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1. S.O.S. Mathematics CyberBoard :: View Topic - Markov And Thue Systems Post Posted Fri, 31 Oct 2003 155754 GMT Post subject Markov and Thue I m somewhat familiar with Markov processes and have come across Thue systems. http://www.sosmath.com/CBB/viewtopic.php?t=3270&sid=3a604a33a7ee2c195ad68947ddc8

2. PlanetMath: Semi-Thue System AMS MSC, 03D03 (Mathematical logic and foundations Computability and recursion theory Thue and Post systems, etc.) http://planetmath.org/encyclopedia/SemiThueProduction.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About semi-Thue system (Definition) A semi-Thue system is a pair where is an alphabet and is a non-empty finite binary relation on , the Kleene star of Elements of are variously called defining relations productions , or rewrite rules , and itself is also known as a rewriting system . If , we call the antecedent , and the consequent . Instead of writing or , we usually write Let be a semi-Thue system. Given a word over , we say that a word over is immediately derivable from if there is a defining relation such that and , for some words (which may be empty) over . If is immediately derivable from , we write Let be the set of all pairs such that . Then , and If , then and for any word Next, take the

3. DC MetaData For: Formal Mathematical Systems Including A Structural Induction Pr MSC 03F03 Proof theory, general 03B70 Logic of programming, See also {68Q55, 68Q60} 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars http://www.math.uni-magdeburg.de/preprints/shadows/02-31report.html

Formal Mathematical Systems including a Structural Induction Principle by M. Kunik Preprint series: 02-31, Preprints MSC 03F03 Proof theory, general 03D03 Thue and Post systems, etc. Abstract This study provides a general frame for formal mathematical systems which may be interesting for people working in formal logic, theoretical computer science and linguistics. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the basic objects under consideration. A recursive system consists of axioms which are special quantifier-free positive horn formulas and of special rules of inference. Its extension to formal mathematical systems includes the predicate calculus as well as a structural induction principle with respect to the axioms of the underlying recursive system. for quite general restrictions in the argument lists of the formulas, which enables different kind of applications. Keywords: Formal mathematical systems, structural induction principle, incompleteness theorems Notes This is a revised and extended version from March 26 (2003) which replaces the old version from September 22 (2002).

4. 03Dxx 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions See also 68Q45, 68Q70, 68R15; 03D10 Turing http://www.ams.org/msc/03Dxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Computability and recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 03D10 Turing machines and related notions [See also 03D15 Complexity of computation [See also 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section

5. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection Thue and Post systems, etc. 03D03 ThueMahler equations 11D59 tight closure characteristic $p$ methods (Frobenius endomorphism) and reduction to http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_60.htm

theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computation or programming) # explicit machine computation and programs (not the theory of computing theory of conformal mappings # general

6. Sachgebiete Der AMS-Klassifikation: 00-09 03C95 Abstract model theory 03C99 None of the above but in this section 03Dxx Recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html

Sachgebiete der AMS-Klassifikation: 00-09 nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen 01-XX 03-XX 04-XX 05-XX 06-XX 08-XX nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

7. Mhb03.htm 03D03, Thue and Post systems, etc. 03D05, Automata and formal grammars in connection with logical questions See also 68Q45, 68Q70, 68R15 http://www.mi.imati.cnr.it/~alberto/mhb03.htm

03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

8. MathNet-Mathematical Subject Classification 03D03, Thue and Post systems, etc. 03D05, Automata and formal grammars in connection with logical questions See also 68Q45, 68Q50, 68Q68 http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

9. HeiDOK 03D03 Thue and Post systems, etc. ( 0 Dok. ) 03D05 Automata and formal grammars in connection with logical questions ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

10. Computability Theory We define Post correspondence systems and show that the problem of We define semiThue processes and show (Post, 1947) that for each e there is a http://caltechmacs117b.wordpress.com/

Computability Theory Goodstein sequences July 27, 2007 by andrescaicedo Will Sladek, a student at Caltech, wrote an excellent introductory paper on incompleteness in PA, The termite and the tower . While Will was working on his paper, I wrote a short note, Goodstein’s function Posted in Undecidability and incompleteness Unsolvable problems - Lecture 3 March 12, 2007 by andrescaicedo At the beginning of the course we built (recursively in ) two incomparable sets A,B . It follows that A and B  have degrees intermediate between and . The construction required that we fixed finite initial segments of A and B  during an inductive construction and so it is not clear whether they are c.e. or not. (A c.e. construction would add elements to a set and we would not have complete control on what is kept out of the set). Post asked whether there is an intermediate c.e. degree and this was solved by Friedberg and Muchnik using what is now called a finite injury priority construction. We show this construction; again, 2 incomparable sets A and B are built and the construction explicitly shows they are c.e. This implies they are not recursive and have degree strictly below

11. Theory Of Computation Qualifier --- Information I. Other equivalent systems/models the RAM model, Post systems, Thue systems and Lambda calculus. J. Oracles and Turing reducibility http://www.cs.mtu.edu/~nilufer/classes/qualifiers/2007-01-Theory/Home.html

