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| Links' Seminars and Public Events |   |
| 2024 | |
|---|---|
Fri 15th Nov 11:00 am 12:15 pm | Seminar by Gabriel Bathie Speaker: Gabriel Bathie (perso.ens-lyon.fr/gabriel.bathie/) Room: B21 Title: The complexity of Testing Regular Languages - Gabriel Bathie, Corto Mascle and Nathanaël Fijalkow (LaBRI, Université de Bordeaux) Abstract: Property testing is concerned with the design of algorithms making sublinear number of queries to distinguish whether the input satisfies a given property or is far from having this property. A seminal paper of Alon, Krivelevich, Newman, and Szegedy in 2001 introduced property testing of formal languages: the goal is to determine whether an input word belongs to a given language, or is far from any word in that language (in terms of Hamming distance). They constructed the first property testing algorithm for the class of all regular languages. Somewhat surprisingly, their algorithm uses a number of queries that does not depend on the length of the input word. This opened up a line of work with improved complexity results and applications to streaming algorithms. In this work, we show a trichotomy result: the class of regular languages can be divided into three classes, each of which is associated with an optimal testing complexity. Our analysis yields effective characterizations for all three classes using so-called minimal blocking sequences, reasoning directly and combinatorially on automata. This talk will give an overview of the methods used since the work of Alon et al. and highlight the main tools used for our combinatorial characterization. Based on joint work with Corto Mascle and Nathanaël Fijalkow. "Lille-Salle B21" |
Tue 12th Nov 2:00 pm 3:30 pm | Seminar from Aliaume Lopez Speaker: Aliaume Lopez (www.lsv.fr/~lopez/) Title: Which polynomials are computed by N-weighted automata? Room: B21 Abstract: Given a semiring K, the notion of K-weighted automata generalizes regular languages to functions from Σ* to K. This model allows us to compute (multivariate) polynomial functions with coefficients in K. We provide a decidable characterization of polynomials with coefficients in Q that can be computed by K-weighted automata for K = (N,+,×) and for K = (Z+,×). As a consequence, we can decide which functions computed by Z-weighted automata are computed by N-weighted automata, under the assumption of commutativity (the order of the letters in the input does not matter) and polynomial growth (the output of the function is bounded by a polynomial in the size of the input). This surprisingly allows us to decide whether such functions are star-free, a notion borrowed from the theory of regular languages. "Lille-Salle B21" |
