1,704 research outputs found
Sources of Superlinearity in Davenport-Schinzel Sequences
A generalized Davenport-Schinzel sequence is one over a finite alphabet that
contains no subsequences isomorphic to a fixed forbidden subsequence. One of
the fundamental problems in this area is bounding (asymptotically) the maximum
length of such sequences. Following Klazar, let Ex(\sigma,n) be the maximum
length of a sequence over an alphabet of size n avoiding subsequences
isomorphic to \sigma. It has been proved that for every \sigma, Ex(\sigma,n) is
either linear or very close to linear; in particular it is O(n
2^{\alpha(n)^{O(1)}}), where \alpha is the inverse-Ackermann function and O(1)
depends on \sigma. However, very little is known about the properties of \sigma
that induce superlinearity of \Ex(\sigma,n).
In this paper we exhibit an infinite family of independent superlinear
forbidden subsequences. To be specific, we show that there are 17 prototypical
superlinear forbidden subsequences, some of which can be made arbitrarily long
through a simple padding operation. Perhaps the most novel part of our
constructions is a new succinct code for representing superlinear forbidden
subsequences
Запрещенные треки и запрещенные подтреки
Поняття заборонених рядків та підпослідовностей, що застосовуються до рядків, узагальнені на треки. Стаття містить розв’язок задач побудови для заданого трека множин заборонених треків та заборонених підтреківThe notions of forbidden strings and forbidden subsequences are generalized to traces. The paper presents algorithms to construct sets of minimum forbidden traces and minimum forbidden subtraces for a given trace
Symbolic dynamics and synchronization of coupled map networks with multiple delays
We use symbolic dynamics to study discrete-time dynamical systems with
multiple time delays. We exploit the concept of avoiding sets, which arise from
specific non-generating partitions of the phase space and restrict the
occurrence of certain symbol sequences related to the characteristics of the
dynamics. In particular, we show that the resulting forbidden sequences are
closely related to the time delays in the system. We present two applications
to coupled map lattices, namely (1) detecting synchronization and (2)
determining unknown values of the transmission delays in networks with possibly
directed and weighted connections and measurement noise. The method is
applicable to multi-dimensional as well as set-valued maps, and to networks
with time-varying delays and connection structure.Comment: 13 pages, 4 figure
Using Regular Languages to Explore the Representational Capacity of Recurrent Neural Architectures
The presence of Long Distance Dependencies (LDDs) in sequential data poses
significant challenges for computational models. Various recurrent neural
architectures have been designed to mitigate this issue. In order to test these
state-of-the-art architectures, there is growing need for rich benchmarking
datasets. However, one of the drawbacks of existing datasets is the lack of
experimental control with regards to the presence and/or degree of LDDs. This
lack of control limits the analysis of model performance in relation to the
specific challenge posed by LDDs. One way to address this is to use synthetic
data having the properties of subregular languages. The degree of LDDs within
the generated data can be controlled through the k parameter, length of the
generated strings, and by choosing appropriate forbidden strings. In this
paper, we explore the capacity of different RNN extensions to model LDDs, by
evaluating these models on a sequence of SPk synthesized datasets, where each
subsequent dataset exhibits a longer degree of LDD. Even though SPk are simple
languages, the presence of LDDs does have significant impact on the performance
of recurrent neural architectures, thus making them prime candidate in
benchmarking tasks.Comment: International Conference of Artificial Neural Networks (ICANN) 201
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