Theory of Computation Spring 2007 Qualifying Exam Information Date: January 10, 2007 (Wednesday) Time: 9:00am - 1:00pm (4 hours) Suggested Reading List [HMU] John E. Hopcroft, Rajeev Motwani and Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation , second edition, Addison-Wesley, 2001. [SIPSER] Michael Sipser, Introduction to the Theory of Computation , second edition, Thomson, 2006. Topics Basic Concepts A. Proof techniques: direct, mathematical induction, proof-by-contradiction B. Sets, functions, relations, equivalence relations and equivalence classes C. Strings and languages D. Countability and enumerability Reading: HMU - Chapter 1; SIPSER - Chapter 0; Section 4.2 Finite Automata (FA) and Regular Languages (RL) A. DFA, NFA, FA with epsilon transitions B. NFA to DFA conversion C. Regular expressions (RE) D. Relationship between DFAs and REs E. Algebraic laws of REs F. Pumping lemma for and closure properties of RLs G. Decision properties of REs H. Equivalence and minimization of automata Reading: HMU - Chapter 2, Chapter 3 and Chapter 4; SIPSER - Chapter 2

12. Developments In Language Theory 2004 From Post systems to the Reachability Problems for Matrix Semigroups and Multicounter Automata. Words Avoiding 7/3Powers and the Thue-Morse Morphism. http://www.informatik.uni-trier.de/~ley/db/conf/dlt/dlt2004.html

DLT 2004: Auckland, New Zealand Cristian Calude Elena Calude Michael J. Dinneen (Eds.): Developments in Language Theory, 8th International Conference, DLT 2004, Auckland, New Zealand, December 13-17, 2004, Proceedings. Lecture Notes in Computer Science 3340 Springer 2004, ISBN 3-540-24014-4 BibTeX Invited Papers Bruno Courcelle Recognizable Sets of Graphs, Hypergraphs and Relational Structures: A Survey. Electronic Edition (link) BibTeX Rodney G. Downey Catherine McCartin Some New Directions and Questions in Parameterized Complexity. Electronic Edition (link) BibTeX Andrzej Ehrenfeucht Grzegorz Rozenberg Basic Notions of Reaction Systems. Electronic Edition (link) BibTeX Blaise Genest Anca Muscholl Dietrich Kuske A Kleene Theorem for a Class of Communicating Automata with Effective Algorithms. Electronic Edition (link) BibTeX Natasa Jonoska Masahico Saito Algebraic and Topological Models for DNA Recombinant Processes. Electronic Edition (link) BibTeX Contributed Papers Marcella Anselmo Dora Giammarresi Maria Madonia Regular Expressions for Two-Dimensional Languages Over One-Letter Alphabet. Electronic Edition (link) BibTeX Maurice H. ter Beek

13. Book (print-only) For example in 1981 he published Thue congruences and the ChurchRosser on the field of rewriting systems was what these students and Post-docs went on http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Book.html

Ronald Vernon Book Born: April 1937 in USA Died: 28 May 1997 in Santa Barbara, California, USA Ron Book was born and grew up in a farming community. He attended Grinnell College, a private institution of higher education in Grinnell, Iowa, and was awarded a B.A. by the College in 1958. He then studied at the Wesleyan University, a private, institution of higher education in Middletown, Connecticut, and was awarded an M.A. in Teaching in 1960 and a second M.A. in 1964. He undertook research at Harvard University under the supervision of Sheila A Greibach and was awarded a Ph.D. in 1969 for his thesis Grammars with Time Functions. In 1970 Book and Greibach published Quasi-realtime languages and they described the contents of the paper as follows:- The quasi-realtime languages are seen to be the languages accepted by nondeterministic multitape Turing machines in real time. The family of quasi-realtime languages forms an abstract family of languages closed under intersection, linear erasing, and reversal. It is identical with the family of languages accepted by non-deterministic multitape Turing machines in linear time. Every quasi-realtime language can be accepted in real time by a nondeterministic one stack, one pushdown store machine, and can be expressed as the length-preserving homomorphic image of the intersection of three context-free languages. Another early work by Book on languages was the paper On languages accepted in polynomial time which he published in 1972. It shows that several different languages are distinct. These are the family of languages accepted by non-deterministic Turing machines in polynomial time, the corresponding family for deterministic Turing machines, the family of context-sensitive languages, the family of languages accepted by deterministic linear bounded automata, and the set of languages accepted by deterministic Turing machines in exponential time. A survey of where the theory of formal languages stood in 1972 was presented by Book in

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English Add URL Forum Introduction ... Index Vietnam Back Interior Materials Real Estate ... Home interior document.write(""); www.waseenco.com.vn Water Supply And Seweaage Construction Company - Construction and installation of water plants, wastewater treatment plants, water supply and drainage pipelines of all scales - Erection of pumping stations, compressed air stations, industrial pipelines. - Construction of industrial, civil and housing works, interior and exterior decoration; Installation of sanitary fittings, water supply and drainage equipment; indoor and outdoor ventilation equipment. - Manufacture and construction of materials, equipment and fittings for water supply and sewerage sector - Import, export and trade of specialized materials, equipment and fittings for water supply and sewerage sector - www.vwp-jsc.com Viet Nam Wind - Power Joint Stock Company www.vinhthai.com www.vinausteel.com.vn Vinausteel - Australia Vietnam Steel Joint Venture Company www.vinaconex.com.vn - Contracting for infrastructure, industrial, civil engineering, water supply, drainage and environ mental projects, reservoirs, power lines, substations etc..., both domestically and internationally. - Supply of manpower to foreign firms, including management staff at site, engineers, technicians, foremen, workers of different professions, common labour. - lmportand export of construction equipment, machinery and materials, furniture, decorations and other commodities, equipment and facilities for automation technology lines, etc. - Production of building material and other products for the construction industry, production installation and repair of equipment and faci lities of automation technology lines. - Consultant services for tending, design, construction, project management, automation technology transfer - Property business, services of goods delivery and transportation

15. General General Mathematics Mathematics For Nonmathematicians Abstract model theory Applications of model theory See also 03C60 None of the above, but in this section Thue and Post systems, etc. http://amf.openlib.org/2001/msc2000.xsd

