Coding partitions

Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD), we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ''unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguous component and other (if any) totally ambiguous components. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes

Monoids and Maximal Codes

In recent years codes that are not Uniquely Decipherable (UD) are been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal code. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a maximal UD code.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Testing decipherability of directed figure codes with domino graphs

Various kinds of decipherability of codes, weaker than unique decipherability, have been studied since mid-1980s. We consider decipherability of directed gure codes, where directed gures are de ned as labelled polyomi- noes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible con icts. This setting ex- tends decipherability questions from words to 2D structures. In the present paper we develop a (variant of) domino graph that will allow us to decide some of the decipherability kinds by searching the graph for speci c paths. Thus the main result characterizes directed gure decipherability by graph properties

Testing decipherability of directed figure codes with domino graphs

Various kinds of decipherability of codes, weaker than unique de- cipherability, have been studied since mid-1980s. We consider decipherability of directed figure codes, where directed figures are defined as labelled polyomi- noes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts. This setting ex- tends decipherability questions from words to 2D structures. In the present paper we develop a (variant of) domino graph that will allow us to decide some of the decipherability kinds by searching the graph for specific paths. Thus the main result characterizes directed figure decipherability by graph properties

Thuật toán xác định tính chất mã của ngôn ngữ chính quy

We present an extension of the test proposed by Sardinas and Patterson (1953) for deciding whether a set of words is a code. As a consequence, we obtain an effective algorithm that decides in ${\cal O}(k)$ time whether a given regular language is a code, where $k$ is the finite index of the syntactic congruence of this language.Trong bài báo này, chúng tôi trình bày một thuật toán mới mở rộng thuật toán Sardinas-Patterson xác định tính chất mã của một ngôn ngữ. Từ đó nhận được một thuật toán với độ phức tạp cỡ ${\cal O}(k)$ để nhận biết một ngôn ngữ chính quy cho trước là mã hay không, với $k$ là chỉ số hữu hạn của tương đẳng cú pháp thỏa ngôn ngữ đó

Methods for relativizing properties of codes

The usual setting for information transmission systems assumes that all words over the source alphabet need to be encoded. The demands on encodings of messages with respect to decodability, error-detection, etc. are thus relative to the whole set of words. In reality, depending on the information source, far fewer messages are transmitted, all belonging to some specific language. Hence the original demands on encodings can be weakened, if only the words in that language are to be considered. This leads one to relativize the properties of encodings or codes to the language at hand. We analyse methods of relativization in this sense. It seems there are four equally convincing notions of relativization. We compare those. Each of them has their own merits for specific code properties. We clarify the differences between the four approaches. We also consider the decidability of relativized properties. If P is a property defining a class of codes and L is a language, one asks, for a given language C, whether C satisfies P relative to L. We show that in the realm of regular languages this question is mostly decidable

A peça musical como uma instância : ensaios acerca da análise musical assistida por computador

Orientadores: Jônatas Manzolli, Moreno AndreattaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Artes e Université Pierre et Marie Curie (França)Resumo: A partir de uma interpretação musicológica do conceito científico de "modelagem e simulação", esta tese apresenta uma abordagem para a análise musical assistida por computador onde partituras são reconstruídas a partir de processos algorítmicos e então simuladas através do uso de diferentes valores paramétricos resultando na geração de variações chamadas "instâncias". Investigar uma obra musical empregando "modelagem e simulações" significa buscar a sua compreensão através da uma atividade "recomposição", aproximando assim perspectivas analíticas e criativas. Esta abordagem foi aplicada em três casos de estudo: uma técnica isolada, a "multiplicação de acordes" usada pelo compositor francês Pierre Boulez (1925-2016) que foi explorada através do prisma formado pelas teorias de H. Hanson, S. Heinemann e L. Koblyakov e sua respectiva implementação computacional; a peça "Spectral Canon for Conlon Nancarrow" (1974) escrita pelo compositor americano James Tenney (1934-2006) na qual a simulação computacional a partir de diferentes valores paramétricos é levada às últimas consequências quando um "espaço de instâncias" é criado e estratégias de visualização são esboçadas; e por último a peça Désordre (1985), o primeiro estudo para piano escrito pelo austro-húngaro György Ligeti (1923-2006) onde os conceitos de "tonalidade combinatória" e "decomposição de um número inteiro (duração) em dois primos" são usados para maximizar o potencial de gerar diferentes variações através do respectivo modelo computacionalAbstract: From a musicological interpretation of the scientific notion of "modeling and simulation", this thesis presents an approach for computer-aided analysis where musical scores are reconstructed from algorithmic processes and then simulated with different sets of parameters from which neighboring variants, called instances, are generated. Studying a musical piece by modelling and simulation means to understand the work by (re)composing it again, blurring boundaries between analytical and creative work. This approach is applied to three case studies: an isolated technique, Pierre Boulez¿ (1925¿2016) Chord Multiplication, which was explored through the prism formed by the theories of H. Hanson, S. Heinemann and L. Koblyakov and by its computational implementation; the piece Spectral Canon for Conlon Nancarrow (1974) by the American composer James Tenney (1934¿2006) to which the computa- tional simulation from different sets of parameters was taken to its ultimate consequences when a "space of instances" is created and strategies of visu- alization and exploration are devised; and finally D ?esordre (1985), the first piano ?etude written by Austro-Hungarian Gyo ?rgy Ligeti (1923¿2006) in which the concepts of "combinatorial tonality" and "decomposition of a number (duration) into two prime numbers" were used to maximize the potential that a model has to produce different variations of the original pieceDoutoradoMúsica, Teoria, Criação e PráticaDoutor em Música2014/08525-8FAPES

