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Logics with Invariantly Used Relations Eickmeyer, Kord (2020)
Logics with Invariantly Used Relations Eickmeyer, Kord (2020) DOI (TUprints): https://doi.org/10.25534/tuprints-00013503 Lizenz: CC-BY 4.0 International - Creative Commons, Attribution Publikationstyp: Habilitation Fachbereich: 04 Department of Mathematics Quelle des Originals: https://tuprints.ulb.tu-darmstadt.de/13503 Fachbereich Mathematik Logics with Invariantly Used Relations vom Fachbereich Mathematik der Technischen Universität Darmstadt genehmigte Habilitationsschrift von Dr. Kord Eickmeyer aus Lage Datum des Habilitationsvortrags: 13. Dezember 2019 1. Gutachter: Prof. Dr. Martin Otto 2. Gutachter: Prof. Dr. Marc Pfetsch 3. Gutachter: Prof. Dr. Rodney Downey 4. Gutachter: Prof. Dr. Mikołaj Bojańczyk D 17 Logics with Invariantly Used Relations Habilitationsschrift Dr. Kord Eickmeyer Contents I Background 11 1 Preliminaries and Notation 13 1.1 Logic Preliminaries . 14 2 Logics with Invariantly Used Relations 25 2.1 Invariantly Used Relations . 25 2.2 Undecidability of the Syntax . 30 3 Structural Properties of Graphs 35 3.1 Trees and Tree Decompositions . 37 3.2 Treedepth . 40 3.3 Graphs of Bounded Genus . 44 3.4 Minors and Topological Subgraphs . 46 II Expressivity and Succinctness 51 4 Variants of First-Order Logic 53 4.1 Separation Results . 54 4.2 Trees . 55 4.3 Locality . 59 4.4 Depth-Bounded Structures . 62 5 Order-Invariant Monadic Second-Order Logic 75 5.1 Depth-Bounded Structures . 75 5.2 Decomposable Structures . 80 III Algorithmic Meta-Theorems 83 6 The Complexity of Model Checking 85 3 7 Successor-Invariant First-Order Logic 91 7.1 Interpreting a Successor Relation . 92 7.2 k-Walks in Graphs with Excluded Minors . 96 7.3 k-Walks in Graphs with Excluded Topological Subgraphs . -
תוארי כבוד Honorary Degrees Conferment Ceremony
טקס הענקת תוארי כבוד Honorary Degrees Conferment Ceremony י“ב באייר תשס“ז • May 2008 17 Board of Governors Board of Governors מושב חבר הנאמנים מושב חבר הנאמנים 2008 2008 1 מתכבדת להזמינכם takes pleasure in inviting you to the לטקס הענקת Honorary Degrees תוארי כבוד Conferment Ceremony במעמד שרת החינוך ,in the presence of Prof. Yuli Tamir פרופ' יולי תמיר Minister of Education ד"ר כבוד לפילוסופיה: :Doctor Philosophiae Honoris Causa פרופ' אלי ויזל, ארה"ב Eli Amir, Israel מרטין ג' ויטמן, ארה"ב Dr. Santiago Calatrava SA, Switzerland פרנסיס מינקוף, שוויץ Prof. Mary-Claire King, USA אלי עמיר, ישראל Francis Minkoff, Switzerland פרופ' הילארי פאטנם, ארה"ב Sruel Prajs, Germany שרול פרייס, גרמניה Prof. Hilary Putnam, USA ד"ר סנטיאגו קלטרבה, שוויץ Lea Koenig Stolper, Israel פרופ' מארי-קלייר קינג, ארה"ב Martin J. Whitman, USA ליא קניג שטולפר, ישראל Prof. Elie Wiesel, USA עמית כבוד: :Honorary Fellowship יחיאל בן-צבי, ישראל Yehiel Ben-Zvi, Israel ג'ון לנדרר, אוסטרליה John Landerer CBE AM, Australia אלן סלווין, אוסטרליה Alan Selwyn, Australia דברים בשם מקבלי התארים: :Response on behalf of the recipients פרופ' הילארי פאטנם Prof. Hilary Putnam מוצאי שבת, י"ב באייר תשס"ח, 17.5.2008 בשעה Saturday, 17 May 2008, at 9:00 p.m. 21:00 אודיטוריום ע"ש מרים ואדולפו סמולרש Miriam and Adolfo Smolarz Auditorium קבלת פנים Reception in the באולם הכניסה ע"ש משפחת סרחיו וקוקי גרוסקופ Kuky and Sergio Grosskopf Family Foyer קריית האוניברסיטה, רמת–אביב Tel Aviv University Campus, Ramat Aviv קוד לבוש: פורמאלי Dress code: dark suit )הטקס וקבלת הפנים על–פי הזמנה בלבד( (By invitation only) הטקס יועבר בשידור ישיר באינטרנט :Ceremony will be broadcast live http://video.tau.ac.il/Honorary_Degrees-08 http://video.tau.ac.il/Honorary_Degrees-08 מושב חבר הנאמנים Board of Governors 17.5.08 PROGRAM Academic Procession Address Mr. -
Successor-Invariant First-Order Logic on Graphs with Excluded Topological Subgraphs
