Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expressivity of Time-Varying Graphs and the Power of Waiting in Dynamic
  Networks   In infrastructure-less highly dynamic networks, computing and performing even
basic tasks (such as routing and broadcasting) is a very challenging activity
due to the fact that connectivity does not necessarily hold, and the network
may actually be disconnected at every time instant. Clearly the task of
designing protocols for these networks is less difficult if the environment
allows waiting (i.e., it provides the nodes with store-carry-forward-like
mechanisms such as local buffering) than if waiting is not feasible. No
quantitative corroborations of this fact exist (e.g., no answer to the
question: how much easier?). In this paper, we consider these qualitative
questions about dynamic networks, modeled as time-varying (or evolving) graphs,
where edges exist only at some times.
  We examine the difficulty of the environment in terms of the expressivity of
the corresponding time-varying graph; that is in terms of the language
generated by the feasible journeys in the graph. We prove that the set of
languages $L_{nowait}$ when no waiting is allowed contains all computable
languages. On the other end, using algebraic properties of quasi-orders, we
prove that $L_{wait}$ is just the family of regular languages. In other words,
we prove that, when waiting is no longer forbidden, the power of the accepting
automaton (difficulty of the environment) drops drastically from being as
powerful as a Turing machine, to becoming that of a Finite-State machine. This
(perhaps surprisingly large) gap is a measure of the computational power of
waiting.
  We also study bounded waiting; that is when waiting is allowed at a node only
for at most $d$ time units. We prove the negative result that $L_{wait[d]} =
L_{nowait}$; that is, the expressivity decreases only if the waiting is finite
but unpredictable (i.e., under the control of the protocol designer and not of
the environment).

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: stat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: eess