16. "Word Problems For Restricted Semi-Thue Systems" By a classical result of Post and Markov, there exist finitely presented by a confluent and terminating semiThue system such that the (characteristic http://www.liafa.jussieu.fr/web9/manifsem/description_fr.php?idcongres=42

17. Computing And Information Technology Interactive Digital Educational Library Rep Confluent and Other Types of Thue systems. By Ronald V. Book Educational level, Postgraduate (research) discussion index Post message http://www.citidel.org/?op=getobj&identifier=oai:DBLP:article.journals/jacm/Book

18. Jozef Gruska Foundations Of Computing International Thompson Buechi and Muller Automata; Finite State Control of Reactive systems Rice s Theorem; Halting Problem; Tiling Problem; Thue Problem; Post Correspondence http://www.fi.muni.cz/usr/gruska/about.html

Jozef Gruska: Foundations of computing International Thompson Computer Press. April 1997. Paperback, xv+716 pages, 214 figures/tables, ISBN: 1-85032-243-0 About the book An innovative, synthetizing, much broader than usual, precise but not too formal and focused presentation of fundamentals of modern computing as rich on interesting/important and indispensible conceptual tools and methods as well as deep/exciting results for undergraduate and graduate students in computing and related areas (engineering, science, mathematics,...). Suitable also as a refernce book or a handbook for all ambitious professionals in computing and related areas with heavy and/or deep use of computing. Main areas covered by the book: analysis of algorithms, discrete mathematics, automata and formal languages, models of (sequential and parallel) computers, computational complexity, computability and limitations of formal systems, rewriting systems, cryptographyand interactive/cryptographical protocols, interconnection (multiprocessor) networks and communication complexity. The book has 11 chapters, 214 figures/tables, 277 examples, algorithms/protocols, 574 exercises in the text, 641 exercises/questions at the end of the chapters, 588 bibliographical references, and a detailed index (48 pages).

19. Lecture Notes In Computer Science, 2004(3340 ) From Post systems to the Reachability Problems for Matrix Semigroups and Words Avoiding 73Powers and The Thue-Morse Morphism / Rampersad, Narad http://www.ucm.es/BUCM/compludoc/W/10501/03029743_27.htm

Sumario Título / Autor(es) Página(s) Developments in Language Theory - 8th International Conference, DLT 2004 . Auckland, New Zealand, December 2004 . Proceedings / Calude, Cristian S Calude, Elena Dinneen, Michael J Invited papers - Recognizable Sets of Graphs, Hypergraphs and Relational Structures: A Survey / Courcelle, Bruno Invited papers - Some New Directions and Questions in Parameterized Complexity / Downey, Rodney G McCartin, Catherine Invited papers - Basic Notions of Reaction Systems / Ehrenfeucht, A Rozenberg, G Invited papers - A Kleene Theorem for a Class of Communicating Automata with Effective Algorithms / Genest, Blaise Muscholl, Anca Kuske, Dietrich Invited papers - Algebraic Topological Models for DNA Recombinant Processes / Jonoska, Natasa Saito, Masahico Regular Expressions for Two-Dimensional Languages Over One-Letter Alphabet / Anselmo, Marcella Giammarresi, Dora Madonia, Maria On Competence in CD Grammar Systems / Beek, Maurice H ter Csuhaj-Varjú, Erzsébet Holzer, Markus Vaszil, György The Dot-Depth and the Polynomial Hierarchy Correspond on the Delta Levels / Borchert, Bernd

20. Computer Science Seminars And Short Courses — 2001/02 Since the work of Markov and Post it is known that there exist Thue systems with undecidable word problems. In order to locate the borderline between http://www.cs.le.ac.uk/seminars/archive/ComputerScience01-02.html

computer science HOME MAP CONTACT ABOUT ... People The Computer Science Group holds regular advanced and research level meetings, mainly during the two University teaching semesters. These meetings take the form of Research Seminars , which consist of one hour talks given by invited speakers or members of the Department on current research; Reading Groups which involve a small number of staff and research students studying an advanced book or research paper; and Lecture Courses which are usually delivered by a member of staff and pitched at advanced postgraduate level. Such lecture courses are also taken by staff and research students. Semester 2 Seminar programme Friday 5 July, 14:30 in Benett LT1 Pr Samson Abramsky (Computer Lab, Oxford University) Friday 31 May, 14:30 in Benett LT1 Dr Steffen van Bakel (Department of Computing, Imperial College) Approximation and Filter Semantics for Combinator Systems Friday 24 May, 14:30 in Benett LT1 Dr Steve Schneider (Department of Computer Science, Royal Holloway, University of London) Non-interference, may testing, and compositionality

21. Semi-Thue System - Wikipedia, The Free Encyclopedia A SemiThue system is a special type of Post canonical system. Semi-Thue systems were developed as part of a program to add additional constructs to http://en.wikipedia.org/wiki/Semi-Thue_system

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Semi-Thue system From Wikipedia, the free encyclopedia Jump to: navigation search The references in this article would be clearer with a different or consistent style of citation footnoting , or external linking This article or section contains too much jargon and may need simplification or further explanation. Please discuss this issue on the talk page , and/or remove or explain jargon terms used in the article. Editing help is available. This article has been tagged since October 2007 In computer science and mathematics a Semi-Thue system is a string rewriting system. It is named after the Norwegian mathematician Axel Thue , who introduced systematic treatment of string rewriting systems in the early 20th century. Contents Definition History and importance The Word problem for Semi-Thue systems See also ... edit Definition A Semi-Thue system (also called a string rewriting system ) is a tuple R where is a finite alphabet . Elements of the set of finite (possibly empty) strings on are called words R is a binary relation on , i.e.

