We address the problem of validity in eventually consistent (EC) systems: In what sense does an EC data structure satisfy the sequential specification of that data structure? Because EC is a very weak criterion, our definition does not describe every EC system; however it is expressive enough to describe any Convergent or Commutative Replicated Data Type (CRDT).

In globally distributed systems, shared state is never perfect. When communication is neither fast nor reliable, we cannot achieve strong consistency, low latency, and availability at the same time. Unfortunately, abandoning strong consistency has wide ramifications. Eventual consistency, though attractive from a performance viewpoint, is challenging to understand and reason about, both for sys...

the main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

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 general theoretical properties of them is known. In this paper, we lay the theoretical foundation of the study of eventually linearizable objects. We prove ...

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns a...

The parents of children with Down syndrome were asked to fill a questionnaire about how much their children understand and how well they use words. It was found that except the frequency, the words that are related to eventual misbalance of the body also influence the word acquisition. Keeping the balance of their body is a typically difficult motor task for DS children, thus the results are in...

Let A be a finite subset of an abelian group G . For every element bi of the sumset 2A={b0, b1, ..., b|2A|−1} we denote by Di={a − a′ : a, a′∈A; a+a′=bi} and ri=|{(a, a′) : a+a′=bi; a, a′∈A}| . After an eventual reordering of 2A , we may assume that r0>r1>...>r|2A|−1. For every 16s6|2A| we define Rs(A) = |D0∪D1∪...∪Ds−1| and Rs(k)= max{Rs(A) : A⊆G, |A|=k}. Bourgain and Katz and Tao obtained an ...