|Links' Seminars and Public Events|
Fri 30th Mar
Fri 23rd Mar
Paul Gallot: High-Order Tree Transducers
Paul présentera le papier de Sylvain, Aurélien et Paul, soumis à LICS 2018, sur le sujet des transducteurs d'arbres d'ordre supérieur.
Wed 21st Mar
Fri 16th Mar
Luc Dartois in Links' Seminar: A Logic for Word Transductions with Synthesis
In this talk I present a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. I argue that LT is a suitable candidate as a specification language for verification of non reactive systems, extending the successful approach of verifying synchronous systems via Mealy Machines and MSO.
In LT, the input/output dependencies are modelled via an origin function which associates to any position of the output word, the input position from which it originates. LT is well-suited to express relations (which are not necessarily functional), and can express all regular functional transductions, i.e. transductions definable for instance by deterministic two-way transducers.
Despite its high expressive power, LT has decidable satisfiability problems. The main contribution is a synthesis result: it is always possible to synthesis a regular function which satisfies the specification.
Finally, I explicit a correspondence between transductions and data words. As a side-result, we obtain a new decidable logic for data words.
Fri 9th Mar
Benjamin Bergougnoux : Counting minimal transversals of hypergraphs
A transversal of a hypergraph H is a subset of vertices that
intersects all the hyper-edges H. The enumeration and the counting of
the minimal transversals have a lot of applications in many domains
(graph theory, AI, datamining, etc). Counting problems are generally
harder than theirs associated decision problems. For example, finding
a minimal transversal is doable in polynomial time but counting them
is #P-complet (the equivalent of NP-complet for counting problems).
We have proved that we can count the minimal transversals of any
beta-acyclique hypergraph in polynomial time. Our result is based on
a recursive decomposition of the beta-acyclique hypergraph founded by
Florent Capelli and by the introduction of a new notion that
generalize the minimal transversals.
A lot of exciting open questions live in the neighborhood of our
result. In particular, our algorithm is able to count the minimum
dominating set of a strong-chordal graph. But counting the minimum
dominating set is #P-complete on split graphs. Is it the beginning of
a complete characterization of the complexity of counting minimal
dominating sets in dense graphs ?