"Establishing justice and telling stories" : paradigms of norm transmission in twelfth- and thirteenth-century Anglo-Norman and Old French literary and legal texts

The texts that comprise the corpus of Old French and Anglo-Norman literature of the twelfth and thirteenth centuries feature numerous portrayals of courtly life. The rules of that life, as they are presented in the literature, are contradictory, fluid, and open to interpretation. The tangle of courtly etiquette in Old French and Anglo-Norman literature, however, possesses certain recognizable recurring elements. These elements form something approaching a corpus of normative behaviours, expectations, and roles. We might even say, as Gadi Algazi and Stephen D. White have suggested, that medieval literature contains templates of various social and legal strategies of which the reader could have availed himself. This thesis seeks to study these norms and templates and how they are communicated. A detailed study of the ways they are transmitted within each text, coupled with an examination of their content, reveals much about authorial voice and stylistic technique. This dual study of form and content also illuminates the author’s understanding of honour, gender, the law, and justice. The literature also offers a glimpse into the psychology and strategy of the medieval legal process. This thesis seeks to build on this thematic connection between legal and literary texts. I therefore compare paradigms of norm transmission not only between individual literary texts, but also with paradigms in law books; specifically, the twelfth- and thirteenth-century coutumiers of Northern France, Glanvill, and Bracton’s De Legibus. The law books are analysed from a stylistic, literary angle, and the ideals of the “law book author” are proposed. Broadly, this thesis considers the process of storytelling, seeking to explain how legal texts tell the story of the law alongside contemporary literary conteurs

From 'Le cri de la nature' to 'Pygmalion' : a study of Jean-Jacques Rousseau's philosophy of music and aesthetic and reform of opera

Merged with duplicate record 10026.1/2742 on 06.20.2017 by CS (TIS)The thesis sets Rousseau's philosophy of music and aesthetic of opera against the wider philosophical backcloth of eighteenth-centuryF rance and in contraposition to the more scopic music-theoredcabl ackdrop,o f which Rameau'sw ritings are takena s a paradigm. The first half of the thesis contends that the philosophy of music is fashioned upon a trinary model which mirrors the philosophy of nature and history. The first sector is an ideal, hypothetical state; the second (the 'fall) is the moment when the ideal state is ruptured, when societal and cultural institutions - and history - commence; the third, is the 'actual state', the culmination of the process of history. It is argued that relativism is at work between the second and third sectorsa nd Rousseaua ssignsa rigorous systemo f value to the processo f history and all points alongi t, the processi tself, taken as a whole, is seena s a degeneratives lide awayf rom nearperfection to imperfection. 7111sce condh alf of the thesis explores the ramifications of the trinary model and the effect the degenerativep rocessh as upon the voice, music and opera. The voice is consideredt he unique phenomenon that connects all sectors of the trinary structure: though objectified and endowed with an ontology, it is not immune to the degenerativep rocess. At the fall-state,t he voice begins to rupture and two entities - melody and language - gradually emerge. Over time, melody and speech are forced further apart until neither bears much resemblance to the other. With the invention of harmony, melody degeneratesh: armony begins to overshadowm elody, until in the eighteenthc entury- consummatedin the music and theoreticalp ostulationso f Rameau- melody is subjugated and subsumed entirely within the harmonic domain of musical production. The impact upon opera is more complex and the concluding chapters explore the radical and largely reform-driven aesthetico f opera. Roussea&sf inal dramaticw ork Py gmalion(1 762)i s considered not simply as an outcome of this aesthetic, but as an embodiment of the philosophy of music itself; the animateds tatuee nunciatesR ousseau'sv ision of the origin of human expression