scholarly journals Projections et cohérence de vues dans les grammaires algébriques

2008 ◽  
Vol Volume 8, Special Issue... ◽  
Author(s):  
Eric Badouel ◽  
Maurice Tchoupé Tchendji
Keyword(s):  
Global Structure ◽  
Lazy Evaluation ◽  
Document Structure ◽  
Legal Structures ◽  
International Audience ◽  
Structured Document ◽  
Partial View ◽  
Context Free ◽  
Infinite Set ◽  
Structural Aspects

International audience A complex structured document is intentionnally represented as a tree decorated with attributes. The set of legal structures is given by an abstract context-free grammar. We forget about the attributes; they are related with semantical issues that can be treated independently of the purely structural aspects that we address in this article. That intentional representation may be asynchronously manipulated by a set of independent tools each of which operates on a distinct partial view of the whole structure. In order to synchronize these various partial views, we are faced to the problem of their coherence: can we decide whether there exists some global structure corresponding to a given set of partial views and in the affirmative, can we produce such a global structure ? We solve this problem in the case where a view is given by a subset of grammatical symbols, those associated with the so-called visible syntactical categories. The proposed algorithm, that strongly relies on the mechanism of lazy evaluation, produces an answer to this problem even if partial views may correspond to an infinite set of related global structures. Un document structuré complexe est représenté intentionnellement sous la forme d'une structure arborescente décorée par des attributs. Les structures licites sont caractérisées par une grammaire algébrique abstraite. Nous faisons ici abstraction des attributs ; ces derniers sont liés à des aspects sémantiques qui peuvent être traités séparément des aspects purement structurels qui nous intéressent ici. Cette représentation intentionnelle peut être manipulée de façon indépendante et éventuellement non synchronisée par divers outils d'édition et de manipulation qui opèrent sur des vues partielles distinctes du même document. Pour la re-synchronisation de ces vues partielles nous devons résoudre le problème de leur cohérence : décider s'il existe un document correspondant à ces différentes vues et dans l'affirmative produire un tel document. Nous montrons comment résoudre ce problème dans le cas où chaque vue est associée à un sous-ensemble des symboles grammaticaux : ceux qui correspondent aux catégories syntaxiques visibles. L'algorithme proposé, qui repose fortement sur le mécanisme d'évaluation paresseuse, résout ce problème même dans le cas où chaque vue partielle correspond à un nombre infini de documents possibles.

scholarly journals Constrained exchangeable partitions

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Alexander Gnedin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Partitions ◽  
Type Representation ◽  
International Audience ◽  
De Finetti ◽  
Infinite Set ◽  
Special Case

International audience For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

scholarly journals Toward the asymptotic count of bi-modular hidden patterns under probabilistic dynamical sources: a case study

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Loïck Lhote ◽  
Manuel E. Lladser
Keyword(s):  
Technical Difficulty ◽  
Memory Length ◽  
Asymptotically Normal ◽  
International Audience ◽  
Finite Memory ◽  
Hidden Patterns ◽  
Context Free ◽  
With Memory ◽  
Random Text

International audience Consider a countable alphabet $\mathcal{A}$. A multi-modular hidden pattern is an $r$-tuple $(w_1,\ldots , w_r)$, where each $w_i$ is a word over $\mathcal{A}$ called a module. The hidden pattern is said to occur in a text $t$ when the later admits the decomposition $t = v_0 w_1v_1 \cdots v_{r−1}w_r v_r$, for arbitrary words $v_i$ over $\mathcal{A}$. Flajolet, Szpankowski and Vallée (2006) proved via the method of moments that the number of matches (or occurrences) with a multi-modular hidden pattern in a random text $X_1\cdots X_n$ is asymptotically Normal, when $(X_n)_{n\geq1}$ are independent and identically distributed $\mathcal{A}$-valued random variables. Bourdon and Vallée (2002) had conjectured however that asymptotic Normality holds more generally when $(X_n)_{n\geq1}$ is produced by an expansive dynamical source. Whereas memoryless and Markovian sequences are instances of dynamical sources with finite memory length, general dynamical sources may be non-Markovian i.e. convey an infinite memory length. The technical difficulty to count hidden patterns under sources with memory is the context-free nature of these patterns as well as the lack of logarithm-and exponential-type transformations to rewrite the product of non-commuting transfer operators. In this paper, we address a case study in which we have successfully overpassed the aforementioned difficulties and which may illuminate how to address more general cases via auto-correlation operators. Our main result shows that the number of matches with a bi-modular pattern $(w_1, w_2)$ normalized by the number of matches with the pattern $w_1$, where $w_1$ and $w_2$ are different alphabet characters, is indeed asymptotically Normal when $(X_n)_{n\geq1}$ is produced by a holomorphic probabilistic dynamical source.

