(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．

下記の要領にて，フランスからJacques Sakarovitch先生を東工大にお招きしSeminar および Lecture を実施いたします．

＊SeminarとLectureで日時・会場が異なりますのでご注意ください．

Sakarovitch先生は現代のオートマトン理論を牽引する世界的研究者であり，この連続講演会は

計算機科学に携わる多くの方に興味を持っていただけると思います．

参加申し込みなどは不要ですので，どうぞふるってご参加ください．

なお，2月28日(水)のLectureでは，古典的なKleeneの定理(正規表現とオートマトンの表現力の等価性)の

精密化・一般化に関する講義をしてもらいます．

本講義では現代的なオートマトン理論の基礎を説明してもらう予定ですので，学生の皆様もどうぞふるってご参加ください．

また，3月1日(木)のSeminarでは，Sakarovitch先生自身のこれまでの研究成果を中心に講演してもらう予定です．

下記のSeminar概要にて述べられている主結果については，拙著サーベイ論文「オートマトン理論再考」

https://www.jstage.jst.go.jp/article/jssst/34/3/34_3_3/_article/-char/ja/

の4.4節でほんの少しだけ解説されていますので，興味のある方はどうぞこちらもご参照ください．

========== Lecture ==========

Time:

15:20 ~ 16:20, 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:

15:20 ~ 16:20, 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/
西9号館までの行き方は
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]

(共催：東京工業大学情報理工学院鹿島亮)