<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">【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】<br class=""></div><div class="">皆様，</div><div class=""><br class=""></div><div class="">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．</div><div class="">水曜と木曜で会場が異なりますのでご注意ください．</div><div class=""><br class=""></div><div class="">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．</div><div class=""><br class=""></div><div class="">参加のご検討，どうぞよろしくお願いします．</div><div class=""><br class=""></div><div class="">秋田大学 数理科学コース 新屋良磨</div><div class=""><br class=""></div><div class=""><div class=""><blockquote type="cite" class=""><div class="">On Feb 9, 2018, at 9:04, 新屋良磨(秋田大) <<a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div class=""><div class="">(重複で受け取られた方はご容赦ください)</div>皆様，<br class=""><br class="">秋田大の新屋です．</div><div class=""><br class=""></div><div class="">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，</div><div class="">概要を改めて再通知させていただきます．</div><div class=""><br class=""></div><div class="">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</div><div class="">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．</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">========== Lecture ========== </div><div class=""><div class=""><div class=""><div class="">Time:</div><div class="">16:30 ~ 17:30, February 28, 2018 (Wed.)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Venue:</div><div class="">Room W935, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 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)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Title:</div><div class="">Automata and expressions</div><div class=""><br class=""></div><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><div class=""><br class="">Abstract:<br class="">Not many results in Computer Science are recognised to be as basic and<br class="">fundamental as Kleene Theorem. It states the equality of two sets of<br class="">objects that we now call languages.<br class=""><br class="">In this lecture, I propose a slight change of focus on this result and show </div><div class="">how it is mainly the combination of two families of algorithms: </div><div class="">algorithms that transform an automaton into an expression on one hand </div><div class="">and algorithms that build an automaton from an expression on the other.</div><div class=""><br class="">The first purpose is to compare the results of these algorithms, </div><div class="">in order to understand they are indeed not so different. </div><div class="">And also to devise means to keep these results as small as possible.<br class=""><br class="">The second benefit of isolating this part of Kleene Theorem is to allow<br class="">its extension much beyond languages: to subsets of arbitrary monoids<br class="">first, and then, with some precaution, to subsets with multiplicity, </div><div class="">that is, to formal power series.</div><div class="">===========================</div></div><div class=""><br class=""></div><div class=""><br class=""></div></div><div class=""><div class=""><div class=""><div class=""><div class="">========== Seminar ========== </div><div class="">Time:</div><div class=""><div class=""><div class="">16:30 ~ 17:30, March 1, 2018 (Thu.)</div><div class=""><br class=""></div></div></div><div class=""><br class=""></div><div class="">Venue:</div><div class=""><div class="">Multi-Purpose Digital Hall, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 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)</div></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div class="">Title:</div></div><div class="">Conjugacy and equivalence of weighted automata</div><div class=""><br class=""></div><div class=""><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><br class="">Abstract:<br class="">As a main thread of this talk, I present the proof of the following result:<br class=""><br class="">If two regular languages $L$ and $K$ have the same generating<br class="">functions, that is, for every integer $n$ they have the same number of<br class="">words of length $n$, there exists a rational bijection realised by a<br class="">letter-to-letter transducer that maps $L$ onto $K$.<br class=""><br class="">This statement is a consequence of a refinement of the decidability of<br class="">the equivalence of two automata with multiplicity in $N$. It gives us<br class="">the opportunity to review first the basic definitions and results on<br class="">weighted finite automata, and second to revisit the `classical' theory<br class="">of reduction of automata with two notions borrowed to symbolic<br class="">dynamics: conjugacy and the Finite Equivalence Theorem.</div><div class="">===========================<br class=""><br class=""></div><div class=""><br class=""></div><div class="">大岡山キャンパスまでの行き方は以下をご覧ください：<br class=""><a href="https://www.titech.ac.jp/maps/" class="">https://www.titech.ac.jp/maps/</a> <br class="">西9号館までの行き方は<br class=""><a href="http://www.dst.titech.ac.jp/outline/facility/hall.html" class="">http://www.dst.titech.ac.jp/outline/facility/hall.html</a><br class="">の中の地図をご覧ください。