22. Decision Problems For Semi-Thue Systems With A Few Rules 30 Robert McNaughton, SemiThue systems with an Inhibitor, Journal of Automated Reasoning, v.26 n.4, p.409-431, May 2001. 31 31 E.L. Post, http://portal.acm.org/citation.cfm?id=1065165

23. Springer Online Reference Works These systems in fact coincide with local canonical Post systems. Every Thue system can be regarded as a Thue semisystem, but the converse is false. http://eom.springer.de/T/t092790.htm

Encyclopaedia of Mathematics T Article referred from Article refers to Thue system An associative calculus , named after A. Thue , who first formulated the problem of recognizing equality of words in associative systems (the Thue problem , see ). If in a given Thue system the only admissible substitutions are taken to be substitutions of right-hand sides of relations into the left-hand sides (that is, the reverse substitutions are excluded), then one obtains a Thue semi-system (or semi-Thue system , or system of substitutions ). These systems in fact coincide with local canonical Post systems. Every Thue system can be regarded as a Thue semi-system, but the converse is false. References Kra. Vidensk. Selsk. Skrifter. S.I. Adyan This text originally appeared in Encyclopaedia of Mathematics - ISBN 1402006098

24. COT5310 Formal Languages And Automata Theory Fall 2007 Show that given a SemiThue, S, you can produce a Post Normal System, NS, such that x = * y in S iff x = * y in NS. You must give the construction of NS http://www.cs.ucf.edu/courses/cot5310/COT5310Fall2007.html

COT5310: Formal Languages and Automata Theory -- Fall 2007 Formal Languages and Automata Theory Fall 2007 Charles E. Hughes School of Electrical Engineering and Computer Science University of Central Florida email: ceh@cs.ucf.edu Structure : MW 19:30-20:45 (7:30PM - 8:45PM), HEC-103 ; 29 class periods, each 75 minutes long. Go To Week Instructor: Charles Hughes; Harris Engineering Center 439C; 823-2762; ceh@cs.ucf.edu Office Hours: MW 17:00-18:15 (5:00PM - 6:15PM) GTA: Greg Tener, TTh 18:30-19:30 (6:30PM - 7:30PM) in HEC 365 Text: There will be no required text. I will use extensive notes.

25. Distributional String-Rewriting Problems The distributional word problem for Thue systems was shown to be averagecase NP-Complete Problems Previous Distributional Post Correspondence http://www.uncg.edu/mat/avg/avgnp/node13.html

Next: Distributional Word Problem Up: Average-Case NP-Complete Problems Previous: Distributional Post Correspondence Distributional String-Rewriting Problems We first consider the word problem for Thue systems. This problem was first studied in modern algebra by Thue . Wang and Belanger studied its bounded version with uniform distributions on instances. Let be a non-empty finite alphabet. An ordered pair of strings on alphabet is called a production (rule, or rewriting rule). It is customary to write the production in the form . Let and be two strings. Let be a production. Write (omitting when there is no ambiguity) if and for (possible null) strings and . Let be a set of productions. Then write if for some . Write if there is a finite sequence: for . The inverse of the production is the production . A Thue system is a non-empty set of productions such that for each , the inverse of is also in . Write to denote both the production and its inverse. Let be a Thue system. Let and be two strings. Then iff . So we write if . We write if there is a finite sequence: for . We write if there exists an such that . This is an equivalence relation, and set of equivalence classes form a monoid under the operation of concatenation.

26. 2x2x2 2 Symbol Systems | Enzymind Cross sections of 3D Thue-Morse patterns, with the slice plane centered on a long diagonal of the Post new comment. Are you a spam bot? (yes or no) * http://enzymind.com/2x2x2_2_symbol_systems

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27. NEW PROOFS OF OLD THEOREMS IN LOGIC AND FORMAL LINGUISTICS, Abstract Theorem 1 constructs, from any word problem in a semiThue system, an equivalent Post correspondence problem, showing the undecidability of the http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0

28. Recursivity: Narad Rampersad's Work On Combinatorics On Words What Narad proved is the following the word t defined by Thue (and now called the Nonsquaring transformation systems start to look semi-random. http://recursed.blogspot.com/2007/11/narad-rampersads-work-on-combinatorics.html

skip to main skip to sidebar Recursivity Recurrent thoughts about mathematics, science, politics, music, religion, and Recurrent thoughts about mathematics, science, politics, music, religion, and Recurrent thoughts about mathematics, science, politics, music, religion, and Recurrent thoughts about .... Saturday, November 10, 2007 Narad Rampersad's Work on Combinatorics on Words My student, Narad Rampersad , had a successful defense (or "defence", as they like to say in Canada) of his Ph. D. thesis yesterday. That's a good excuse to discuss some aspects of combinatorics on words. In combinatorics on words, we are interested in words and their properties. By a word , I mean a finite or infinite string of symbols. The Norwegian mathematician Axel Thue initiated this field a hundred years ago in his study of infinite words avoiding squares and overlaps. A square is a word of the form xx , where x is a nonempty word. For example, the English word murmur is a square, with x mur . Thue asked, is it possible to create an infinite word over a finite alphabet, such that it avoids squares (i.e., contains no squares)? Over a two-letter alphabet, this can't be done: the first letter is

29. \documentstyle[12pt]{article} \oddsidemargin -2mm \evensidemargin Church suggested to Post to study also the decidability problem for Thue s systems known also as the word problem for monoids or semigroups. http://www.calculemus.org/MathUniversalis/7/01muraw.txt