SUCCESSOR-INVARIANT FIRST-ORDER LOGIC ON GRAPHS WITH EXCLUDED TOPOLOGICAL SUBGRAPHS KORD EICKMEYER AND KEN-ICHI KAWARABAYASHI Abstract. We show that the model-checking problem for successor- invariant first-order logic is fixed-parameter tractable on graphs with excluded topological subgraphs when parameterised by both the size of the input formula and the size of the exluded topo- logical subgraph. Furthermore, we show that model-checking for order-invariant first-order logic is tractable on coloured posets of bounded width, parameterised by both the size of the input for- mula and the width of the poset. Results of this form, i.e. showing that model-checking for a cer- tain logic is tractable on a certain class of structures, are often referred to as algorithmic meta-theorems since they give a unified proof for the tractability of a whole range of problems. First-order logic is arguably one of the most important logics in this context since it is powerful enough to express many computational prob- lems (e.g. the existence of cliques, dominating sets etc.) and yet its model-checking problem is tractable on rich classes of graphs. In fact, Grohe et al. [21] have shown that model-checking for FO is tractable on all nowhere dense classes of graphs. Successor-invariant FO is a semantic extension of FO by allow- ing the use of an additional binary relation which is interpreted as a directed Hamiltonian cycle, restricted to formulae whose truth value does not depend on the specific choice of a Hamiltonian cy- cle. While this is very natural in the context of model-checking (after all, storing a structure in computer memory usually brings with it a linear order on the structure), the question of how the computational complexity of the model-checking problem for this arXiv:1605.01198v1 [cs.LO] 4 May 2016 richer logic compares to that of plain FO is still open. -
Jewish Philosophy Department of Hebrew Culture Studies Faculty of Social Sciences and Humanities Tel Aviv University
Jewish Philosophy Department of Hebrew Culture Studies Faculty of Social Sciences and Humanities Tel Aviv University Report of the External Evaluation Team for The Council of Higher Education August 2010 The following document is the Evaluation Committee's report on the Jewish Philosophy Track at Tel Aviv University to the Quality Assessment Unit of the Council for Higher Education (CHE). General Background In response to the invitation of the Minister of Education and the Council of Higher Education a Committee of four members was created in early 2009 to review the undergraduate and graduate programs in Jewish thought in four Israeli universities, Ben Gurion University of the Negev, the Hebrew University of Jerusalem, Tel Aviv University, and Bar Ilan University. The Committee is comprised of: Professor David Novak, University of Toronto; Professor Alfred Ivry, New York University (Emeritus); Professor Moshe Idel, the Hebrew University of Jerusalem; and Professor Steven T. Katz, Boston University. Professor Katz also serves as the Chair of the Committee. Ms. Michal Kabatznik coordinated the committee on behalf of the CHE. The Committee's letter of appointment is attached as Appendix 1. The first round of meetings was held in May, 2009. It involved discussions in Jerusalem and 2 day on-site visits to Ben Gurion University and The Hebrew University of Jerusalem. The second round of Committee meetings was held in December, 2009. It involved discussions in Tel Aviv and on-site two day visits to Tel Aviv University and Bar Ilan University. In the present report the Visiting Committee will provide its views on, and recommendations concerning, Tel Aviv University. -
Proposal for a Joint Special Session at the AMS-ASL Meeting of 2009, January 5-8, 2009, Washington, D.C
Proposal for a Joint Special Session at the AMS-ASL Meeting of 2009, January 5-8, 2009, Washington, D.C. Approved by the ASL, still needs approval of the AMS. Model Theoretic Methods in Finite Combinatorics Organizers: • Martin Grohe Institut fur¨ Informatik, Humboldt-Universit¨at zu Berlin Berlin, Germany homepage: www2.informatik.hu-berlin.de/∼grohe/ e-mail: [email protected] • Johann A. Makowsky (corresponding organizer) Department of Computer Science, Technion - Israel Institute of Technology, Haifa, Israel homepage: www.cs.technion.ac.il/∼janos e-mail: [email protected] Purpose of the special session We want to bring the various aspects of the interaction between Model Theory and Finite Combinatorics to a wider audience. Altough the work on 0-1 laws is by now widely known, the other applications on counting functions, graph polynomials, extremal combinatorics, graph minors and regularity lemmas, have not yet