Related papers: A Simple Object that Spans the Whole Consensus Hie…
This paper introduces the atomic Write and Read Next ($\text{WRN}_{k}$) deterministic shared memory object, that for any $k\ge3$, is stronger than read-write registers, but is unable to implement $2$-processor consensus. In particular, it…
The consensus number of an object is the maximum number of processes among which binary consensus can be solved using any number of instances of the object and read-write registers. Herlihy [6] showed in his seminal work that if an object…
We show that Naming-- the existence of distinct IDs known to all-- is a hidden but necessary assumption of Herlihy's universality result for Consensus. We then show in a very precise sense that Naming is harder than Consensus and bring to…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
The consensus number of a w-bit register supporting logical left shift and right shift operations is exactly w, giving an example of a class of types, widely implemented in practice, that populates all levels of the consensus hierarchy.…
The well-known randomized consensus algorithm by Aspnes and Herlihy for asynchronous shared-memory systems was proved to work, even against a strong adversary, under the assumption that the registers that it uses are atomic registers. With…
Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on…
All consensus hierarchies in the literature assume that we have, in addition to copies of a given object, an unbounded number of registers. But why do we really need these registers? This paper considers what would happen if one attempts to…
This article studies the synchronization power of AllowList and DenyList objects under the lens provided by Herlihy's consensus hierarchy. It specifies AllowList and DenyList as distributed objects and shows that while they can both be seen…
Consensus ranking is a technique used to derive a single ranking that best represents the preferences of multiple individuals or systems. It aims to aggregate different rankings into one that minimizes overall disagreement or distance from…
We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured…
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…
We introduce a higher simplicial generalization of the linear consensus model which shares several common features. The well-known linear consensus model is a gradient flow with a sum of squares of distances between each pair of points. Our…
Eventually linearizable objects are novel shared memory programming constructs introduced as an analogy to eventual consistency in message-passing systems. However, their behaviors in shared memory systems are so mysterious that very little…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
The celebrated Asynchronous Computability Theorem of Herlihy and Shavit (STOC 1993 and STOC 1994) provided a topological characterization of the tasks that are solvable in a distributed system where processes are communicating by writing…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney…
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…