Terminating Non-Disjoint Combined Unification (Extended Abstract)

International audienc

Terminating Non-Disjoint Combined Unification

International audienceThe equational unification problem, where the underlying equational theory may be given as the union of component equational theories, appears often in practice in many fields such as automated reasoning, logic programming, declarative programming, and the formal analysis of security protocols. In this paper, we investigate the unification problem in the non-disjoint union of equational theories via the combination of hierarchical unification procedures. In this context, a unification algorithm known for a base theory is extended with some additional inference rules to take into account the rest of the theory. We present a simple form of hierarchical unification procedure. The approach is particularly well-suited for any theory where a unification procedure can be obtained in a syntactic way using transformation rules to process the axioms of the theory. Hierarchical unification procedures are exemplified with various theories used in protocol analysis. Next, we look at modularity methods for combining theories already using a hierarchical approach. In addition, we consider a new complexity measure that allows us to obtain terminating (combined) hierarchical unification procedures

Non-disjoint Combined Unification and Closure by Equational Paramodulation

Extended version available at https://hal.inria.fr/hal-03329075International audienceClosure properties such as forward closure and closure via paramodulation have proven to be very useful in equational logic, especially for the formal analysis of security protocols. In this paper, we consider the non-disjoint unification problem in conjunction with these closure properties. Given a base theory E, we consider classes of theory extensions of E admitting a unification algorithm built in a hierarchical way. In this context, a hierarchical unification procedure is obtained by extending an E-unification algorithm with some additional inference rules to take into account the rest of the theory. We look at hierarchical unification procedures by investigating an appropriate notion of E-constructed theory, defined in terms of E-paramodulation. We show that any E-constructed theory with a finite closure by E-paramodulation admits a terminating hierarchical unification procedure. We present modularity results for the unification problem modulo the union of E-constructed theories sharing only symbols in E. Finally, we also give sufficient conditions for obtaining terminating (combined) hierarchical unification procedures in the case of regular and collapse-free E-constructed theories

Non-disjoint Combined Unification and Closure by Equational Paramodulation (Extended Version)

Short version published in the Proceedings of FroCoS 2021Closure properties such as forward closure and closure via paramodulation have proven to be very useful in equational logic, especially for the formal analysis of security protocols. In this paper, we consider the non-disjoint unification problem in conjunction with these closure properties. Given a base theory E, we consider classes of theory extensions of E admitting a unification algorithm built in a hierarchical way. In this context, a hierarchical unification procedure is obtained by extending an E-unification algorithm with some additional inference rules to take into account the rest of the theory. We look at hierarchical unification procedures by investigating an appropriate notion of E-constructed theory, defined in terms of E-paramodulation. We show that any E-constructed theory with a finite closure by E-paramodulation admits a terminating hierarchical unification procedure. We present modularity results for the unification problem modulo the union of E-constructed theories sharing only symbols in E. Finally, we also give sufficient conditions for obtaining terminating (combined) hierarchical unification procedures in the case of regular and collapse-free E-constructed theories

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Mecanismos dinâmicos de segurança para redes softwarizadas e virtualizadas

