Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sublinear-Time Computation in the Presence of Online Erasures   We initiate the study of sublinear-time algorithms that access their input
via an online adversarial erasure oracle. After answering each query to the
input object, such an oracle can erase $t$ input values. Our goal is to
understand the complexity of basic computational tasks in extremely adversarial
situations, where the algorithm's access to data is blocked during the
execution of the algorithm in response to its actions. Specifically, we focus
on property testing in the model with online erasures. We show that two
fundamental properties of functions, linearity and quadraticity, can be tested
for constant $t$ with asymptotically the same complexity as in the standard
property testing model. For linearity testing, we prove tight bounds in terms
of $t$, showing that the query complexity is $\Theta(\log t)$. In contrast to
linearity and quadraticity, some other properties, including sortedness and the
Lipschitz property of sequences, cannot be tested at all, even for $t=1$. Our
investigation leads to a deeper understanding of the structure of violations of
linearity and other widely studied properties.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci