Byzantine fault-tolerant (BFT) consensus in an asynchronous system can only tolerate up to floor[(n-1)/3] faulty processes in a group of n processes. This is quite a strict limit in certain application scenarios, for example a group consisting of only 3 processes. In order to break through this limit, we can leverage a hybrid fault model, in which a subset of the system is...

Consider a point-to-point message-passing network. We are interested in the asynchronous crash-tolerant consensus problem in incomplete networks. We study the feasibility and efficiency of approximate consensus under different restrictions on topology knowledge and the relay depth, i.e., the maximum number of hops any message can be relayed. These two constraints are common in...

The replicated list object is frequently used to model the core functionality of replicated collaborative text editing systems. Since 1989, the convergence property has been a common specification of a replicated list object. Recently, Attiya et al. proposed the strong/weak list specification and conjectured that the well-known Jupiter protocol satisfies the weak list...

In this paper we examine the issues involved in adding concurrency to the Robin Hood hash table algorithm. We present a non-blocking obstruction-free K-CAS Robin Hood algorithm which requires only a single word compare-and-swap primitive, thus making it highly portable. The implementation maintains the attractive properties of the original Robin Hood structure, such as a low...

This paper considers the modeling and the analysis of the performance of lock-free concurrent search data structures. Our analysis considers such lock-free data structures that are utilized through a sequence of operations which are generated with a memoryless and stationary access pattern. Our main contribution is a new way of analyzing lock-free concurrent search data...

A non-blocking chromatic tree is a type of balanced binary search tree where multiple processes can concurrently perform search and update operations. We prove that a certain implementation has amortized cost O(dot{c} + log n) for each operation, where dot{c} is the maximum number of concurrent operations at any point during the execution and n is the maximum number of keys in...

Distributed tasks such as constructing a maximal independent set (MIS) in a network, or properly coloring the nodes or the edges of a network with reasonably few colors, are known to admit efficient distributed randomized algorithms. Those algorithms essentially proceed according to some simple generic rules, by letting each node choosing a temptative value at random, and...

This paper presents fast, distributed, O(1)-approximation algorithms for metric facility location problems with outliers in the Congested Clique model, Massively Parallel Computation (MPC) model, and in the k-machine model. The paper considers Robust Facility Location and Facility Location with Penalties, two versions of the facility location problem with outliers proposed by...

We show how to multiply two n x n matrices S and T over semirings in the Congested Clique model, where n nodes communicate in a fully connected synchronous network using O(log{n})-bit messages, within O(nz(S)^{1/3} nz(T)^{1/3}/n + 1) rounds of communication, where nz(S) and nz(T) denote the number of non-zero elements in S and T, respectively. By leveraging the sparsity of the...

Distributed systems are constantly faced with difficult decisions to make, such as in scheduling, caching, and traffic routing, to name a few. In most of these scenarios, the optimal decision is unknown and depends heavily on context. How can a system designer know if they have deployed the best decision-making policy, or if a different policy would perform better? As a community...

Significant paradigm shifts are occurring in Access patterns are widely dispersed and large scale analysis requires real-time responses. Many of the fundamental challenges have been studied and explored by both the distributed systems and the database communities for decades. However, the current changing and scalable setting often requires a rethinking of basic assumptions and...

I will provide a historical perspective on wait-free simulations of multi-bit shared registers using single-bit shared registers, starting with classical results from the last century and ending with an overview of the recent resurgence of interest in the topic. Particular emphasis will be placed on the space and step complexities of such simulations.

In this note we remark on the problem of equality of objects in categories formalized in Martin-L�f's constructive type theory. A standard notion of category in this system is E-category, where no such equality is specified. The main observation here is that there is no general extension of E-categories to categories with equality on objects, unless the principle Uniqueness of...

This paper investigates Voevodsky's univalence axiom in intensional Martin-L�f type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms...

We have formalized a range of proof systems for classical propositional logic (sequent calculus, natural deduction, Hilbert systems, resolution) in Isabelle/HOL and have proved the most important meta-theoretic results about semantics and proofs: compactness, soundness, completeness, translations between proof systems, cut-elimination, interpolation and model existence.

We present the PML_2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in terms of classical logic), it supports general recursion and a very general form of (implicit, non-coercive) subtyping. In the system...

In previous work it has been shown how to generate natural deduction rules for propositional connectives from truth tables, both for classical and constructive logic. The present paper extends this for the constructive case with proof-terms, thereby extending the Curry-Howard isomorphism to these new connectives. A general notion of conversion of proofs is defined, both as a...

We show that recognizing axiomatizations of the Hilbert-style calculus containing only the axiom a -> (b -> a) is undecidable (a reduction from the Post correspondence problem is formalized in the Lean theorem prover). Interestingly, the problem remains undecidable considering only axioms which, when seen as simple types, are principal for some lambda-terms in beta-normal form...

We start from an untyped, well-scoped lambda-calculus and introduce a bidirectional typing relation corresponding to a Multiplicative-Additive Intuitionistic Linear Logic. We depart from typical presentations to adopt one that is well-suited to the intensional setting of Martin-L�f Type Theory. This relation is based on the idea that a linear term consumes some of the resources...

K�nig-Egerv�ry graphs form an important graph class which has been studied extensively in graph theory. Much attention has also been paid on K�nig-Egerv�ry subgraphs and K�nig-Egerv�ry graph modification problems. In this paper, we focus on one K�nig-Egerv�ry subgraph problem, called the Maximum Edge Induced K�nig Subgraph problem. By exploiting the classical Gallai-Edmonds...

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani 1966) for extremal problems on geometric graphs, but is also related to graph...

Assume for a graph G=(V,E) and an initial configuration, where each node is blue or red, in each discrete-time round all nodes simultaneously update their color to the most frequent color in their neighborhood and a node keeps its color in case of a tie. We study the behavior of this basic process, which is called majority model, on the Erd�s-R�nyi random graph G_{n,p} and...

Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani 1966) for extremal problems on geometric graphs, but is also related to graph...