received their deserved attention. Background In the last twenty years several applications of Logic, in particular Model theory, to problems in Combinatorics emerged. Among them we have • 0-1 laws and their variations. This is well summarized in the book by J. Spencer [Spe01]. • Modular linear recurrence relations for combinatorial counting functions (The Specker-Blatter Theorem) This theorem has remained widely unnoticed, and deserves wider attention and further study [Spe88, Fis03, FM03] • Recent progress in undertanding the ultimate periodicity of finite spectra by Y. Gurevich and S. Shelah, and E. Fischer and J.A. Makowsky [FM04]. • Applications of meta-theorems which apply to whole families of combina- torial problems, instead of just specific problems. -
Tel Aviv University Evaluation Report
The Committee for the Evaluation of Nursing Study-Programs Tel Aviv University Evaluation Report November 2010 1 Contents Chapter 1: Background…………………………………………………………….3 Chapter 2: Committee Procedures………...……………………………………….4 Chapter 3: Evaluation of the Department of Nursing at Tel Aviv University………………..……….……………………………………....5 Appendices: Appendix 1 – Letter of Appointment Appendix 2 - Schedule of the visit 2 Chapter 1 - Background At its meeting on October 7, 2008 the Council for Higher Education (CHE) decided to evaluate study programs in the field of Nursing. Following the decision of the CHE, the Minister of Education who serves ex officio as a Chairperson of the CHE, appointed a committee consisting of: • Prof. Erika Froelicher- School of Nursing and Department of Epidemiology & Biostatistics, University of California, USA- Committee Chair • Prof. Joyce Fitzpatrick- Frances Payne Bolton School of Nursing, Case Western Reserve University, USA1 • Prof. Miriam Hirschfeld- Department of Nursing, Jezreel Valley College, Israel • Prof. Barbara Kelley- College of Nursing, Northeastern University, USA • Prof. Jane Robinson- University of Nottingham, United Kingdom Ms. Alisa Elon, Coordinator of the committee on behalf of the CHE Within the framework of its activity, the Committee was requested to2: 1. Examine the self-evaluation reports submitted by institutions that provide study programs in Nursing, and to conduct on-site visits at those institutions. 2. Submit to the CHE an individual report on each of the evaluated departments, including the Committee's findings and recommendations. 3. Submit to the CHE a general report on the state of the discipline in the Israeli system of higher education, including recommendations for standards in the evaluated field of study. -
Rapport D'activité 2007-2012
Laboratoire d’Informatique Algorithmique : Fondements et Applications LIAFA Rapport d’activites´ 1er janvier 2007 – 30 juin 2012 Laboratoire d’Informatique Algorithmique : Fondements et Applications (LIAFA) UMR CNRS 7089 Universite´ Paris Diderot - Paris 7 Case 7014 75205 Paris Cedex 13 Tel. +33 (0)1 57 27 92 56 Fax. +33 (0)1 57 27 94 09 [email protected] http://www.liafa.univ-paris-diderot.fr Table des matieres` Preambule´ 1 I Rapport et projet scientifique du LIAFA 3 1 Rapport scientifique du laboratoire 5 2 Projet scientifique du laboratoire 29 II Algorithms and Complexity team 37 1 Research report: Algorithms and Complexity 39 2 Fiche resum´ e:´ Algorithmes et Complexite´ 45 3 Executive Summary: Algorithms and Complexity 47 4 Research project: Algorithms and Complexity 49 5 List of publications: Algorithms and Complexity 57 6 Appendix: Algorithms and Complexity 67 III Equipe Algorithmes Distribues´ et Graphes 77 1 Rapport scientifique : Algorithmes Distribues´ et Graphes 79 2 Fiche resum´ e´ : Algorithmes Distribues´ et Graphes 85 3 Executive Summary : Distributed Algorithms and Graphs 87 4 Projet scientifique : Algorithmes Distribues´ et Graphes 89 5 Liste des publications : Algorithmes Distribues´ et Graphes 95 6 Annexes : Algorithmes Distribues´ et Graphes 119 i TABLE DES MATIERES` IV Automata and Applications team 143 1 Research report: Automata and Applications 145 2 Fiche resum´ e:´ Automates et applications 151 3 Executive Summary: Automata and Applications 153 4 Research project: Automata and Applications 155 -
On Structural Similarities of Finite Automata and Turing Machine Enumerability Classes
