299 research outputs found
Breadth-first serialisation of trees and rational languages
We present here the notion of breadth-first signature and its relationship
with numeration system theory. It is the serialisation into an infinite word of
an ordered infinite tree of finite degree. We study which class of languages
corresponds to which class of words and,more specifically, using a known
construction from numeration system theory, we prove that the signature of
rational languages are substitutive sequences.Comment: 15 page
Automatic sequences: from rational bases to trees
The th term of an automatic sequence is the output of a deterministic
finite automaton fed with the representation of in a suitable numeration
system. In this paper, instead of considering automatic sequences built on a
numeration system with a regular numeration language, we consider these built
on languages associated with trees having periodic labeled signatures and, in
particular, rational base numeration systems. We obtain two main
characterizations of these sequences. The first one is concerned with -block
substitutions where morphisms are applied periodically. In particular, we
provide examples of such sequences that are not morphic. The second
characterization involves the factors, or subtrees of finite height, of the
tree associated with the numeration system and decorated by the terms of the
sequence.Comment: 25 pages, 15 figure
Paronyms for Accelerated Correction of Semantic Errors
* Work done under partial support of Mexican Government (CONACyT, SNI), IPN (CGPI, COFAA) and Korean Government (KIPA
Professorship for Visiting Faculty Positions). The second author is currently on Sabbatical leave at Chung-Ang University.The errors usually made by authors during text preparation are classified. The notion of semantic
errors is elaborated, and malapropisms are pointed among them as “similar” to the intended word but
essentially distorting the meaning of the text. For whatever method of malapropism correction, we propose to
beforehand compile dictionaries of paronyms, i.e. of words similar to each other in letters, sounds or morphs.
The proposed classification of errors and paronyms is illustrated by English and Russian examples being valid
for many languages. Specific dictionaries of literal and morphemic paronyms are compiled for Russian. It is
shown that literal paronyms drastically cut down (up to 360 times) the search of correction candidates, while
morphemic paronyms permit to correct errors not studied so far and characteristic for foreigners
Characterizing morphic sequences
Morphic sequences form a natural class of infinite sequences, extending the
well-studied class of automatic sequences. Where automatic sequences are known
to have several equivalent characterizations and the class of automatic
sequences is known to have several closure properties, for the class of morphic
sequences similar closure properties are known, but only limited equivalent
characterizations. In this paper we extend the latter. We discuss a known
characterization of morphic sequences based on automata and we give a
characterization of morphic sequences by finiteness of a particular class of
subsequences. Moreover, we relate morphic sequences to rationality of infinite
terms and describe them by infinitary rewriting
On Buffon Machines and Numbers
The well-know needle experiment of Buffon can be regarded as an analog (i.e.,
continuous) device that stochastically "computes" the number 2/pi ~ 0.63661,
which is the experiment's probability of success. Generalizing the experiment
and simplifying the computational framework, we consider probability
distributions, which can be produced perfectly, from a discrete source of
unbiased coin flips. We describe and analyse a few simple Buffon machines that
generate geometric, Poisson, and logarithmic-series distributions. We provide
human-accessible Buffon machines, which require a dozen coin flips or less, on
average, and produce experiments whose probabilities of success are expressible
in terms of numbers such as, exp(-1), log 2, sqrt(3), cos(1/4), aeta(5).
Generally, we develop a collection of constructions based on simple
probabilistic mechanisms that enable one to design Buffon experiments involving
compositions of exponentials and logarithms, polylogarithms, direct and inverse
trigonometric functions, algebraic and hypergeometric functions, as well as
functions defined by integrals, such as the Gaussian error function.Comment: Largely revised version with references and figures added. 12 pages.
In ACM-SIAM Symposium on Discrete Algorithms (SODA'2011
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