Signature-free asynchronous Byzantine consensus

Participant : Michel Raynal.

Randomized mutual exclusion with constant amortized RMR complexity on the DSM

Participant : George Giakkoupis.

Reliable shared memory abstraction on top of asynchronous Byzantine message-passing systems

Participants : Michel Raynal, Julien Stainer.

This work is on the construction and the use of a shared memory abstraction on top of an asynchronous message-passing system in which up to t processes may commit Byzantine failures. This abstraction consists of arrays of n single-writer/multi-reader atomic registers, where $n$ is the number of processes. Differently from usual atomic registers which record a single value, each of these atomic registers records the whole history of values written to it. A distributed algorithm building such a shared memory abstraction it first presented. This algorithm assumes $t\hspace{0.17em}<\hspace{0.17em}n/3$, which is shown to be a necessary and sufficient condition for such a construction. Hence, the algorithm is resilient-optimal. Then we present distributed algorithms built on top of this shared memory abstraction, which cope with up to $t$ Byzantine processes. The simplicity of these algorithms constitutes a strong motivation for such a shared memory abstraction in the presence of Byzantine processes. For a lot of problems, algorithms are more difficult to design and prove correct in a message-passing system than in a shared memory system. Using a protocol stacking methodology, the aim of the proposed abstraction is to allow an easier design (and proof) of distributed algorithms, when the underlying system is an asynchronous message-passing system prone to Byzantine failures.

Distributed Universality

Participants : Michel Raynal, Julien Stainer.

A notion of a universal construction suited to distributed computing has been introduced by M. Herlihy in his celebrated paper “Wait-free synchronization” (ACM TOPLAS, 1991). A universal construction is an algorithm that can be used to wait-free implement any object defined by a sequential specification. Herlihy’s paper shows that the basic system model, which supports only atomic read/write registers, has to be enriched with consensus objects to allow the design of universal constructions. The generalized notion of a $k$-universal construction has been recently introduced by Gafni and Guerraoui (CONCUR 2011). A $k$-universal construction is an algorithm that can be used to simultaneously implement $k$ objects (instead of just one object), with the guarantee that at least one of the $k$ constructed objects progresses forever. While Herlihy’s universal construction relies on atomic registers and consensus objects, a $k$-universal construction relies on atomic registers and $k$-simultaneous consensus objects (which are wait-free equivalent to $k$-set agreement objects in the read/write system model). This work significantly extends the universality results introduced by Herlihy and Gafni-Guerraoui. In particular, we present a $k$-universal construction which satisfies the following five desired properties, which are not satisfied by the previous $k$-universal construction: (1) among the $k$ objects that are constructed, at least $\ell$ objects (and not just one) are guaranteed to progress forever; (2) the progress condition for processes is wait-freedom, which means that each correct process executes an infinite number of operations on each object that progresses forever; (3) if any of the $k$ constructed objects stops progressing, all its copies (one at each process) stop in the same state; (4) the proposed construction is contention-aware, in the sense that it uses only read/write registers in the absence of contention; and (5) it is generous with respect to the obstruction-freedom progress condition, which means that each process is able to complete any one of its pending operations on the $k$ objects if all the other processes hold still long enough. The proposed construction, which is based on new design principles, is called a ($k$,$\ell$)-universal construction. It uses a natural extension of $k$-simultaneous consensus objects, called ($k$,$\ell$)-simultaneous consensus objects (($k$,$\ell$)-SC). Together with atomic registers, ($k$,$\ell$)-SC objects are shown to be necessary and sufficient for building a ($k$,$\ell$)-universal construction, and, in that sense, ($k$,$\ell$)-SC objects are ($k$,$\ell$)-universal.

Computing in the presence of concurrent solo executions

Participants : Michel Raynal, Julien Stainer.

In a wait-free model any number of processes may crash. A process runs solo when it computes its local output without receiving any information from other processes, either because they crashed or they are too slow. While in wait-free shared-memory models at most one process may run solo in an execution, any number of processes may have to run solo in an asynchronous wait-free message-passing model. This work is on the computability power of models in which several processes may concurrently run solo. It first introduces a family of round-based wait-free models, called the d-solo models, $1\hspace{0.17em}\le \hspace{0.17em}d\hspace{0.17em}\le \hspace{0.17em}n$, where up to $d$ processes may run solo. We then give a characterization of the colorless tasks that can be solved in each $d$-solo model. We also introduce the ($d$,$ϵ$)-solo approximate agreement task, which generalizes $ϵ$-approximate agreement, and proves that ($d$,$ϵ$)-solo approximate agreement can be solved in the $d$-solo model, but cannot be solved in the $(d\hspace{0.17em}+\hspace{0.17em}1)$-solo model. We study also the relation linking $d$-set agreement and ($d$,$ϵ$)-solo approximate agreement in asynchronous wait-free message-passing systems. These results establish for the first time a hierarchy of wait-free models that, while weaker than the basic read/write model, are nevertheless strong enough to solve non-trivial tasks.

A simple broadcast algorithm for recurrent dynamic systems

Participants : Michel Raynal, Julien Stainer.

This work presents a simple broadcast algorithm suited to dynamic systems where links can repeatedly appear and disappear. The algorithm is proved correct and a simple improvement is introduced, that reduces the number and the size of control messages. As it extends in a simple way a classical network traversal algorithm to the dynamic context, the proposed algorithm has also pedagogical flavor.

Fisheye consistency: Keeping data in synch in a georeplicated world

Participants : Michel Raynal, François Taïani.