30. WORD PROBLEMS FOR BIDIRECTIONAL, SINGLE-PREMISE POST SYSTEMS One class of bidirectional Post systems, the T hue systems first defined in 71, have been extensively studied. Thue systems with unsolvable word problems http://www.priorartdatabase.com/IPCOM/000128697/

December 24, 2007 Document Info IPCOM # Published Subscription feature Number of pages Language Subscription feature Format(s) PDF (HTML) WORD PROBLEMS FOR BIDIRECTIONAL, SINGLE-PREMISE POST SYSTEMS A bidireetionaZ, single-premise Post system is a Post canonical form F where, if [Equation ommitted] is a rule, then [Equation ommitted] is also a rule. One class of bidirectional Post systems, the T hue systems first defined in [71, have been extensively studied. Thue systems with unsolvable word problems were shown to exist by Post [51 and, more recently, Overbeek 14] demonstrated that this class of problems represents every recursively enumerable (r. e.) many-one degree of unsolvability. In this paper we extend Overbeek's result to include bidirectional extensions of Post. normal systems, tag systems and the one-letter systems introduced by Hosken [1]. Post Systems. Let E be ,a finite set of symbols and let [Equation ommitted] On be new ... Page 1 of 12 THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL. WORD PROBLEMS FOR BIDIRECTIONAL, SINGLE-PREMISE POST SYSTEMS

31. Welcome To The Post's Correspondence Problem! To describe subclasses of Post’s Correspondence Problem, we use PCPs to Decision problems for semiThue systems with a few rules, Proceedings, http://www.cs.ualberta.ca/~zhao/PCP/

PCP News PCPSolver version 0.0.3 is released with source code. README (Nov 16, 2003) PCPSolver version 0.0.2 is released with source code. (April 25, 2003) I published a paper named Tackling Post's Correspondence Problem in the Third International Conference on Computer and Games in 2002. (July 26, 2002) My Master's thesis about solving PCP is now available. (March 7, 2002) What's Post's Correspondence Problem (PCP)? Definition: Given an alphabet S , one instance of Post's correspondence problem of size s is a finite set of pairs of strings ( g i h i i = 1...s s>=1) over the alphabet S A solution of length n >= 1 to this instance is a sequence i i i n of selections such that the strings g g ... g in and h h ... h in formed by concatenation are identical. Width of a PCP instance is the length of the longest string in g i and h i i s Pair i is the short name for pair ( g i h i ), where g i and h i are the top string and bottom string of the pair respectively. Mostly, people are interested in optimal solution , which has the shortest length over all possible solutions to an instance. The corresponding length is called optimal length . We use the word hard or difficult to describe instances whose optimal lengths are very large. For simplicity, we restrict the alphabet

32. IBM Archives: Horace W. Thue In March 1965, Thue was named vice president, plans and controls, of the IBM systems Manufacturing Division. A year later, he was appointed as general http://www-03.ibm.com/ibm/history/exhibits/builders/builders_thue.html

United States change Home Products My IBM ... IBM Builders reference room Horace W. Thue Horace W. (Bud) Thue joined IBM in 1957, and served as corporate director of manufacturing planning, general manager of the company's Endicott, N.Y., plant, and vice president of manufacturing of the IBM General Products Division, among other managerial positions in the early years of his IBM career. In March 1965, Thue was named vice president, plans and controls, of the IBM Systems Manufacturing Division. A year later, he was appointed as general manager of IBM's manufacturing and development facility in Rochester, Minn. , a post he held until 1969. Thue held a B.S. degree in industrial engineering from the University of North Dakota. The Builders details Ray S. Abuzayyad

33. Bibliografía Finally published on Complex systems vol 15, number 1 (2004) pp 1 40.). . 44 Post, E. L. Recursive unsovability of a problem of Thue. http://computacion.cs.cinvestav.mx/~acaceres/docs/tesis/node115.html

Siguiente: Subir: Anterior: Conclusiones y trabajos posteriores A DAMATZKY, A. Collision-Based computing Springer-Verlag, 2002. A RBIB, M. A. Simple self-reproducing universal automata. Information and Control 9 , 2 (April 1966), 177-189. B EAUCHAT, J.-L., AND H AENNI, J.-O. Von Neumann's 29-state cellular automaton: A hardware implementation. IEEE Transactions on education 43 , 3 (August 2000), 300-308. B ERGER, R. The undecibility of the domino problem , vol. 66 of Memoirs of the AMS American Mathematical Society, 1966. B UCKINGHAM, D. J. Some facts of life. Byte 2 (December 1978), 54-67. C HOPARD, B., AND D ROZ, M. Cellular Automata Modeling of Physical Systems Cambridge University Press, 1998. C ODD, E. F. Cellular automata ACM Monograph Series. Academic Press NY, 1968. C ONWAY, J. H., AND S LOANE, N. J. A. Sphere Packings, Lattices and Groups , 1 ed ed., vol. 290 of Grundlehren der Mathematischen Wissenschaften Springer, New York, 1988. C OOK, M. Introduction to the activity of rule 110-(1998 unpublished). Document avalaible by e-mail request to acaceres@computacion.cs.cinvestav.mx (On e-mail communication-2003. Finally published on Complex Systems vol 15, number 1 (2004) pp 1 - 40.).

