On Feb 9, 2018, at 9:04, 新屋良磨(秋田大) <[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/ 
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)

Begin forwarded message:

From: "新屋良磨(秋田大)" <[email protected]>

Subject: [jssst-ppl] Talk by Prof. Jacques Sakarovitch (March 2, 2018)

Date: February 16, 2018 12:14:47 JST

To: [email protected], [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]

==========

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.

==========

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