scholarly journals Grammatical compression: compressed equivalence and other problems

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Alberto Bertoni ◽  
Roberto Radicioni
Keyword(s):  
Strategic Games ◽  
Special Issue ◽  
Ability To Work ◽  
Inclusion Problems ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
International Audience ◽  
Context Free ◽  
Compressed Data ◽  
Straight Line Programs

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience In this work, we focus our attention to algorithmic solutions for problems where the instances are presented as straight-line programs on a given algebra. In our exposition, we try to survey general results by presenting some meaningful examples; moreover, where possible, we outline the proofs in order to give an insight of the methods and the techniques. We recall some recent results for the problem PosSLP, consisting of deciding if the integer defined by a straight-line program on the ring Z is greater than zero; we discuss some implications in the areas of numerical analysis and strategic games. Furthermore, we propose some methods for reducing Compressed Word Problem from an algebra to another; reductions from trace monoids to the semiring of nonnegative integers are exhibited and polynomial time algorithms for compressed equivalence in monoids related to Dyck reductions are shown. Finally, we consider inclusion problems for context-free languages, proving how in some cases efficient algorithms for these problems benefit from the ability to work with compressed data.

scholarly journals Regular languages and associative language descriptions

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Marcella Anselmo ◽  
Alessandra Cherubini ◽  
Pierluigi San Pietro
Keyword(s):  
Regular Languages ◽  
Brain Organization ◽  
Constituent Structure ◽  
International Audience ◽  
Explanatory Adequacy ◽  
Context Free ◽  
Language Description

International audience The Associative Language Description model (ALD) is a combination of locally testable and constituent structure ideas. It is consistent with current views on brain organization and can rather conveniently describe typical technical languages such as Pascal or HTML. ALD languages are strictly enclosed in context-free languages but in practice the ALD model equals CF grammars in explanatory adequacy. Various properties of ALD have been investigated, but many theoretical questions are still open. For instance, it is unknown, at the present, whether the ALD family includes the regular languages. Here it is proved that several known classes of regular languages are ALD: threshold locally testable languages, group languages, positive commutative languages and commutative languages on 2-letter alphabets. Moreover, we show that there is an ALD language in each level of (restricted) star height hierarchy. These results seem to show that ALD languages are well-distributed over the class of regular languages.

scholarly journals Coefficients of algebraic functions: formulae and asymptotics

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Cyril Banderier ◽  
Michael Drmota
Keyword(s):  
Critical Exponents ◽  
Entire Functions ◽  
Limit Laws ◽  
Context Free Grammar ◽  
Algebraic Functions ◽  
Strongly Connected ◽  
International Audience ◽  
Planar Maps ◽  
Dyadic Numbers ◽  
Context Free

International audience This paper studies the coefficients of algebraic functions. First, we recall the too-little-known fact that these coefficients $f_n$ have a closed form. Then, we study their asymptotics, known to be of the type $f_n \sim C A^n n^{\alpha}$. When the function is a power series associated to a context-free grammar, we solve a folklore conjecture: the appearing critical exponents $\alpha$ can not be $^1/_3$ or $^{-5}/_2$, they in fact belong to a subset of dyadic numbers. We extend what Philippe Flajolet called the Drmota-Lalley-Woods theorem (which is assuring $\alpha=^{-3}/_2$ as soon as a "dependency graph" associated to the algebraic system defining the function is strongly connected): We fully characterize the possible critical exponents in the non-strongly connected case. As a corollary, it shows that certain lattice paths and planar maps can not be generated by a context-free grammar (i.e., their generating function is not $\mathbb{N}-algebraic). We end by discussing some extensions of this work (limit laws, systems involving non-polynomial entire functions, algorithmic aspects). Cet article a pour héros les coefficients des fonctions algébriques. Après avoir rappelé le fait trop peu connu que ces coefficients $f_n$ admettent toujours une forme close, nous étudions leur asymptotique $f_n \sim C A^n n^{\alpha}$. Lorsque la fonction algébrique est la série génératrice d'une grammaire non-contextuelle, nous résolvons une vieille conjecture du folklore : les exposants critiques $\alpha$ ne peuvent pas être $^1/_3$ ou $^{-5}/_2$ et sont en fait restreints à un sous-ensemble des nombres dyadiques. Nous étendons ce que Philippe Flajolet appelait le théorème de Drmota-Lalley-Woods (qui affirme que $\alpha=^{-3}/_2$ dès lors qu'un "graphe de dépendance" associé au système algébrique est fortement connexe) : nous caractérisons complètement les exposants critiques dans le cas non fortement connexe. Un corolaire immédiat est que certaines marches et cartes planaires ne peuvent pas être engendrées par une grammaire non-contextuelle non ambigüe (i. e., leur série génératrice n'est pas $\mathbb{N}-algébrique). Nous terminons par la discussion de diverses extensions de nos résultats (lois limites, systèmes d'équations de degré infini, aspects algorithmiques).