34. Www.cyclingnews.presents Road Racing From Around The World systems 58 Cédric Fragniere (Sui) Phonak Hearing systems 59 Hansen Thue Phonak Hearing systems 69 Anton Chantyr (Rus) Team CoastPost Swiss Team 70 http://www.cyclingnews.com/results/2000/feb00/gpumag003.shtml

Tech Features Road MTB ... Feedback Grand Prix UMag #3 - Cat. 1.5 Croatia, February 18, 2000 Results Home Search Cyclingnews Store Survey ... Site-Tech FAQs All of the content published on cyclingnews.com Cyclingnews . Cyclingnews is the trademark of Future Publishing (Overseas) Limited, a Future plc group company. Editorial department for further information. Telephone: Fax: Contacts: Editorial Advertising Systems: Economic Outlook

35. Digital Farming: Two Well Established Irish Post Entities Team Up To Create A Fu The Farm provided a onestop-shop for all 1the Post work for the whole range some of the Thue Lives documentary series and Reeling in the Years for RTE. http://findarticles.com/p/articles/mi_m0HNN/is_3_18/ai_99206538

@import url(/css/us/pub_page_article.css); @import url(/css/us/template_503.css); @import url(/css/us/tabs_503.css); @import url(/css/us/fa_bnet.css); @import url(http://i.bnet.com/css/fa.css); BNET Research Center Find 10 Million Articles BNET.com Advanced Search Find in free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Explore Publications in: all Arts Autos Business ... Technology Content provided in partnership with FIND IN free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Advanced Search print share ... March, 2003 by Bob Pank DUBLIN, IRELAND For many involved with the post industry, 2002 was not the easiest year, but in Ireland the prevailing boom conditions have led to industry expansion. This has created the right environment for the formation of The Farm Digital Post Production (www.thefarm.ie) late in the year from two top-ranking Dublin post houses. Blade, which is no longer, had established credentials with its expertise in video editing, and the original Farm had been mixing audio for a broad range of clients from commercials to international pop stars since 1995. Now, their combined forces, along with a $4 million investment in new equipment and talent, has lifted their capabilities to a full post production service, including visual and audio post, as well as digital effects. There is a broad range of video equipment, including a six-seat Avid Unity server network connecting one online and three offline Media Composers, an online Symphony and an Avid Xpress, which has many uses, including loading new material into the Unity server. The Farm scores a European first by running both Quantel's iQ and eQ editing systems each operating with any SD or HD formats. Editing is supported by a substantial graphics department, which includes an HD Flame and Combustion from Discreet, two Softimage IXSI workstations and Adobe After Effects. Equipment is connected by Ireland's first 2 Gigabit Ethernet network Audio mixing facilities are based around Avid Audio Vision and Digidesign Pro Tools systems. In all there are five online rooms.

36. Automata And Formal Languages the set of finite languages in SL is enumerable Post Correspondence Problem G and some right linear G unrestricted grammars (aka semiThue or type 0 or http://carlstrom.com/stanford/comps/Automata-and-Formal-Languages.txt

=1, and for all i>=0, uv^iw is in L. Furthermore, n is no greater than the number of states of the samllest FA accepting L. regular sets are closed under union, concatenation, kleene closure complement intersection substitution homomorphisms and inverse homomorphisms quotient with arbitrary sets the set of sentences accepted by an FA M with n states is: nonempty iff the FA accepts a sentence of length less than n infinite iff the FA accepts a sentence of length l where n <=l <=i <=n and 1 <=j <01) is undecidable (Godel's incompleteness theorem) theory of reals with addition IS DECIDABLE presburger arithmetic IS DECIDABLE (Z+= <01) - highlights of other important language classes auxillary PDA (deterministic or nondeterministic) read only input tape with w FSM r/w tape of length of input string w a stack stack automaton (SA) is a PDA plus input is two-way read only with end markers the stack head can traverse the stack in read only mode - P decidable vs decidable but not P (NP-complete vs PSPACE) vs undecidable

37. GeorgeSzpiro.com As a highschool student Thue showed the first signs of a superior ability by . and an oscillator systems with unparalleled stability had to be built. http://www.georgeszpiro.com/index.asp?page=kepler/chapter04.htm

38. Universality Emil Post, 1920s, String replacement rules designed to prove SemiThue systems Axel Thue, 1910, Apply string replacement rules in arbitrary order. http://www.cs.princeton.edu/introcs/75universality/

Intro to Programming 1. Elements of Programming 1.1 Your First Program 1.2 Built-in Types of Data ... Programming Assignments 7.5 Universality This section under major construction. One of the crowning scientific achievements of the 20th century was formalizing the notion of computation . In this section we address the fundamental question of what is computable in this Universe. Surprising revelation of 20th century is that a general purpose computer is capable of performing any computation that any other computer can. Perhaps the most important idea in all of computer science. Many different types of computational devices: Cray supercomputer, Dell PC, iMac, Palm Pilot, XBox, Tivo, Turing machine, TOY machine, Java programming language, Microsoft Excel, Java cell phone, quantum computer, Perl programming language. Is there any fundamental different between what these things can do and what a Gaggia espresso maker can do? Turing machines are equivalent in power to TOY and Java. Can simulate any Turing machine with a Java program, can simulate TOY with a Turing machine, can simulate, Java with a TOY machine. Same idea works for C, C++, C#, Python, Excel, Outlook. Also Mac, PC, Cray, ENIAC, Konrad Zuse's Z3 (but not proved until 1998), Palm pilot. And TiVo, Xbox, Java cell phone/ But not DFA, Gaggia espresso maker, or this Tinker Toy computer that MIT students built to play Tic-Tac-Toe.

