550 research outputs found
Algebraic synchronization criterion and computing reset words
We refine a uniform algebraic approach for deriving upper bounds on reset
thresholds of synchronizing automata. We express the condition that an
automaton is synchronizing in terms of linear algebra, and obtain upper bounds
for the reset thresholds of automata with a short word of a small rank. The
results are applied to make several improvements in the area.
We improve the best general upper bound for reset thresholds of finite prefix
codes (Huffman codes): we show that an -state synchronizing decoder has a
reset word of length at most . In addition to that, we prove
that the expected reset threshold of a uniformly random synchronizing binary
-state decoder is at most . We also show that for any non-unary
alphabet there exist decoders whose reset threshold is in .
We prove the \v{C}ern\'{y} conjecture for -state automata with a letter of
rank at most . In another corollary, based on the recent
results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture
does not hold for a random synchronizing binary automaton is exponentially
small in terms of the number of states, and also that the expected value of the
reset threshold of an -state random synchronizing binary automaton is at
most .
Moreover, reset words of lengths within all of our bounds are computable in
polynomial time. We present suitable algorithms for this task for various
classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata,
for which our results can be applied.Comment: 18 pages, 2 figure
Error resilient image transmission using T-codes and edge-embedding
Current image communication applications involve image transmission over noisy channels, where the image gets damaged. The loss of synchronization at the decoder due to these errors increases the damage in the reconstructed image. Our main goal in this research is to develop an algorithm that has the capability to detect errors, achieve synchronization and conceal errors.;In this thesis we studied the performance of T-codes in comparison with Huffman codes. We develop an algorithm for the selection of best T-code set. We have shown that T-codes exhibit better synchronization properties when compared to Huffman Codes. In this work we developed an algorithm that extracts edge patterns from each 8x8 block, classifies edge patterns into different classes. In this research we also propose a novel scrambling algorithm to hide edge pattern of a block into neighboring 8x8 blocks of the image. This scrambled hidden data is used in the detection of errors and concealment of errors. We also develop an algorithm to protect the hidden data from getting damaged in the course of transmission
A prefix encoding for a constructed language
This work focuses in the formal and technical analysis of some aspects of a constructed
language.
As a first part of the work, a possible coding for the language will be studied, emphasizing the
pre x coding, for which an extension of the Hu man algorithm from binary to n-ary will be
implemented.
Because of that in the language we can't know a priori the frequency of use of the words, a
study will be done and several strategies will be proposed for an open words system, analyzing
previously the existing number of words in current natural languages.
As a possible upgrade of the coding, we'll take also a look to the synchronization loss problem,
as well as to its solution: the self-synchronization, a t-codes study with the number of possible
words for the language, as well as other alternatives.
Finally, and from a less formal approach, several applications for the language have been
developed: A voice synthesizer, a speech recognition system and a system font for the use
of the language in text processors. For each of these applications, the process used for its
construction, as well as the problems encountered and still to solve in each will be detailed
Lemon: an MPI parallel I/O library for data encapsulation using LIME
We introduce Lemon, an MPI parallel I/O library that is intended to allow for
efficient parallel I/O of both binary and metadata on massively parallel
architectures. Motivated by the demands of the Lattice Quantum Chromodynamics
community, the data is stored in the SciDAC Lattice QCD Interchange Message
Encapsulation format. This format allows for storing large blocks of binary
data and corresponding metadata in the same file. Even if designed for LQCD
needs, this format might be useful for any application with this type of data
profile. The design, implementation and application of Lemon are described. We
conclude with presenting the excellent scaling properties of Lemon on state of
the art high performance computers
Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel
A stochastic process's statistical complexity stands out as a fundamental
property: the minimum information required to synchronize one process generator
to another. How much information is required, though, when synchronizing over a
quantum channel? Recent work demonstrated that representing causal similarity
as quantum state-indistinguishability provides a quantum advantage. We
generalize this to synchronization and offer a sequence of constructions that
exploit extended causal structures, finding substantial increase of the quantum
advantage. We demonstrate that maximum compression is determined by the
process's cryptic order---a classical, topological property closely allied to
Markov order, itself a measure of historical dependence. We introduce an
efficient algorithm that computes the quantum advantage and close noting that
the advantage comes at a cost---one trades off prediction for generation
complexity.Comment: 10 pages, 6 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/oqs.ht
Algebraic synchronization criterion and computing reset words
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain new upper bounds for automata with a short word of small rank. The results are applied to make several improvements in the area. In particular, we improve the upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an n-state synchronizing decoder has a reset word of length at most O(nlog3n). In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary n-state decoder is at most O(nlog n). We prove the Černý conjecture for n-state automata with a letter of rank ≤6n−63. In another corollary, we show that the probability that the Černý conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and that the expected value of the reset threshold is at most n3/2+o(1). Moreover, all of our bounds are constructible. We present suitable polynomial algorithms for the task of finding a reset word of length within our bounds. © 201
Algebraic synchronization criterion and computing reset words
We refine results about relations between Markov chains and synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an n-state synchronizing decoder has a reset word of length at most O(n log3 n). Also, we prove the Černý conjecture for n-state automata with a letter of rank at most 3√6n-6. In another corollary, based on the recent results of Nicaud, we show that the probability that the Čern conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states. It follows that the expected value of the reset threshold of an n-state random synchronizing binary automaton is at most n7/4+o(1). Moreover, reset words of the lengths within our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata for which our results can be applied. These include (quasi-)one-cluster and (quasi-)Eulerian automata. © Springer-Verlag Berlin Heidelberg 2015
The further chameleon groups of Richard Thompson and Graham Higman : automorphisms via dynamics for the Higman groups Gn,r
Funding: The first and second authors wish to acknowledge support from EPSRC grant EP/R032866/1 received during the editing process of this article. The fourth author would like to thank St. Andrews University for its hospitality during the Workshop on the Extended Family of Thompson’s Groups in 2014, and acknowledges the support of DySYRF (Anillo Project 1103, CONICYT) and Fondecyt’s project 1120131. The fifth author was partly supported by Leverhulme Trust Research Project Grant RPG-2017-159.We characterise the automorphism groups of the Higman groups Gn,r as groups of specific homeomorphisms of Cantor spaces Cn,r, through the use of Rubin's theorem. This continues a thread of research begun by Brin, and extended later by Brin and Guzmán: to characterise the automorphism groups of the 'Chameleon groups of Richard Thompson,' as Brin referred to them in 1996. The work here completes the first stage of that twenty-year-old program, containing (amongst other things) a characterisation of the automorphism group of V, which was the 'last chameleon.' As it happens, the homeomorphisms which arise naturally fit into the framework of Grigorchuk, Nekrashevich, and Suschanskiī's rational group of transducers, and exhibit fascinating connections with the theory of reset words for automata (arising in the Road Colouring Problem), while also appearing to offer insight into the nature of Brin and Guzmán's exotic automorphisms.PostprintPeer reviewe
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