【明日，明後日および明々後日の講演会のリマインダーです】 皆様，
2月28日(水)~3月1日(木)，東工大にて両日16:30からSakarovitch先生による連続講演会があります． 水曜と木曜で会場が異なりますのでご注意ください．
3月2日(金)にも東大にて13:30からSakarovitch先生の講演会が開催されます．
参加のご検討，どうぞよろしくお願いします．
秋田大学 数理科学コース 新屋良磨
On Feb 9, 2018, at 9:04, 新屋良磨(秋田大) <[email protected] mailto:[email protected]> wrote:
(重複で受け取られた方はご容赦ください) 皆様，
秋田大の新屋です．
2月28日〜3月1日の東工大でのJacques Sakarovitch先生の連続講演会について，開催時間が変更されましたので， 概要を改めて再通知させていただきます．
同日に東工大にて行われるプログラミング研究会と時間が重なっていたため，開始時刻を遅らせて Lecture/Seminar ともに16:30からの開始とさせていただきました．＊会場は変更ありません．
========== Lecture ========== Time: 16:30 ~ 17:30, February 28, 2018 (Wed.)
Venue: Room W935, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus) 東京工業大学大岡山キャンパス 西9号館 W935講義室 (西9号館東側(芝生スロープ側)入口を入って階段を1階上がって左側)
Title: Automata and expressions
Jacques Sakarovitch CNRS / Paris Diderot University and Telecom ParisTech
Abstract: Not many results in Computer Science are recognised to be as basic and fundamental as Kleene Theorem. It states the equality of two sets of objects that we now call languages.
In this lecture, I propose a slight change of focus on this result and show how it is mainly the combination of two families of algorithms: algorithms that transform an automaton into an expression on one hand and algorithms that build an automaton from an expression on the other.
The first purpose is to compare the results of these algorithms, in order to understand they are indeed not so different. And also to devise means to keep these results as small as possible.
The second benefit of isolating this part of Kleene Theorem is to allow its extension much beyond languages: to subsets of arbitrary monoids first, and then, with some precaution, to subsets with multiplicity, that is, to formal power series. ===========================
========== Seminar ========== Time: 16:30 ~ 17:30, March 1, 2018 (Thu.)
Venue: Multi-Purpose Digital Hall, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus) 東京工業大学大岡山キャンパス 西9号館 ディジタル多目的ホール (西9号館東側(芝生スロープ側)入口を入ってすぐ)
Title: Conjugacy and equivalence of weighted automata
Jacques Sakarovitch CNRS / Paris Diderot University and Telecom ParisTech
Abstract: As a main thread of this talk, I present the proof of the following result:
If two regular languages $L$ and $K$ have the same generating functions, that is, for every integer $n$ they have the same number of words of length $n$, there exists a rational bijection realised by a letter-to-letter transducer that maps $L$ onto $K$.
This statement is a consequence of a refinement of the decidability of the equivalence of two automata with multiplicity in $N$. It gives us the opportunity to review first the basic definitions and results on weighted finite automata, and second to revisit the `classical' theory of reduction of automata with two notions borrowed to symbolic dynamics: conjugacy and the Finite Equivalence Theorem. ===========================
大岡山キャンパスまでの行き方は以下をご覧ください： https://www.titech.ac.jp/maps/ https://www.titech.ac.jp/maps/ 西9号館までの行き方は http://www.dst.titech.ac.jp/outline/facility/hall.html http://www.dst.titech.ac.jp/outline/facility/hall.html の中の地図をご覧ください。
以上，どうぞよろしくお願いします．
秋田大学 数理科学コース 新屋良磨 [email protected] mailto:[email protected] (共催：東京工業大学 情報理工学院 鹿島亮)
Begin forwarded message:
From: "新屋良磨(秋田大)" <[email protected] mailto:[email protected]> Subject: [jssst-ppl] Talk by Prof. Jacques Sakarovitch (March 2, 2018) Date: February 16, 2018 12:14:47 JST To: [email protected] mailto:[email protected], [email protected] mailto:[email protected]
(重複で受け取られた方はご容赦ください) 皆様，
秋田大学の新屋です．
以下の要領で3/2(金)に東大にてJacques Sakarovitch先生の講演会が開催されます．
なお，前日(2/28~3/1)の東工大でのSakarovitch先生の連続講演会とは講演内容が別の 新規なものとなっております．どうぞふるってご参加ください．
秋田大学 数理科学コース 新屋良磨 [email protected] mailto:[email protected]
========== Time: 1:30pm, March. 2, 2018
Venue: Room 236, East Building of Department of Chemistry, Faculty of Science(化学東館), University of Tokyo
Title: Mysteries and marvels of rational base numeration systems
Jacques Sakarovitch CNRS / Paris Diderot University and Telecom ParisTech
Abstract: The definition of numeration systems with rational base, in a joint work with S. Akiyama and Ch. Frougny (Israel J. Math., 2008), has allowed to make some progress in a number theoretic problem, by means of automata theory and combinatorics of words. At the same time, it raised the problem of understanding the structure of the sets of the representations of the integers in these systems from the point of view of formal language theory.
At first sight, these sets look rather chaotic and do not fit well in the classical Chomsky hierarchy of languages. They all enjoy a property that makes them defeat, so to speak, any kind of iteration lemma. On the other hand, these sets also exhibit remarkable regularity properties.
During the recent years, these regularities have been studied in a series of joint papers with my student V. Marsault. In particular, we have shown that periodic signatures are characteristic of the representation languages in rational base numeration systems and studied, jointly with S. Akiyama, a kind of autosimilarity property that also leads to the construction of Cantor-like sets.
These languages still keep most of their mystery. The partial results which will be presented call for further investigations on the subject even stronger. ========== _______________________________________________ jssst-ppl mailing list [email protected] mailto:[email protected] http://www.fos.kuis.kyoto-u.ac.jp/cgi-bin/mailman/listinfo/jssst-ppl http://www.fos.kuis.kyoto-u.ac.jp/cgi-bin/mailman/listinfo/jssst-ppl