3,984 research outputs found
Iterative methods based on splittings for stochastic automata networks
Cataloged from PDF version of article.This paper presents iterative methods based on splittings (Jacobi, Gauss-Seidel, Successive Over Relaxation) and their block versions for Stochastic Automata Networks (SANs). These methods prove to be better than the power method that has been used to solve SANs until recently. With the help of three examples we show that the time it takes to solve a system modeled as a SAN is still substantial and it does not seem to be possible to solve systems with tens of millions of states on standard desktop workstations with the current state of technology. However, the SAN methodology enables one to solve much larger models than those could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense. (C) 1998 Elsevier Science B.V. All rights reserved
A Fast Algorithm Finding the Shortest Reset Words
In this paper we present a new fast algorithm finding minimal reset words for
finite synchronizing automata. The problem is know to be computationally hard,
and our algorithm is exponential. Yet, it is faster than the algorithms used so
far and it works well in practice. The main idea is to use a bidirectional BFS
and radix (Patricia) tries to store and compare resulted subsets. We give both
theoretical and practical arguments showing that the branching factor is
reduced efficiently. As a practical test we perform an experimental study of
the length of the shortest reset word for random automata with states and 2
input letters. We follow Skvorsov and Tipikin, who have performed such a study
using a SAT solver and considering automata up to states. With our
algorithm we are able to consider much larger sample of automata with up to
states. In particular, we obtain a new more precise estimation of the
expected length of the shortest reset word .Comment: COCOON 2013. The final publication is available at
http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1
Complexity of Road Coloring with Prescribed Reset Words
By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic
directed multigraph with a constant out-degree can be colored such that the
resulting automaton admits a reset word. There may also be a need for a
particular reset word to be admitted. For certain words it is NP-complete to
decide whether there is a suitable coloring of a given multigraph. We present a
classification of all words over the binary alphabet that separates such words
from those that make the problem solvable in polynomial time. We show that the
classification becomes different if we consider only strongly connected
multigraphs. In this restricted setting the classification remains incomplete.Comment: To be presented at LATA 201
On the Two-View Geometry of Unsynchronized Cameras
We present new methods for simultaneously estimating camera geometry and time
shift from video sequences from multiple unsynchronized cameras. Algorithms for
simultaneous computation of a fundamental matrix or a homography with unknown
time shift between images are developed. Our methods use minimal correspondence
sets (eight for fundamental matrix and four and a half for homography) and
therefore are suitable for robust estimation using RANSAC. Furthermore, we
present an iterative algorithm that extends the applicability on sequences
which are significantly unsynchronized, finding the correct time shift up to
several seconds. We evaluated the methods on synthetic and wide range of real
world datasets and the results show a broad applicability to the problem of
camera synchronization.Comment: 12 pages, 9 figures, Computer Vision and Pattern Recognition (CVPR)
201
Preimage problems for deterministic finite automata
Given a subset of states of a deterministic finite automaton and a word
, the preimage is the subset of all states mapped to a state in by the
action of . We study three natural problems concerning words giving certain
preimages. The first problem is whether, for a given subset, there exists a
word \emph{extending} the subset (giving a larger preimage). The second problem
is whether there exists a \emph{totally extending} word (giving the whole set
of states as a preimage)---equivalently, whether there exists an
\emph{avoiding} word for the complementary subset. The third problem is whether
there exists a \emph{resizing} word. We also consider variants where the length
of the word is upper bounded, where the size of the given subset is restricted,
and where the automaton is strongly connected, synchronizing, or binary. We
conclude with a summary of the complexities in all combinations of the cases
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