# On the k-atomicity-verification problem

### Venue

The 33rd International Conference on Distributed Computing Systems, IEEE (2013)

### Publication Year

2013

### Authors

Wojciech Golab, Jeremy Hurwitz, Xiaozhou Li

### BibTeX

## Abstract

Modern Internet-scale storage systems often provide weak consistency in exchange
for better perfor- mance and resilience. An important weak consistency prop- erty
is k-atomicity, which bounds the staleness of values returned by read operations.
The k-atomicity-verification problem (or k-AV for short) is the problem of deciding
whether a given history of operations is k-atomic. The 1-AV problem is equivalent
to verifying atomicity/linearizability, a well-known and solved problem. However,
for k ? 2, no polynomial-time k-AV algorithm is known. This paper makes the
following contributions towards solving the k-AV problem. First, we present a
simple 2- AV algorithm called LBT, which is likely to be efficient (quasilinear)
for histories that arise in practice, although it is less efficient (quadratic) in
the worst case. Second, we present a more involved 2-AV algorithm called FZF, which
runs efficiently (quasilinear) even in the worst case. To our knowledge, these are
the first algorithms that solve the 2-AV problem fully. Third, we show that the
weighted k-AV problem, a natural extension of the k-AV problem, is NP-complete.