The relationship between attackers and defenders has traditionally been asymmetric, with attackers having time as an upper hand to devise an exploit that compromises the defender. The push towards the Cloudification of the world makes matters more challenging, as it lowers the cost of an attack, with a de facto standardization on a set of protocols. The discovery of a vulnerability now has a broader impact on various verticals (business use cases), while previously, some were in a segregated protocol stack requiring independent vulnerability research. Furthermore, defining a perimeter within a cloudified system is non-trivial, whereas before, the dedicated equipment already created a perimeter. This proposal takes the newer technologies of network softwarization and virtualization, both Cloud-enablers, to create new dynamic security mechanisms that address this asymmetric relationship using novel Moving Target Defense (MTD) approaches. The effective use of the exploration space, combined with the reconfiguration capabilities of frameworks like Network Function Virtualization (NFV) and Management and Orchestration (MANO), should allow for adjusting defense levels dynamically to achieve the required security as defined by the currently acceptable risk. The optimization tasks and integration tasks of this thesis explore these concepts. Furthermore, the proposed novel mechanisms were evaluated in real-world use cases, such as 5G networks or other Network Slicing enabled infrastructures.A relação entre atacantes e defensores tem sido tradicionalmente assimétrica, com os atacantes a terem o tempo como vantagem para conceberem uma exploração que comprometa o defensor. O impulso para a Cloudificação do mundo torna a situação mais desafiante, pois reduz o custo de um ataque, com uma padronização de facto sobre um conjunto de protocolos. A descoberta de uma vulnerabilidade tem agora um impacto mais amplo em várias verticais (casos de uso empresarial), enquanto anteriormente, alguns estavam numa pilha de protocolos segregados que exigiam uma investigação independente das suas vulnerabilidades. Além disso, a definição de um perímetro dentro de um sistema Cloud não é trivial, enquanto antes, o equipamento dedicado já criava um perímetro. Esta proposta toma as mais recentes tecnologias de softwarização e virtualização da rede, ambas facilitadoras da Cloud, para criar novos mecanismos dinâmicos de segurança que incidem sobre esta relação assimétrica utilizando novas abordagens de Moving Target Defense (MTD). A utilização eficaz do espaço de exploração, combinada com as capacidades de reconfiguração de frameworks como Network Function Virtualization (NFV) e Management and Orchestration (MANO), deverá permitir ajustar dinamicamente os níveis de defesa para alcançar a segurança necessária, tal como definida pelo risco actualmente aceitável. As tarefas de optimização e de integração desta tese exploram estes conceitos. Além disso, os novos mecanismos propostos foram avaliados em casos de utilização no mundo real, tais como redes 5G ou outras infraestruturas de Network Slicing.Programa Doutoral em Engenharia Informátic

Beyond the Frontiers of Timeline-based Planning

Any agent, either biological or artificial, understands how to behave in its environment according to its prior knowledge and to its prior experience. The process of deciding which actions to undertake and how to perform them so as to achieve some desired objective is called deliberation. In particular, planning is an abstract and explicit deliberation process that chooses and organizes actions, by anticipating their expected outcomes, with the aim to achieve, as best as possible, some pre-stated objectives called goals. Among the most widespread approaches to automated planning, the classical approach broadly pursues to the following definition of planning: starting from a description of the initial state of the world, a description of the desired goals, and a description of a set of possible actions, the planning problem consists in synthesizing a plan, i.e., a sequence of actions, that is guaranteed, when applied to the initial state, to generate a state, called a goal state, which contains the desired goals. In order to cope with computational complexity, however, the classical approach to planning introduces some restrictive assumptions. Among them, for example, there is no explicit model of time and concurrency is treated only roughly. Additionally, goals are specified as a set of goal states, therefore, objectives such as states to be avoided and constraints on state trajectories or utility functions are not handled. In order to relax these restrictions, some alternative approaches have been proposed over the years. The timeline-based approach to planning, in particular, represents an effective alternative to classical planning for complex domains requiring the use of both temporal reasoning and scheduling features. This thesis focuses on timeline-based planning, aiming at solving some efficiency issues which inevitably raise as a consequence of the drop out of these restrictions. Regardless of the followed approach, indeed, it turns out that automated planning is a rather complex task from a computational point of view. Furthermore, not all of the approaches proposed in literature can rely on effective heuristics for efficiently tackling the search. This is particularly true in the case of the more recent and hence less investigated timeline-based formulation. Most of the timeline-based planners, in particular, have usually neglected the advantages triggered in classical planning from the use of Graphplan and/or modern heuristic search, namely the capability of reasoning on the whole domain model. This thesis aims at reducing the performance gap between the classical approach at planning and the timeline-based one. Specifically, the overall goal is to improve the efficiency of timeline-based reasoners taking inspiration from techniques applied in more classical approaches to planning. The main contributions of this thesis, therefore, are a) a new formalism for timeline-based planning which overcomes some limitations of the existing ones; b) a set of heuristics, inspired by the classical approach, that improve the performance of the timeline-based approach to planning; c) the introduction of sophisticated techniques like the non-chronological backtracking and the no-good learning, commonly used in other fields such as Constraint Processing, into the search process;d) the reorganization of the existing solver architectures, of a new solver called ORATIO, that allows to push the reasoning process beyond the sole automated planning, winking at emerging fields like, for example, Explainable AI and e) the introduction of a new language for expressing timeline-based planning problems called RIDDLE