39. JSTOR Recursive Unsolvability Of A Problem Of Thue. Post s proof is in three parts. (1) He first considers a semiThue system, in which only the replacements of A ~ by B~ are allowed. http://links.jstor.org/sici?sici=0022-4812(194709)12:3<90:RUOAPO>2.0.CO;2-3

40. IngentaConnect Semi-Thue Systems With An Inhibitor A semiThue system with an inhibitor is one having a special symbol, called an inhibitor, that appears on the right side of every rule but does not appear http://www.ingentaconnect.com/content/klu/jars/2001/00000026/00000004/00207710

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Semi-Thue Systems with an Inhibitor Author: McNaughton R. Source: Journal of Automated Reasoning , Volume 26, Number 4, May 2001 , pp. 409-431(23) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: A semi-Thue system with an inhibitor is one having a special symbol, called an inhibitor, that appears on the right side of every rule but does not appear on the left side of any rule. The main result of this paper is that the uniform halting problem is decidable for the class of such systems. The concept of inhibitor is related to the concept of well-behaved derivation in systems without an inhibitor. The latter concept has received some attention from those interested in the open question as to whether the uniform termination problem for one-rule semi-Thue systems is decidable.

41. POST OFFICE MATTERS.; The Delivery System --Newspaper Boxes--The New O... - Arti The Post Office department at Washington has in contemplation several changes in Ille ito at City II;LII Pu.rk very Bt., , ,,ll , ,; Thue Ccitlill http://query.nytimes.com/gst/abstract.html?res=F10C15F734551A7493CAA9178CD85F4D8

42. Computability Complexity Logic Book Simulation of 37 other explication concepts modular machines, 2register machines, Thue systems, Markov algorithms, ordered vector addition systems (Petri http://www.di.unipi.it/~boerger/cclbookcontents.html

Studies in Logic and the Foundations of Mathematics, vol. 128, North-Holland, Amsterdam 1989, pp. XX+592. CONTENTS Graph of dependencies XIV Introduction XV Terminology and prerequisites XVIII Book One ELEMENTARY THEORY OF COMPUTATION 1 Chapter A. THE MATHEMATICAL CONCEPT OF ALGORITHM 2 PART I. CHURCH'S THESIS 2 1. Explication of Concepts. Transition systems, 2 Computation systems, Machines (Syntax and Semantics of Programs), Turing machines. structured (Turing- and register-machine) programs (TO, RO). 2. Equivalence theorem, 26 LOOP-Program Synthesis for primitive recursive functions. 3. Excursus into the semantics of programs. 34 Equivalence of operational and denotational semantics for RM-while programs, fixed-point meaning of programs, proof of the fixed-point theorem. 4*. Extended equivalence theorem. Simulation of 37 other explication concepts: modular machines, 2-register machines, Thue systems, Markov algorithms, ordered vector addition systems (Petri nets), Post calculi (canonical and regular), Wang's non-erasing half-tape machines, word register machines. 5. Church's Thesis 48

43. "Thue" - Topic Profile :: BoardReader JM Yeah, that was me being dumb befoer Aeson/Thue gave me an edumacation on components. What do you think about what I have listed in Post 14? http://boardreader.com/tp/Thue.html

My Account Login Sign Up Loading... Loading... Search in: Message Boards Images Forums Advanced search Home Topic profile for "Thue" google_ads_inner='adsense_search_1'; google_ads_sub_style = 'adsense_search'; google_ads_inner_width='468'; google_ads_inner_height='15'; google_ads_direction = 'cols'; google_ads_enable_text = 'off'; google_ads_enable_excerpt = 'off'; google_ads_caption_is_first = 'on'; google_ads_max_ads_nums = 1; google_afs_tracker_query = google_afs_query = 'Thue'; //google_afs_ad = 'w15'; // specify the number of ads you are requesting google_afs_client = 'pub-4537085524273794'; // substitute your client ID google_afs_channel = '9090258875'; // enter your comma-separated channel IDs google_afs_ie = 'utf8'; // select input encoding scheme google_afs_oe = 'utf8'; // select output encoding scheme google_afs_query_words = google_afs_query.split(" "); google_afs_ad = 'w10'; google_afs_adtest = 'off'; // ** set parameter to off before launch to production google_afs_adsafe = 'off'; // ** set parameter to off before launch to production google_afs_i = 0; stored_google_ads = false; google_ads_is_enabled = false; google_afs_request_has_done = false; google_afs_title_keywords = ''; google_afs_text_keywords = ''; Topic profile for "Thue" google_ads_inner='adsense_leaderboard_2'; google_ads_sub_style = 'ad_leaderboard'; google_ads_inner_width='728'; google_ads_inner_height='90'; google_ads_direction = 'cols'; google_ads_min_ads_nums = 1; google_ads_max_ads_nums = 4;

44. 0 Top The TOP Concept In The Hierarchy. 1 Adverbial Modification 169 abstraction 17 Post algebra 170 application 171 conversion 172 lambda . 328 theory of numerations 329 Thue system 33 unicorn 330 undecidability 331 http://staff.science.uva.nl/~caterina/LoLaLi/soft/ch-data/gloss.txt

45. 2001 - Freeciv.org The noteworthy difference from the second beta (1.11.8) is that a bug that caused it to not compile on some operating systems has been fixed. Thue Janus http://freeciv.wikia.com/wiki/2001

From Freeciv Jump to: navigation search edit News archive ... edit New maintainer 28 December 2001 A new maintainer has joined the Freeciv development team. He is Mike Kaufman Mike has been the maintainer of CivWorld the Freeciv scenario editor and helped in the creation of the new city dialog now in CVS. Have a happy new year! Vasco Alexandre da Silva Costa edit Freeciv Feature at O'Reilly 26 November 2001 C heck out the cool Freeciv feature at the O'Reilly Network Paul Zastoupil edit New Tutorial 21 November 2001 J acky Mallett has provided a new turorial for multiplayer called The Art of Freeciv . It is a wonderful read, and will probably help players of just about any level. Paul Zastoupil edit New experimental metaserver link 11 October 2001 A new experimental page for the metaserver has been added. It shows all the players currently connected to civserver.freeciv.org servers on the metaserver with their rankings. Check it out. Paul Zastoupil edit Italian Freeciv news site 20 September 2001 P aolo Sammicheli and Lino Mastrodomenico has put together a nice Italian Freeciv news site kudo's to you guys.

