A Timed IO monad

Programming with explicit timing information is often tedious and error prone. This is especially visible in music programming where, when played, the specified durations of notes and rests must be shortened in order to compensate the actual duration of all surrounding processing. In this paper, we develop the notion of timed extension of a monad that aims at relieving programmers from such a burden. We show how, under simple conditions, such extensions can be built, and how useful features of monad programming such as asynchronous concurrency with promises or data-flow programming with monadic streams can be uniformly lifted to the resulting timed programming framework. Even though presented and developed in the abstract, the notion of timed extension of a monad is nevertheless illustrated by two concrete instances: a default timed IO monad where programmers specify durations in mi-croseconds, and a musically timed IO monad, where programmers specify durations in number of beats, the underlying tempo, that is, the speed of the music in beats per minute, possibly changed whenever needed

A robust algebraic framework for high-level music writing and programming

International audienceIn this paper, we present a new algebraic model for music programming : tiled musical graphs. It is based on the idea that the definition of musical objects : what they are, and the synchronization of these objects : when they should be played, are two orthogonal aspects of music programming that should be kept separate although handled in a combined way. This leads to the definition of an algebra of music objects : tiled music graphs, which can be combined by a single operator : the tiled product, that is neither sequential nor parallel but both. From a mathematical point of view, this algebra is known to be especially robust since it is an inverse monoid. Various operators such as the reset and the coreset projections derive from these algebra and turned out to be fairly useful for music modeling. From a programming point of view, it provide a high level domain specific language (DSL) that is both hierarchical and modular. This language is currently under implementation in the functional programming language Haskell. From an applicative point of view, various music modeling examples are provided to show how notes, chords, melodies, musical meters and various kind of interpretation aspects can easily and robustly be encoded in this formalism

Automata for the mu-calculus and Related Results

The propositional mu-calculus as introduced by Kozen in [4] isconsidered. The notion of disjunctive formula is defined and it is shownthat every formula is semantically equivalent to a disjunctive formula.For these formulas many difficulties encountered in the general case maybe avoided. For instance, satisfiability checking is linear for disjunctiveformulas. This kind of formula gives rise to a new notion of finite automatonwhich characterizes the expressive power of the mu-calculus overall transition systems

On labeled birooted tree languages: algebras, automata and logic

International audienceWith an aim to developing expressive language theoretical tools applicable to inverse semigroup languages, that is, subsets of inverse semigroups, this paper explores the language theory of finite labeled birooted trees: Munn's birooted trees extended with vertex labeling. To this purpose, we define a notion of finite state birooted tree automata that simply extends finite state word automata semantics. This notion is shown to capture the class of languages that are definable in Monadic Second Order Logic and upward closed with respect to the natural order defined in the inverse monoid structure induced by labeled birooted trees. Then, we derive from these automata the notion of quasi-recognizable languages, that is, languages recognizable by means of (adequate) premorphisms into finite (adequately) ordered monoids. This notion is shown to capture finite Boolean combinations of languages as above. Applied to a simple encoding of finite (mono-rooted) labeled tree languages in of labeled birooted trees, we show that classical regular languages of finite (mono-rooted) trees are quasi-recognizable in the above sense. The notion of quasi-recognizability thus appears as an adequate remedy to the known collapse of the expressive power of classical algebraic tools when applied to inverse semigroups. Illustrative examples, in relation to other known algebraic or automata theoretic frameworks for defining languages of finite trees, are provided throughout

Towards a Higher-Dimensional String Theory for the Modeling of Computerized Systems

International audienceRecent modeling experiments conducted in computational music give evidence that a number of concepts, methods and tools belonging to inverse semigroup theory can be attuned towards the concrete modeling of time-sensitive interactive systems. Further theoretical developments show that some related notions of higher-dimensional strings can be used as a unifying theme across word or tree automata theory. In this invited paper, we will provide a guided tour of this emerging theory both as an abstract theory and with a view to concrete applications

Inverse monoids of higher-dimensional strings

International audienceHalfway 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 mor-phism. A simple set of generators is characterized. As a subsemigroup example, we show how all finite grids are finitely generated. Last, simple additional restrictions on products lead to the definition of subclasses with decidable Monadic Second Order (MSO) language theory

Free inverse monoids up to rewriting

In this paper, generalizing the study of free partially commutative inverse monoids [5], for any rewriting system T over an alphabet A, we define the notion of T-compatible inverse A-generated monoids, we show there is a free T-compatible monoid FIM(A,T) generated by A and we provide an explicit construction of this monoid. Then, as examples, free partially commutative inverse monoid and free partially semi-commutative inverse monoids are studied and shown to have effective representations

Realistic protein-protein association rates from a simple diffusional model neglecting long-range interactions, free energy barriers, and landscape ruggedness

We develop a simple but rigorous model of protein-protein association kinetics based on diffusional association on free energy landscapes obtained by sampling configurations within and surrounding the native complex binding funnels. Guided by results obtained on exactly solvable model problems, we transform the problem of diffusion in a potential into free diffusion in the presence of an absorbing zone spanning the entrance to the binding funnel. The free diffusion problem is solved using a recently derived analytic expression for the rate of association of asymmetrically oriented molecules. Despite the required high steric specificity and the absence of long-range attractive interactions, the computed rates are typically on the order of 10^4-10^6 M-1 s-1, several orders of magnitude higher than rates obtained using a purely probabilistic model in which the association rate for free diffusion of uniformly reactive molecules is multiplied by the probability of a correct alignment of the two partners in a random collision. As the association rates of many protein-protein complexes are also in the 10^5-10^6 M-1 s-1, our results suggest that free energy barriers arising from desolvation and/or side-chain freezing during complex formation or increased ruggedness within the binding funnel, which are completely neglected in our simple diffusional model, do not contribute significantly to the dynamics of protein-protein association. The transparent physical interpretation of our approach that computes association rates directly from the size and geometry of protein-protein binding funnels makes it a useful complement to Brownian dynamics simulations.Comment: 9 pages, 5 figures, 1 table. One figure and a few comments added for clarificatio

Causalité dans les calculs d'événements

National audienceSi l'on considère un événement comme une valeur quelconque associée à une date de réception, un calcul d'événements est une fonction produisant un ensemble d'événements à partir d'un ensemble d'événements reçus. Un sous-ensemble particulièrement intéressant de ces fonctions correspond aux fonctions causales dont les événements produits avant une date donnée ne dépendent que des événements reçus avant cette même date. Dans cet article, nous proposons une définition très simple permettant de caractériser ces fonctions causales