On Structural Similarities of Finite Automata and Turing Machine Enumerability Classes Till Tantau A A¯ × A A A¯ A¯ × × On Structural Similarities of Finite Automata and Turing Machine Enumerability Classes vorgelegt von Diplom-Informatiker und Diplom-Mathematiker Till Tantau von der Fakult¨at iv { Elektrotechnik und Informatik der Technischen Universit¨atBerlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften { Dr. rer. nat. { genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. Bernd Mahr Berichter: Prof. Dr. Dirk Siefkes Berichter: Prof. Dr. Johannes K¨obler Tag der wissenschaftlichen Aussprache: 17. Februar 2003 Berlin 2003 D 83 Preface This dissertation presents the lion's share of the research I did since I started working at the Technical University of Berlin at the end of 1999. Unfortunately, since I failed to focus my research on a single subject during the last three years, the results of several interesting research projects could not be included. If I had included them, the title would have had to be `On a Bunch of Interesting, but Unrelated Theorems of Theoretical Computer Science'. When I went to my advisor Dirk Siefkes at the beginning of 2002, we pondered on which papers would be fit to form the basis of a dissertation. There were two alternatives: either two papers on a new concept, namely enumerability by finite automata; or different technical reports on reducibility to selective languages, prover-verifier protocols, and reachability problems. Reducibility classes of selective languages would have been more `en vogue' and the results applicable in standard complexity theory and in practice (like a constant parallel time reachability algorithm for tournaments). -
Stal Aanderaa Hao Wang Lars Aarvik Martin Abadi Zohar Manna James
Don Heller J. von zur Gathen Rodney Howell Mark Buckingham Moshe VardiHagit Attiya Raymond Greenlaw Henry Foley Tak-Wah Lam Chul KimEitan Gurari Jerrold W. GrossmanM. Kifer J.F. Traub Brian Leininger Martin Golumbic Amotz Bar-Noy Volker Strassen Catriel Beeri Prabhakar Raghavan Louis E. Rosier Daniel M. Kan Danny Dolev Larry Ruzzo Bala Ravikumar Hsu-Chun Yen David Eppstein Herve Gallaire Clark Thomborson Rajeev Raman Miriam Balaban Arthur Werschulz Stuart Haber Amir Ben-Amram Hui Wang Oscar H. Ibarra Samuel Eilenberg Jim Gray Jik Chang Vardi Amdursky H.T. Kung Konrad Jacobs William Bultman Jacob Gonczarowski Tao Jiang Orli Waarts Richard ColePaul Dietz Zvi Galil Vivek Gore Arnaldo V. Moura Daniel Cohen Kunsoo Park Raffaele Giancarlo Qi Zheng Eli Shamir James Thatcher Cathy McGeoch Clark Thompson Sam Kim Karol Borsuk G.M. Baudet Steve Fortune Michael Harrison Julius Plucker NicholasMichael Tran Palis Daniel Lehmann Wilhelm MaakMartin Dietzfelbinger Arthur Banks Wolfgang Maass Kimberly King Dan Gordon Shafee Give'on Jean Musinski Eric Allender Pino Italiano Serge Plotkin Anil Kamath Jeanette Schmidt-Prozan Moti Yung Amiram Yehudai Felix Klein Joseph Naor John H. Holland Donald Stanat Jon Bentley Trudy Weibel Stefan Mazurkiewicz Daniela Rus Walter Kirchherr Harvey Garner Erich Hecke Martin Strauss Shalom Tsur Ivan Havel Marc Snir John Hopcroft E.F. Codd Chandrajit Bajaj Eli Upfal Guy Blelloch T.K. Dey Ferdinand Lindemann Matt GellerJohn Beatty Bernhard Zeigler James Wyllie Kurt Schutte Norman Scott Ogden Rood Karl Lieberherr Waclaw Sierpinski Carl V. Page Ronald Greenberg Erwin Engeler Robert Millikan Al Aho Richard Courant Fred Kruher W.R. Ham Jim Driscoll David Hilbert Lloyd Devore Shmuel Agmon Charles E. -
LOGIC AS REGULAR BEHAVIOUR 1. Expressions to Logic Fix a Finite Set
LOGIC AS REGULAR BEHAVIOUR KAMAL LODAYA 1. Expressions to logic Fix a finite set A as an alphabet. Its elements are called letters. A finite sequence of letters w : f1; : : : ; ng ! A, such as aabab, is called a word over the alphabet. A set of words is called a language. The set of all words over A is written A∗. The empty word is written ". In general, given a language L, its iteration L∗ is the language formed by concatenating words from L to form another word. For instance, given the language faa; ab; bg, also written aa [ ab [ b, the word aabab is in faa; ab; bg∗, but the word ba is not. The null word " is always in any L∗ (by taking words from L zero times). This notation, with some ad hoc extensions, can be used to describe languages. We will not look into the details of the notation: these are called regular expressions, and are defined in any book on automata theory. We assume that the reader is familiar with such material. With this background, the aim of this article is to examine some subclasses of regular languages which can be characterized using logic as well as algebra. Proofs are barely sketched. The interested reader should try to follow up the material and construct more detailed proofs. 