Advanced Synchronization of Audio or Symbolic Musical Patterns: An Algebraic Approach

Berthaut, Florent; Janin, David; Martin, Benjamin

doi:10.1109/icsc.2012.11

Cited by 8 publications

(11 citation statements)

References 9 publications

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“…Plus précisément, comme illustré Figure 10, la nature tout à la fois C'est cette caractéristique qui nous a conduits à définir et à utiliser le modèle des bi-arbres dans le domaine de la modélisation [11,4,15] ou la programmation [14]ămusicale. Son utilisation dans un contexte plus général reste à explorer.…”

Section: Resultsunclassified

Modélisation algébrique du dîner des philosophes

Dicky¹,

Janin²

2013

Journal Européen des Systèmes Automatisés

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Section: Resultsunclassified

Modélisation algébrique du dîner des philosophes

Dicky¹,

Janin²

2013

Journal Européen des Systèmes Automatisés

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“…Formally, L is the least relation over words such that, for all u 0 and v 0 ∈ A * , u 0 L v 0 when for all w 0 , w 2 , w 3 and w 4 ∈ A * , if u = (w 1 u 0 w 2 , w 3 , w 4 ) and v = (w 1 v 0 w 2 , w 3 , w 4 ), or if u = (w 1 , w 2 u 0 w 3 , w 4 ) and v = (w 1 , w 2 v 0 w 3 , w 4 ), or if u = (w 1 , w 2 , w 3 u 3 w 4 ) and v = (w 0 , w 2 …”

Section: A Word Congruence For Languages Of Tilesmentioning

confidence: 99%

“…For this, it is enough to check that for any two non zero tiles u = (u 1 , u 2 , u 3 ) and 2 ) and thus this just amounts to check that…”

Section: Proof (Sketch Of) For All Non Zero Tilementioning

confidence: 99%

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On Languages of One-Dimensional Overlapping Tiles

Janin

2013

Lecture Notes in Computer Science

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A one-dimensional tile with overlaps is a standard finite word that carries some more information that is used to say when the concatenation of two tiles is legal. Known since the mid 70's in the rich mathematical field of inverse monoid theory, this model of tiles with the associated partial product have yet not been much studied in theoretical computer science despite some implicit appearances in studies of two-way automata in the 80's.In this paper, after giving an explicit description of McAlister monoid, we define and study several classical classes of languages of tiles: from recognizable languages (REC) definable by morphism into finite monoids up to languages definable in monadic second order logic (MSO).We show that the class of MSO definable languages of tiles is both simple: these languages are finite sums of Cartesian products of rational languages, and robust: the class is closed under product, iterated product (star), inverse and projection on context tiles. A equivalent notion of regular expression is deduced from these results.The much smaller class of REC recognizable languages of tiles is then studied. We describe few examples and we prove that these languages are tightly linked with covers of periodic bi-infinite words.

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“…Inverse semigroup theory has also been used to study reversible computations [10,1]. More recently, various modeling experiments have been conducted in computational music [3,21]. These last experiments also led to the definition of a Domain Specific (Programing) Language (DSL) which semantics is based on concepts arising from inverse semigroup theory [22,14].…”

Section: Introductionmentioning

confidence: 99%

Inverse Monoids of Higher-Dimensional Strings

Janin

2015

Theoretical Aspects of Computing - ICTAC 2015

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Abstract.Halfway between graph transformation theory and inverse semigroup theory, we define higher dimensional strings as bi-deterministic graphs with distinguished sets of input roots and output roots. We show that these generalized strings can be equipped with an associative product so that the resulting algebraic structure is an inverse semigroup. Its natural order is shown to capture existence of root preserving graph morphism. A simple set of generators is characterized. As a subsemigroup example, we show how all finite grids are finitely generated. Finally, simple additional restrictions on products lead to the definition of subclasses with decidable Monadic Second Order (MSO) language theory.

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Advanced Synchronization of Audio or Symbolic Musical Patterns: An Algebraic Approach

Cited by 8 publications

References 9 publications

Modélisation algébrique du dîner des philosophes

Modélisation algébrique du dîner des philosophes

On Languages of One-Dimensional Overlapping Tiles

Inverse Monoids of Higher-Dimensional Strings

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