</div><div class=""><br class=""></div></div></div></div></div><div class=""><div class="">以上，どうぞよろしくお願いします．</div></div><div class=""><br class=""></div><div class="">秋田大学 数理科学コース 新屋良磨 <a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a></div><div class=""><div class="">(共催：東京工業大学 情報理工学院 鹿島亮)</div></div></div></div></div></blockquote><br class=""></div><div class=""><br class=""></div><div class=""><div class=""></div><blockquote type="cite" class=""><div class="">Begin forwarded message:</div><br class="Apple-interchange-newline"><div class="" style="margin: 0px;"><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><b class="">From: </b></span><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;">"新屋良磨(秋田大)" <<a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a>><br class=""></span></div><div class="" style="margin: 0px;"><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><b class="">Subject: </b></span><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><b class="">[jssst-ppl] Talk by Prof. Jacques Sakarovitch (March 2, 2018)</b><br class=""></span></div><div class="" style="margin: 0px;"><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><b class="">Date: </b></span><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;">February 16, 2018 12:14:47 JST<br class=""></span></div><div class="" style="margin: 0px;"><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><b class="">To: </b></span><span class="" style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;"><a href="mailto:logic-ml@fos.kuis.kyoto-u.ac.jp" class="">logic-ml@fos.kuis.kyoto-u.ac.jp</a>, <a href="mailto:jssst-ppl@fos.kuis.kyoto-u.ac.jp" class="">jssst-ppl@fos.kuis.kyoto-u.ac.jp</a><br class=""></span></div><br class=""><div class=""><div class="" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">(重複で受け取られた方はご容赦ください)<br class="">皆様，<br class=""><br class="">秋田大学の新屋です．<br class=""><br class=""><div class="">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．</div><div class=""><br class=""></div><div class="">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</div><div class="">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．</div><div class=""><div class=""><div class=""><br class="">秋田大学 数理科学コース 新屋良磨 <a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a></div><div class=""><br class="">==========</div><div class=""><div class="">Time:</div><div class="">1:30pm, March. 2, 2018</div><div class=""><br class=""><br class=""></div><div class="">Venue:</div><div class="">Room 236, East Building of Department of Chemistry, Faculty of Science(化学東館), University of Tokyo<br class=""><br class=""></div><div class=""><br class=""></div><div class="">Title:</div><div class="">Mysteries and marvels of rational base numeration systems<br class=""><br class="">Jacques Sakarovitch<br class="">CNRS / Paris Diderot University and Telecom ParisTech<br class=""><br class=""><br class="">Abstract:<br class="">The definition of numeration systems with rational base, in a joint<br class="">work with S. Akiyama and Ch. Frougny (Israel J. Math., 2008),<br class="">has allowed to make some progress in a number theoretic problem,<br class="">by means of automata theory and combinatorics of words.<br class="">At the same time, it raised the problem of understanding the<br class="">structure of the sets of the representations of the integers in these<br class="">systems from the point of view of formal language theory.<br class=""><br class="">At first sight, these sets look rather chaotic and do not fit well<br class="">in the classical Chomsky hierarchy of languages. They all enjoy a<br class="">property that makes them defeat, so to speak, any kind of iteration<br class="">lemma. On the other hand, these sets also exhibit remarkable<br class="">regularity properties.<br class=""><br class="">During the recent years, these regularities have been studied in a<br class="">series of joint papers with my student V. Marsault. In particular, we<br class="">have shown that periodic signatures are characteristic of the<br class="">representation languages in rational base numeration systems and<br class="">studied, jointly with S. Akiyama, a kind of autosimilarity property<br class="">that also leads to the construction of Cantor-like sets.<br class=""><br class="">These languages still keep most of their mystery. The partial results<br class="">which will be presented call for further investigations on the subject<br class="">even stronger.</div></div></div><div class="">==========</div></div></div>_______________________________________________<br class="">jssst-ppl mailing list<br class=""><a href="mailto:jssst-ppl@fos.kuis.kyoto-u.ac.jp" class="">jssst-ppl@fos.kuis.kyoto-u.ac.jp</a><br class=""><a href="http://www.fos.kuis.kyoto-u.ac.jp/cgi-bin/mailman/listinfo/jssst-ppl" class="">http://www.fos.kuis.kyoto-u.ac.jp/cgi-bin/mailman/listinfo/jssst-ppl</a></div></blockquote></div></div></body></html>