a constraint of memory and we design algorithm under this constraint.

This thesis addresses the issue of “Executable Knowledge Representation” in the context of molecular biology. We introduce the foundation of a logical framework, termed iota, whose aim is to facilitate knowledge collation of molecular interactions at the level of proteins and at the same time allows the modeler to compile a reasonable fragment of the logic into a finite set of executable graph rewriting rules. We define a logic FO[↓] over cell state transitions. States represent cell contents; domain elements are protein parts and relations are protein-protein bindings. The unary logical operator ↓ selects transitions where as little as possible happens. Formulas over transitions also may runs, which are finite or infinite sequences of transitions. Every transition formula is also associated to a set of rewriting rules equipped with an operational semantics. We introduce two deductive systems that act as “typing” for formulas. We show that if a formula is typable in the first system then the execution of its associated rule set produces exactly the runs denoted by the formula, and that if it is typable in the second system then its associated rule set is finite. We introduce a grammar that produces formulas typable in both systems, up to logical equivalence. Finally we study decidability and definability properties of fragments of FO[↓]. In particular, we show that formulas typable in the second system are in a tight fragment of FO, which implies that the operator ↓ can then be eliminated.

Manuscript

In this thesis, I present the application of software engineering methods and knowledge to the development, maintenance, and evolution of Coq —an interactive proof assistant based on type theory— and its package ecosystem. Coq has been developed at Inria since 1984, but has only more recently seen a surge in its user base, which leads to much stronger concerns about its maintainability, and the involvement of external contributors in the evolution of both Coq, and its ecosystem of plugins and libraries.

Recent years have seen important changes in the development processes of Coq, of which I have been a witness and an actor (adoption of GitHub as a development platform, first for its pull request mechanism, then for its bug tracker, adoption of continuous integration, switch to shorter release cycles, increased involvement of external contributors in the open source development and maintenance process). The contributions of this thesis include a historical description of these changes, the refinement of existing processes, and the design of new ones, the design and implementation of new tools to help the application of these processes, and the validation of these changes through rigorous empirical evaluation.

Involving external contributors is also very useful at the level of the package ecosystem. This thesis additionally contains an analysis of package distribution methods, and a focus on the problem of the long-term maintenance of single-maintainer packages.

Manuscript

The aim of this thesis is to use algorithmic game theory tools to study various games inspired from real world problems in the fields of information networks and biology. These games are characterized by a large number of players, each with incomplete information about other players. In classical game theory, these games fall into the category of extensive games with imperfect information, which are modeled using trees. However, these games remain very difficult to analyze in details, because of their intrinsic complexity, which is linked with their possibly infinite tree depth. Nevertheless, we have taken up the challenge of this task, while diversifying the methods of resolution, and emphasizing its interdisciplinary aspect.

Besides the introduction and the conclusion, the thesis is divided into three parts. In the first part, we adopt the point of view of classical game theory. We propose a game that corresponds to a wide class of problems encountered in the theory of distributed computing. The main contributions of this part are, on the one hand, to show how to transform a purely algorithmic problem into a game, and, on the other hand, to prove the existence of satisfactory equilibria for the resulting class of games. This second point is essential, as it guarantees that game theory is adapted to the study of distributed games, despite their complexity.

The second part is dedicated to the study of a game omnipresent within biological systems, that we call dispersion game. This game models the situation in which a group of animals must share a certain amount of resources scattered among different geographical sites. The difficulty of the game comes from the fact that some sites contain more resources than others, but may also attract more players. We propose a rule for the distribution of resources which makes it possible to maximize the resources exploited by the whole group. This part of the thesis is also an opportunity to revisit the close links between the concept of ideal free distribution, very present in the theory of foraging, and the concept of evolutionarily stable strategy, a key concept of evolutionary game theory.

The third part focuses on the study of the behavior of a specific species of small bats living in Mexico, in the Sonoran Desert, and feeding at night from the nectar of the giant Saguaro cacti, a protected species. After the presentation of the experimental results obtained in the field, we propose a computer simulation of their behavior. The results of these simulations make it possible to formulate interesting hypotheses about the cerebral activities of these small mammals. We then study a theoretical model of game inspired by this real situation. The study of this abstract model allows us to distinguish the fundamental characteristics of the game, and to reinforce our approach of theorizing foraging behavior. This study also opens the way to applying this type of model to other situations, involving animal or human behavior.

Cette thèse propose une étude quantitative de plusieurs modèles de calcul de l’informatique fondamentale et de la théorie de la démonstration. Deux approches sont menées : la première consiste à examiner les mécanismes d’approximation multilinéaires dans des systèmes issus du λ-calcul et de la Logique Linéaire. La seconde consiste à étudier les modèles topologiques pour les systèmes distribués et à les adapter aux algorithmes probabilistes.