1.1. Expressions. The starfree expressions are those where the iteration L∗ is not allowed. The dot depth of a starfree expression is the maximum number of nested alternations of the boolean operations (e1 [ e2 and e) and concatenations (e1e2 : : : en). -
Mathematical Logic in Computer Science
Mathematical Logic in Computer Science Assaf Kfoury June 1, 2017 (last update: February 1, 2018) 1 Introduction Others have written about the influences of mathematical logic on computer science. I single out two articles, which I have read and re-read over the years: 1. “Influences of Mathematical Logic on Computer Science,” by M. Davis [29], 2. “On the Unusual Effectiveness of Logic in Computer Science,” by J. Halpern, R. Harper, N. Immerman, P. Kolaitis, M. Vardi, and V. Vianu [60]. The first of these two articles takes stock of what had already become a productive cross-fertilization by the mid-1980’s; it is one of several interesting articles of historical character by M. Davis [27, 28, 30] which all bring to light particular aspects of the relationship between the two fields. The second article gives an account of this relationship in five areas of computer science by the year 2000. More on the second article, denoted by the acronym UEL, in Section 3 below. I wanted to write an addendum to the two forementioned articles, in the form of a timeline of significant moments in the history relating the two fields, from the very beginning of computer science in the mid-1950’s till the present. The result is this paper. One way of judging what I produced is to first read the penultimate section entitled ‘Timeline’, Section 5 below, and then go back to earlier sections whenever in need of a justification for one of my inclusions or one of my omissions. Disclaimer: This is not a comprehensive history, not even an attempt at one, of mathematical logic arXiv:1802.03292v1 [cs.LO] 7 Feb 2018 in computer science. -
Business Unusual in the Ivory Tower - Haaretz - Israel News Page 1 of 5
Business unusual in the ivory tower - Haaretz - Israel News Page 1 of 5 Subscribe to Print Edition | Thu., July 23, 2009 Av 2, 5769 | | Israel Time: 22:06 (EST+7) Search Back to Homepage web haaretz.com Haaretz Toolbar Diplomacy Defense Jewish World Opinion National Print Edition Car Rental Books Haaretz Magazine Business Real Estate Maccabiah Travel Week's End Anglo File Share | Business unusual in the ivory tower By Or Kashti Tags: Israel News Ads by Google Reuters Salary Reuters Jobs News on Israel Israel Rabbi Special Offers June 19 was the last day of classes at Tel Aviv University, but unlike in previous Advertisement years, it was far from heralding the beginning of a relaxing summer vacation. hotel Jerusalem David Citadel Hotel, come Eleven days later, university president Zvi Galil unexpectedly announced his stay at the finest of resignation, and tension erupted between two of the highest-ranking forums at Jerusalem hotels. this important institution: the executive council, some of whose members are ISRAEL ARMY businessmen, and the senate, the supreme academic body, which consists of SURPLUS STORE IDF insignia,Uniforms, deans and senior professors. The resignation was at first presented as a personal Paladium Boots Watches, decision by Galil, but it soon emerged that his departure was the outcome of a Israel Army T-shirts & passionate struggle revolving around a single question: Who controls the largest Collectibles Dead Sea Skin Care university in Israel? Quality cosmetics from the Dead Sea. Coupon code "That was the first public battle between the businessmen and us, the HAARETZ for 12% off! academics," declared one TAU professor this week.