Modélisation algébrique du dîner des philosophes

SOFSEM 2014: Theory and Practice of Computer Science

2014

Self Cite

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

Section: Resulting Idempotents (System States)mentioning

confidence: 99%

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

SOFSEM 2014: Theory and Practice of Computer Science

2014

Self Cite

“…A formal framework for the composition of such overlapping objects is given by the theory of inverse semigroups [19]. Recent applications of this theory include the modelling of music [8], interactive music systems [1,14], and distributed systems [6]. As already observed in [16,17] and developed further in [13], inverse semigroup theory conveys a notion of a higher dimensional string that seems particularly relevant in the context of such applications.…”

Section: Introductionmentioning

confidence: 99%

A syntactic congruence for languages of birooted trees

Blumensath

2014

Semigroup Forum

Self Cite

International audienceThe study of languages of labelled birooted trees, that is, elements of the free inverse monoid enriched by a vertex labelling, has led to the notion of quasi-recognisability. It generalises the usual notion of recognisability by replacing homomorphisms by certain prehomomorphism into finite ordered monoids, called adequate, that only preserve some products: the so-called disjoint ones. In this paper we study the underlying partial algebra setting and we define a suitable notion of a syntactic congruence such that (i) having a syntactic congruence of finite index captures MSO-definability; (ii) a certain order-bisimulation refinement of the syntactic congruence captures quasi-recognisability in the same way

“…Overlapping structures, be them linear shaped as in McAlister monoids [17], tree shaped as in free inverse monoids [22,19] or more generally higher-dimensional (overlapping) strings as in Kellendonk's tiling monoids [13,14], are promising high level models of system behaviors as already illustrated in musical application modeling [12] and the associated programming language proposal [11], or in distributed behavior modeling [2]. Be them for modeling/typing purposes or system analysis, there is incentive to develop the language theory of overlapping tiles.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Tools for the Overlapping Tile Product

Dubourg

Language and Automata Theory and Applications

2014

Self Cite

Overlapping tile automata and the associated notion of recognizability by means of (adequate) premorphisms in finite ordered monoids have recently been defined for coping with the collapse of classical recognizability in inverse monoids. In this paper, we investigate more in depth the associated algebraic tools that allows for a better understanding of the underlying mathematical theory. In particular, addressing the surprisingly difficult problem of language product and star, we eventually found some deep links with classical notions of inverse semigroup theory such as the notion of restricted product.