On étudie d’abord le développement de Taylor des réseaux de preuve de la Logique Linéaire. On introduit des méthodes de démonstration qui utilisent la géométrie de l’élimination des coupures des réseaux multiplicatifs, et qui permettent de manipuler des sommes infinies de réseaux de façon sûre et correcte, pour en extraire des propriétés sur les réductions qui sont à l’œuvre.

Ensuite, nous introduisons un langage permettant de définir le développement de Taylor syntaxique pour l’Appel-Par-Pousse-Valeur (Call-By-Push-Value), en capturant certaines propriétés de la sémantique dénotationelle liées aux morphismes de coalgèbres.

Puis nous nous intéressons aux systèmes distribués (à mémoire partagée, tolérants aux pannes), et au problème du Consensus. On utilise un modèle topologique qui permet d’interpréter la communication dans les complexes simpliciaux, et on l’adapte de façon à transformer les résultats d’impossibilité bien connus en résultats de borne inférieure de probabilité pour des algorithmes probabilistes.

English version:

This Phd thesis presents a quantitative study of various computation models of fundamental computer science and proof theory, in two principad directions: the first consists in the examination of mecanismis of multilinear approximations in systems related to λ-calculus and Linear Logic. The second consists in a study of topological models for asynchronous distributed systems, and probabilistic algorithms.

We first study Taylor expansion in Linear Logic proof nets. We introduce proof methods using the geometry of cut elimination in multiplicative nets, and which allow to work with infinite sums of nets in a safe and correct way, in order to extract properties about reduction.

Then, we introduce a language allowing us to define Taylor expansion for Call-By-Push-Value, while capturing some properties of the denotational semantics, related to coalgebras morphisms.

We focus then on fault tolerant-distributed systems with shared memory, and to Consensus problem. We use a topological model which allows to interpret communication with simplicial complexes, and we adapt in so as to transform the well-known impossibility results in lower bounds for probabilistic algorithms.

Manuscript: https://www.irif.fr/~chouquet/these.html

Twenty-five years ago, Hyland and Ong resolved the full abstraction problem for the PCF language by constructing a game semantics based on the fundamental notion of innocent strategy. We carry on their work in this thesis, and construct a 2-dimensional category of non-deterministic and innocent strategies extending their original deterministic innocent game model.

Our starting point in the thesis is provided by the combinatorial approach to innocent strategies developed by Harmer, Hyland and Melliès in a work published ten years ago. In this work, they elaborate a combinatorial description of the pointer structures of arena games, and establish that innocence can be recovered by taking advantage of a number of remarkable categorical properties, most notably the existence of a distributive law between the monad generating the Player views and the comonad generating the Opponent views.

In this thesis, we study in great detail the reconstruction of the innocent game model identified by Harmer, Hyland and Melliès, and extend this model in two directions. In the first direction, we explain how to see the Harmer-Hyland-Melliès game model as a specific instance of a dialogue category, a notion originally introduced by Melliès, using the underlying symmetry between Opponent and Player in categories of games and strategies.

In the second direction, we construct a 2-dimensional game semantics of non-deterministic PCF by equipping every game with a presheaf of non-deterministic strategies, instead of just a set of strategies. In order to perform this shift of dimension from sets to presheaves, we adapt very carefully the categorical constructions involved in the Harmer-Hyland-Melliès model, and construct in particular a pseudo-distributive law between the pseudo-monad generating the Player views and the pseudo-comonad generating the Opponent views in our non-determinic game model. We obtain in this way a bicategory of games, non-deterministic innocent strategies and simulations — which we then compare with alternative formulations of non-deterministic and innocent game semantics appearing in the literature.

A Self modifying code is code that modifies its own instructions during execution time. It is nowadays widely used, especially in malware to make the code hard to analyse and to detect by anti-viruses. Thus, the analysis of such self modifying programs is a big challenge. Pushdown Systems (PDSs) is a natural model that is extensively used for the analysis of sequential programs because it allows to accurately model procedure calls and mimic the program’s stack. In this thesis, we propose to extend the PushDown System model with self-modifying rules. We call the new model Self-Modifying PushDown System (SM-PDS). A SM-PDS is a PDS that can modify its own set of transitions during execution. First, we show how SM-PDSs can be used to naturally represent self-modifying programs and provide efficient algorithms to compute the backward and forward reachable configurations of SM-PDSs. Then, we consider the LTL model-checking problem of self-modifying code. We reduce this problem to the emptiness problem of Self-modifying Büchi Pushdown Systems (SM-BPDSs). We also consider the CTL model-checking problem of self-modifying code. We reduce this problem to the emptiness problem of Self-modifying Alternating Büchi Pushdown Systems (SM-ABPDSs). We implement our techniques in a tool called SMODIC. We obtained encouraging results. In particular, our tool was able to detect several self-modifying malwares; it could even detect several malwares that well-known anti-viruses such as McAfee, Norman, BitDefender, Kinsoft, Avira, eScan, Kaspersky, Qihoo-360, Avast and Symantec failed to detect.