46. Freeciv-dev May 2001 FreecivDev Re Freeciv Re Trouble Staring CIV, Thue, 1240 Re inactive game for days (see game number) (PR 763), Reinier Post, 1557 http://lists.complete.org/freeciv-dev@freeciv.org/2001/05/index.html.gz

Complete.Org Mailing Lists Archives freeciv-dev ... May 2001 date index freeciv-dev May 2001 Thread Index Top All Lists [Prev Page] Last Modified: Thu May 31 17:10:52 2001 Messages in reverse chronological order [Next Page] May 31, 2001 [Freeciv-Dev] City state update delayed (PR#792) Christian Knoke May 30, 2001 [Freeciv-Dev] new civworld patch Mike Kaufman [Freeciv-Dev] Feedback request: Enhanced macro spiral_outward Ross W. Wetmore [Freeciv-Dev] Re: Server confused about war and attack states (PR#791) Thue [Freeciv-Dev] Server confused about war and attack states (PR#791) Christian Knoke [Freeciv-Dev] Re: Time to stop spam! Myrddin Ambrosius [Freeciv-Dev] Re: core file on civserver, http://civserver.freeciv.org/games/14401 Thue [Freeciv-Dev] Re: Time to stop spam! Tuomas Airaksinen [Freeciv-Dev] Re: Time to stop spam! dnh [Freeciv-Dev] Time to stop spam! Erik Sigra [Freeciv-Dev] Returned mail: see transcript for details (PR#790) Mail Delivery Subsystem MAGICWEB-TV MAGICWEB-TV [Freeciv-Dev] core file on civserver, http://civserver.freeciv.org/games/14401 freeciv Carl Albert Schreiber [Freeciv-Dev] Re: (no subject) Mika Korhonen [Freeciv-Dev] (no subject) Mikael Kauttu [Freeciv-Dev] Returned mail: see transcript for details (PR#786) Mail Delivery Subsystem MAGICWEB-TV [Freeciv-Dev] Returned mail: see transcript for details (PR#787) Mail Delivery Subsystem MAGICWEB-TV [Freeciv-Dev] New polish.ruleset V2

47. Games.freeciv.cvs (date) Re Thue Make Leonardo s Workshop choose a random unit , Reinier Post, 1738; Re Thue Layer view; you can choose not to display some , Erik Sigra, http://osdir.com/ml/games.freeciv.cvs/2001-02/index.html

var addthis_pub = 'comforteagle'; games.freeciv.cvs (date) Thread Index Top All Lists Prev Period ... Next Period February 28, 2001 thue: Don't accept most packets before the game has ... freeciv thue: Don't announce various governments with no pre... freeciv egbert: New HOWTOPLAY.de Translated by Frank Osterfe... freeciv sebauer: MUI client: Doubleclick on an messagewindow... freeciv February 27, 2001 thue: Add a space to a linebroken LOG_ERROR message. freeciv thue: A bit more checking when accepting players. In... freeciv thue: If no argument is given to server save command... freeciv thue: Small fixes to key shortcut helptexts. Patch ... freeciv February 26, 2001 egbert: de.po updated freeciv thue: Cities can now have trade (used to have a lo... freeciv pjkersten: Cleaned up nl.po, spelling corrections, r... freeciv freeciv pjkersten: Updated nl.po freeciv February 25, 2001 thue: Revert fix for goto bug and implement a better... freeciv thue: Fix case where the client would try to draw a ... freeciv vasc: Renamed Reboot to quitidle for more clarit... freeciv sebauer: MUI client: The units below the active unit...

48. Turing Complete@Everything2.com Examples of Turing complete formal systems include the following (along with the These various Turing complete formal systems have become the basis for http://everything2.com/index.pl?node=Turing complete

49. Pushing The Limits Of Game AI Technology — AiGameDev.com The system uses principles from developmental psychology to restrict the complexity (229 Kb) David Thue, Vadim Bulitko, Marcia Spetch, Eric Wasylishen http://aigamedev.com/coverage/aiide-2007-papers

Game AI for Developers Pushing the Limits of Game AI Technology Share This Coverage starts tomorrow ( Artificial Intelligence and Interactive Digital Entertainment ), featuring the most cutting edge research in game AI. The proceedings (Update: Also check out the papers for the poster session A Lightweight Intelligent Virtual Cinematography System for Machinima Production Machinima is a low-cost alternative to full production filmmaking. This paper introduces a lightweight artificial intelligence system, Cambot , that can be used to assist in machinima production. Cambot takes a script as input and produces a cinematic visualization — using an offline algorithm and a library of reusable cinematic knowledge. One of the advantages of this approach to virtual cinematography is a tight coordination between the positions and movements of the camera and the actors. A Lightweight Intelligent Virtual Cinematography System for Machinima Production (2.1 Mb) David K. Elson, Mark O. Riedl Wubble World Introducing Wubble World The system uses principles from developmental psychology to restrict the complexity of this learning task: a shared attention model that includes deictic pointing, and a concept acquisition system that allows for rapid learning of new words from a limited number of exposures.

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