2,847 research outputs found
Geodesic growth in virtually abelian groups
We show that the geodesic growth function of any finitely generated virtually
abelian group is either polynomial or exponential; and that the geodesic growth
series is holonomic, and rational in the polynomial growth case. In addition,
we show that the language of geodesics is blind multicounter.Comment: 23 pages, 1 figure, improved readabilit
Automates à contraintes semilinéaires = Automata with a semilinear constraint
Cette thèse présente une étude dans divers domaines de l'informatique
théorique de modèles de calculs combinant automates finis et contraintes
arithmétiques. Nous nous intéressons aux questions de décidabilité,
d'expressivité et de clôture, tout en ouvrant l'étude à la complexité, la
logique, l'algèbre et aux applications. Cette étude est présentée au travers
de quatre articles de recherche.
Le premier article, Affine Parikh Automata, poursuit l'étude de Klaedtke et Ruess
des automates de Parikh et en définit des généralisations et restrictions.
L'automate de Parikh est un point de départ de cette thèse; nous montrons que
ce modèle de calcul est équivalent à l'automate contraint que nous
définissons comme un automate qui n'accepte un mot que si le nombre de fois
que chaque transition est empruntée répond à une contrainte arithmétique.
Ce modèle est naturellement étendu à l'automate de Parikh affine qui
effectue une opération affine sur un ensemble de registres lors du
franchissement d'une transition. Nous étudions aussi l'automate de
Parikh sur lettres: un automate qui n'accepte un mot que si le nombre de
fois que chaque lettre y apparaît répond à une contrainte arithmétique.
Le deuxième article, Bounded Parikh Automata, étudie les langages
bornés des automates de Parikh. Un langage est borné s'il existe des
mots w_1, w_2, ..., w_k tels que chaque mot du langage peut s'écrire
w_1...w_1w_2...w_2...w_k...w_k. Ces langages sont
importants dans des domaines applicatifs et présentent usuellement de bonnes
propriétés théoriques. Nous montrons que dans le contexte des langages
bornés, le déterminisme n'influence pas l'expressivité des automates de
Parikh.
Le troisième article, Unambiguous Constrained Automata, introduit les
automates contraints non ambigus, c'est-à-dire pour lesquels il
n'existe qu'un chemin acceptant par mot reconnu par l'automate. Nous
montrons qu'il s'agit d'un modèle combinant une meilleure expressivité et de
meilleures propriétés de clôture que l'automate contraint déterministe. Le
problème de déterminer si le langage d'un automate contraint non ambigu est
régulier est montré décidable.
Le quatrième article, Algebra and Complexity Meet Contrained Automata,
présente une étude des représentations algébriques qu'admettent les automates
contraints et les automates de Parikh affines. Nous déduisons de ces
caractérisations des résultats d'expressivité et de complexité. Nous
montrons aussi que certaines hypothèses classiques en complexité
computationelle sont reliées à des résultats de séparation et de non clôture
dans les automates de Parikh affines.
La thèse est conclue par une ouverture à un possible approfondissement, au
travers d'un certain nombre de problèmes ouverts.This thesis presents a study from the theoretical computer science
perspective of computing models combining finite automata and arithmetic
constraints. We focus on decidability questions, expressiveness, and closure
properties, while opening the study to complexity, logic, algebra, and
applications. This thesis is presented through four research articles.
The first article, Affine Parikh Automata, continues the study of Klaedtke
and Ruess on Parikh automata and defines generalizations and restrictions of
this model. The Parikh automaton is one of the starting points of this
thesis. We show that this model of computation is equivalent to the
constrained automaton that we define as an automaton which accepts a word
only if the number of times each transition is taken satisfies a given
arithmetic constraint. This model is naturally extended to affine Parikh
automata, in which an affine transformation is applied to a set of registers
on taking a transition. We also study the Parikh automaton on letters, that
is, an automaton which accepts a word only if the number of times each letter
appears in the word verifies an arithmetic constraint.
The second article, Bounded Parikh Automata, focuses on the
bounded languages of Parikh automata. A language is bounded if there
are words w_1, w_2, ..., w_k such that every word in the language can be
written as w_1...w_1w_2...w_2 ... w_k...w_k. These languages
are important in applications and usually display good theoretical
properties. We show that, over the bounded languages, determinism does not
influence the expressiveness of Parikh automata.
The third article, Unambiguous Constrained Automata, introduces the
concept of unambiguity in constrained automata. An automaton is
unambiguous if there is only one accepting path per word of its language. We
show that the unambiguous constrained automaton is an appealing model of
computation which combines a better expressiveness and better closure
properties than the deterministic constrained automaton. We show that it is
decidable whether the language of an unambiguous constrained automaton is
regular.
The fourth article, Algebra and Complexity Meet Constrained Automata,
presents a study of algebraic representations of constrained automata and
affine Parikh automata. We deduce expressiveness and complexity results from
these characterizations. We also study how classical computational
complexity hypotheses help in showing separations and nonclosure properties
in affine Parikh automata.
The thesis is concluded by a presentation of possible future avenues of
research, through several open problems
Two-Way Visibly Pushdown Automata and Transducers
Automata-logic connections are pillars of the theory of regular languages.
Such connections are harder to obtain for transducers, but important results
have been obtained recently for word-to-word transformations, showing that the
three following models are equivalent: deterministic two-way transducers,
monadic second-order (MSO) transducers, and deterministic one-way automata
equipped with a finite number of registers. Nested words are words with a
nesting structure, allowing to model unranked trees as their depth-first-search
linearisations. In this paper, we consider transformations from nested words to
words, allowing in particular to produce unranked trees if output words have a
nesting structure. The model of visibly pushdown transducers allows to describe
such transformations, and we propose a simple deterministic extension of this
model with two-way moves that has the following properties: i) it is a simple
computational model, that naturally has a good evaluation complexity; ii) it is
expressive: it subsumes nested word-to-word MSO transducers, and the exact
expressiveness of MSO transducers is recovered using a simple syntactic
restriction; iii) it has good algorithmic/closure properties: the model is
closed under composition with a unambiguous one-way letter-to-letter transducer
which gives closure under regular look-around, and has a decidable equivalence
problem
Advances in architectural concepts to support distributed systems design
This paper presents and discusses some architectural concepts for distributed systems design. These concepts are derived from an analysis of limitations of some currently available standard design languages. We conclude that language design should be based upon the careful consideration of architectural concepts. This paper aims at supporting designers by presenting a methodological design framework in which they can reason about the design and implementation of distributed systems. The paper is also meant for language developers and formalists by presenting a collection of architectural concepts which deserve consideration for formal support
Solving the Weighted HOM-Problem With the Help of Unambiguity
The HOM-problem, which asks whether the image of a regular tree language
under a tree homomorphism is again regular, is known to be decidable by [Godoy,
Gim\'enez, Ramos, \`Alvarez: The HOM problem is decidable. STOC (2010)].
Research on the weighted version of this problem, however, is still in its
infancy since it requires customized investigations. In this paper we address
the weighted HOM-problem and strive to keep the underlying semiring as general
as possible. In return, we restrict the input: We require the tree homomorphism
h to be tetris-free, a condition weaker than injectivity, and for the given
weighted tree automaton, we propose an ambiguity notion with respect to h.
These assumptions suffice to ensure decidability of the thus restricted
HOM-problem for all zero-sum free semirings by allowing us to reduce it to the
(decidable) unweighted case.Comment: In Proceedings AFL 2023, arXiv:2309.0112
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