In this work we study some dynamical properties of symbolic dynamical systems, with particular emphasis on the role played by the invariant probability measures of such systems. We approach the study of the set of invariant measures from a topological, combinatorial and geometrical point of view. From a topological point of view, we focus on the problem of orbit equivalence and strong orbit equivalence between dynamical systems given by minimal actions of Z, through the study of an algebraic invariant, namely the dynamical dimension group. Our work presents a description of the dynamical dimension group for two particular classes of subshifts: S-adic subshifts and dendric subshifts. From a combinatorial point of view, we are interested in the problem of balance in minimal uniquely ergodic systems given by actions of Z. We investigate the behavior regarding balance for substitutive, S-adic and dendric subshifts. We give necessary conditions for a minimal substitutive system with rational frequencies to be balanced on its factors, obtaining as a corollary the unbalance in the factors of length at least 2 in the subshift generated by the Thue-Morse sequence. Finally, from the geometrical point of view, we investigate the problem of realization of Choquet simplices as sets of invariant probability measures associated to systems given by minimal actions of amenable groups on the Cantor set. We introduce the notion of congruent monotileable amenable group, we prove that every virtually nilpotent amenable group is congruent monotileable, and we show that for a discrete infinite group G with this property, every Choquet simplex can be obtained as the set of invariant measures of a minimal G-subshift.

This dissertation deals with the field of usable security, particularly in the contexts of online authentication and verifiable voting systems.The ever-expanding role of online accounts in our lives, from social networks to banking or online voting, has led to some initially counterproductive solutions. As recent research has shown, the problem is not just technical but has a very real psychosocial component. Password-based authentication, the subject of most of this thesis, is intrinsically linked to the unconscious mechanisms people use when interacting with security systems. Everyday, users face trade-offs between protecting their security and spending valuable mental resources, with a choice made harder by conflicting recommendations, a lack of standards, and the ad-hoc constraints still frequently encountered. Moreover, as recent results from usable security are often ignored, the problem might stem from a fundamental disconnect between the users, the developers and the researchers. We try to address those problems with solutions that are not only simplified for the user's sake but also for the developer's. To this end, we use tools from cryptography and psychology, and report on seven usability experiments.The first part of the contributions uses a service provider's point of view, with two tools to improve the end-user's experience without requiring their cooperation. We start by analysing how easily codes of different structures can be transcribed, with a proposal that reduces error rates while increasing speed. We then look at how servers can accept typos in passwords without changing the general hashing protocol, and how this could improve security. The second part focuses on end-users, starting by a proposed mental password manager that only depends on remembering only a single passphrase and PIN, with guarantees on the mutual security of generated passwords if some get stolen. We also provide a better way to create such passphrases. As mental computing models are central to expanding this field, we finish by empirically showing why the main model used today is not adapted to the purpose.In the third part, we focus on voting protocols, and investigate why changing the ones used in practice is an uphill battle. We try to answer a demand for simple paper-based systems by providing low-tech versions of the first paper-based verifiable voting scheme. To conclude, we propose a set of low-tech primitives combined in a protocol that allows usable verifiable voting with no electronic means in small elections.

The manuscript is available at: http://research.crubille.lautre.net/main.pdf

We study set-theoretic types: types that include union, intersection, and negation connectives. Set-theoretic types, coupled with a suitable subtyping relation, are useful to type several programming language constructs – including conditional branching, pattern matching, and function overloading – very precisely. We define subtyping following the semantic subtyping approach, which interprets types as sets and defines subtyping as set inclusion. Our set-theoretic types are polymorphic, that is, they contain type variables to allow parametric polymorphism.We extend previous work on set-theoretic types and semantic subtyping by showing how to adapt them to new settings and apply them to type various features of functional languages. More precisely, we integrate semantic subtyping with three important language features.In Part I we study implicitly typed languages with let-polymorphism and type inference (previous work on semantic subtyping focused on explicitly typed languages). We describe an implicitly typed lambda-calculus and a declarative type system for which we prove soundness. We study type inference and prove results of soundness and completeness. Then, we show how to make type inference more precise when programs are partially annotated with types.In Part II we study gradual typing. We describe a new approach to add gradual typing to a static type system; the novelty is that we give a declarative presentation of the type system, while previous work considered algorithmic presentations. We first illustrate the approach on a Hindley-Milner type system without subtyping. We describe declarative typing, compilation to a cast language, and sound and complete type inference. Then, we add set-theoretic types, defining a subtyping relation on set-theoretic gradual types, and we describe sound type inference for the extended system.In Part III we consider non-strict semantics. The existing semantic subtyping systems are designed for call-by-value languages and are unsound for non-strict semantics. We adapt them to obtain soundness for call-by-need. To do so, we introduce an explicit representation for divergence in the types, allowing the type system to distinguish the expressions that are already evaluated from those that are computations which might diverge.