Reliable communication via semilattice properties of partial knowledge

A fundamental communication primitive in distributed computing is Reliable Message Transmission (RMT), which refers to the task of correctly sending a message from a party to another, despite the presence of Byzantine corruptions. In this work we address the problem in the general adversary model of Hirt and Maurer [5], which subsumes earlier models such as the global or local threshold adversaries. Regarding the topology knowledge, we employ the recently introduced Partial Knowledge Model [12], which encompasses both the full knowledge and the ad hoc model; the latter assumes knowledge of the local neighborhood only. Our main contribution is a tight condition for achieving RMT in the partial knowledge model under a general adversary. A key algorithmic tool that we define and use is the joint view operation which imposes a semilattice structure on the partial knowledge possessed by different parties. In this context, we prove that the worst possible adversary structure, conforming with the initial knowledge of a set of parties, can be expressed as the supremum of the parties’ knowledge under the semilattice partial order. The new operation allows for the definition of an appropriate network separator notion that yields a necessary condition for achieving RMT. In order to show the sufficiency of the condition, we propose the RMT Partial Knowledge Algorithm (RMT-PKA), an algorithm that also employs the joint view operation to solve RMT whenever the condition is met. This implies that RMT-PKA achieves reliable message transmission in every instance where this is possible, therefore it is a unique algorithm [13]. To the best of our knowledge, this is the first unique protocol for RMT against general adversaries in the partial knowledge model. Due to the generality of the model, our results provide, for any level of topology knowledge and any adversary structure, an exact characterization of instances where RMT is possible and an algorithm to achieve RMT on such instances

Resource theories of knowledge

How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.Comment: 28 pages featuring figures, examples, map and neatly boxed theorems, plus appendi

Efficient state-based CRDTs by delta-mutation

CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs ensure convergence through disseminating the entire state, that may be large, and merging it to other replicas; whereas operation-based CRDTs disseminate operations (i.e., small states) assuming an exactly-once reliable dissemination layer. We introduce Delta State Conflict-Free Replicated Datatypes (δ-CRDT) that can achieve the best of both worlds: small messages with an incremental nature, disseminated over unreliable communication channels. This is achieved by defining δ-mutators to return a delta-state, typically with a much smaller size than the full state, that is joined to both: local and remote states. We introduce the δ-CRDT framework, and we explain it through establishing a correspondence to current state-based CRDTs. In addition, we present an anti-entropy algorithm that ensures causal consistency, and two δ-CRDT specifications of well-known replicated datatypes.This work is co-financed by the North Portugal Regional Operational Programme (ON.2, O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF), within project NORTE07-0124-FEDER-000058; and by EU FP7 SyncFree project (609551)

Distributed execution of bigraphical reactive systems

The bigraph embedding problem is crucial for many results and tools about bigraphs and bigraphical reactive systems (BRS). Current algorithms for computing bigraphical embeddings are centralized, i.e. designed to run locally with a complete view of the guest and host bigraphs. In order to deal with large bigraphs, and to parallelize reactions, we present a decentralized algorithm, which distributes both state and computation over several concurrent processes. This allows for distributed, parallel simulations where non-interfering reactions can be carried out concurrently; nevertheless, even in the worst case the complexity of this distributed algorithm is no worse than that of a centralized algorithm

Approaches to Conflict-free Replicated Data Types

Conflict-free Replicated Data Types (CRDTs) allow optimistic replication in a principled way. Different replicas can proceed independently, being available even under network partitions, and always converging deterministically: replicas that have received the same updates will have equivalent state, even if received in different orders. After a historical tour of the evolution from sequential data types to CRDTs, we present in detail the two main approaches to CRDTs, operation-based and state-based, including two important variations, the pure operation-based and the delta-state based. Intended as a tutorial for prospective CRDT researchers and designers, it provides solid coverage of the essential concepts, clarifying some misconceptions which frequently occur, but also presents some novel insights gained from considerable experience in designing both specific CRDTs and approaches to CRDTs.Comment: 36 page

On Extend-Only Directed Posets and Derived Byzantine-Tolerant Replicated Data Types

We uncover the extend-only directed posets (EDP) structure as unification of recently discussed DAG-based Byzantine-tolerant conflict-free replicated data types (CRDT). We also derive an EDP-based key-value map, and give an outlook on an EDP-based systemic access control CRDT as formalization of the CRDT used in the Matrix messaging system

On Extend-Only Directed Posets and Derived Byzantine-Tolerant Replicated Data Types (Extended Version)

We uncover the extend-only directed posets (EDP) structure as a unification of recently discussed DAG-based Byzantine-tolerant conflict-free replicated data types (CRDT). We also show how a key-value map model can be derived from the EDP formulation, and give an outlook on an EDP-based systemic access control CRDT as a formalization of the CRDT used in the Matrix messaging system.Comment: With the inclusion of an appendix of a formalization and CRDT proof sketch of an EDP-based CRDT with systemic access control, this is an extended version of the paper presented at the 10th Workshop on Principles and Practice of Consistency for Distributed Data (PaPoC), 2023-05-08, Rome, Ital