scholarly journals Structure of Stable Sand Piles Model

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Thi Ha Duong Phan ◽  
Thi Thu Huong Tran
Keyword(s):  
Lattice Structure ◽  
Stable Configuration ◽  
Recursive Structure ◽  
Evolution Rule ◽  
Generating Tree ◽  
International Audience ◽  
Sand Piles ◽  
Infinite Set

International audience In this paper we study a variant of the Sand Piles Model, where the evolution rule consists of the falling down of one grain to a random column and an avalanche to reach a stable configuration. We prove that the infinite set of all stable configurations have a lattice structure which is a sublattice of Young lattice. At the end, based on a discussion about avalanches, we construct a generating tree of this model and show its strongtly recursive structure.

scholarly journals Cache efficient simple dynamic programming

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Cary Cherng ◽  
Richard E. Ladner
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Recognition Algorithm ◽  
Programming Algorithm ◽  
Language Recognition ◽  
International Audience ◽  
Cache Efficient ◽  
Programming Algorithms ◽  
Context Free ◽  
Cache Oblivious

International audience New cache-oblivious and cache-aware algorithms for simple dynamic programming based on Valiant's context-free language recognition algorithm are designed, implemented, analyzed, and empirically evaluated with timing studies and cache simulations. The studies show that for large inputs the cache-oblivious and cache-aware dynamic programming algorithms are significantly faster than the standard dynamic programming algorithm.

scholarly journals A Context free language associated with interval maps

2016 ◽  
Vol Vol. 18 no. 3 ◽  
Author(s):  
M Archana ◽  
V Kannan
Keyword(s):  
Periodic Points ◽  
Interval Maps ◽  
Context Free Language ◽  
Interval Map ◽  
International Audience ◽  
Context Free ◽  
Free Language

International audience For every interval map with finitely many periodic points of periods 1 and 2, we associate a word by taking the periods of these points from left to right. It is natural to ask which words arise in this manner. In this paper we give two different characterizations of the language obtained in this way.

scholarly journals Multi-dimensional Boltzmann Sampling of Languages

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Olivier Bodini ◽  
Yann Ponty
Keyword(s):  
Frequency Of Occurrence ◽  
Random Generation ◽  
Tolerance Intervals ◽  
Strong Connectivity ◽  
Expected Time ◽  
Context Free Language ◽  
Different Types ◽  
International Audience ◽  
Context Free ◽  
Free Language

International audience We address the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers. We show that, under mostly $\textit{strong-connectivity}$ hypotheses, our samplers return a word of size in $[(1- \epsilon)n, (1+ \epsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega (\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate our approach on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.

scholarly journals E-unification by means of tree tuple synchronized grammars

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Sébastien Limet ◽  
Pierre Réty
Keyword(s):  
Equational Theory ◽  
International Audience ◽  
Infinite Set ◽  
Rewrite System

International audience The goal of this paper is both to give an E-unification procedure that always terminates, and to decide unifiability. For this, we assume that the equational theory is specified by a confluent and constructor-based rewrite system, and that four additional restrictions are satisfied. We give a procedure that represents the (possibly infinite) set of solutions thanks to a tree tuple synchronized grammar, and that can decide upon unifiability thanks to an emptiness test. Moreover, we show that if only three of the four additional restrictions are satisfied then unifiability is undecidable.

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