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Post’s system of tag – A simple discrete nonlinear system
 Center for Theoretical Physics, University of Twente, Enschede, The Netherlands
, 1992
"... Abstract − We consider an instance T 0 of Post’s system of tag for which we show that it is nonlinear. Then we discuss some computer simulations and study the periodic behavior of T 0. 1. ..."
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Abstract − We consider an instance T 0 of Post’s system of tag for which we show that it is nonlinear. Then we discuss some computer simulations and study the periodic behavior of T 0. 1.
A Simple Discrete System with Chaotic Behavior*
"... Abstract — We discuss the behavior of a particular discrete system, viz. Post’s system of tag with alphabet {0,1}, deletion number d = 3, and rules: 0 → 00, 1 → 1101. As initial string we consider all strings of length less than or equal to 15 as well as all ‘‘worst case’ ’ inputs of the form (100) ..."
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Abstract — We discuss the behavior of a particular discrete system, viz. Post’s system of tag with alphabet {0,1}, deletion number d = 3, and rules: 0 → 00, 1 → 1101. As initial string we consider all strings of length less than or equal to 15 as well as all ‘‘worst case’ ’ inputs of the form (100) m with 1 ≤ m ≤ 128. 1.
1 An Inefficient Representation of the Empty Word
"... 49 in the Oosterparkneighborhood of Amsterdam. A couple of weeks after I arrived, Paul and I moved together with Arie de Bruin to a freshly painted room which happened to be the half of a former class room, like many offices in that old school building, separated from its companion by a rather thin ..."
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49 in the Oosterparkneighborhood of Amsterdam. A couple of weeks after I arrived, Paul and I moved together with Arie de Bruin to a freshly painted room which happened to be the half of a former class room, like many offices in that old school building, separated from its companion by a rather thin wall. Without difficulty or any intention we could hear at least 50 % of our neighbors ’ conversations as they could from ours. And the view from our room was something special too: a 19th century part of the former Amstel brewery which happened to be of too little interest to industrial archeology in order to survive in later days. Another wellknown feature of the old Mathematical Centre was its library: famous for its outstanding collection of books, journals and reports on mathematics and computer science, and remarkable for the dishes of rat poison on the floors, inviting the nightly intruders to commit suicide rather than nibbling at the precious volumes. In 1978 both Paul and I finished our Ph.D. work on parallel rewriting, although our theses have very little in common; cf. [1, 7]. But we both had the intention to change our subject into the direction of computational complexity: a subject in which Paul achieved much more than I did; see e.g. [4], which also gives me the opportunity to turn to a more serious matter that is related to the title of this note. 2
Extensions, Automorphisms, and Definability
 CONTEMPORARY MATHEMATICS
"... This paper contains some results and open questions for automorphisms and definable properties of computably enumerable (c.e.) sets. It has long been apparent in automorphisms of c.e. sets, and is now becoming apparent in applications to topology and dierential geometry, that it is important to ..."
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This paper contains some results and open questions for automorphisms and definable properties of computably enumerable (c.e.) sets. It has long been apparent in automorphisms of c.e. sets, and is now becoming apparent in applications to topology and dierential geometry, that it is important to know the dynamical properties of a c.e. set We , not merely whether an element x is enumerated in We but when, relative to its appearance in other c.e. sets. We present here
Computing Science A Question of Numbers
"... Note: This document is available in other formats. In my daydream, Neil Sloane and Simon Plouffe are contestants on "Jeopardy, " the TV game show. Sloane ..."
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Note: This document is available in other formats. In my daydream, Neil Sloane and Simon Plouffe are contestants on "Jeopardy, " the TV game show. Sloane
Date Title Source JanFeb, 1996 A Question of Numbers American Scientist, Vol 84 A Question of Numbers
"... numbers? " Later it is Plouffe's turn, and he selects "Real Numbers " for $1,000. Trebek reads out an answer: "1.618033989, " and Plouffe responds with the question: "What is phi, or the golden meanthe limiting value of the ratio of successive Fibonacci numbers?" In real life Sloane and Plouffe ar ..."
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numbers? " Later it is Plouffe's turn, and he selects "Real Numbers " for $1,000. Trebek reads out an answer: "1.618033989, " and Plouffe responds with the question: "What is phi, or the golden meanthe limiting value of the ratio of successive Fibonacci numbers?" In real life Sloane and Plouffe are not competitors but collaborators. Sloane is a mathematician at AT&T Bell Laboratories, well known for his work in graph theory, combinatorics and geometry. He is also the author of the Handbook of Integer Sequences, a compendium of some 2,300 sequences, published in 1973. Plouffe, a mathematician now at Simon Fraser University in British Columbia, is another collector of numbers and sequences, who volunteered a few years ago to help revise and expand the Handbook. Sloane and Plouffe are coauthors of the new edition, published last year as the Encyclopedia of Integer Sequences. It is a muchenlarged and enriched work, with more than 5,400 entries. Sloane's sequence database is also accessible by electronic mail. If you send a message to the Internet address
Internal Examiner: Dr. James Power
"... My supervisor Damien Woods deserves a special thank you. His help and guidance went far beyond the role of supervisor. He was always enthusiastic, and generous with his time. This work would not have happened without him. I would also like to thank my supervisor Paul Gibson for his advice and suppor ..."
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My supervisor Damien Woods deserves a special thank you. His help and guidance went far beyond the role of supervisor. He was always enthusiastic, and generous with his time. This work would not have happened without him. I would also like to thank my supervisor Paul Gibson for his advice and support. Thanks to the staff and postgraduates in the computer science department at NUI Maynooth for their support and friendship over the last few years. In particular, I would like to mention Niall Murphy he has always been ready to help whenever he could and would often lighten the mood in dark times with some rousing Gilbert and Sullivan. I thank the following people for their interesting discussions and/or advice:
Computing Science A Question of Numbers
"... he selects "Real Numbers " for $1,000. Trebek reads out an answer: "1.618033989, " and Plouffe responds with the question: "What is (J), or the golden mean—the limiting value of the ratio of successive Fibonacci numbers?" In real life Sloane and Plouffe are not competi tors but collaborators. Sloane ..."
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he selects "Real Numbers " for $1,000. Trebek reads out an answer: "1.618033989, " and Plouffe responds with the question: "What is (J), or the golden mean—the limiting value of the ratio of successive Fibonacci numbers?" In real life Sloane and Plouffe are not competi tors but collaborators. Sloane is a mathematician at AT&T Bell Laboratories, well known for his work in graph theory, combinatorics and geome try. He is also the author of the Handbook of Integer Sequences, a compendium of some 2,300 se quences, published in 1973. Plouffe, a mathe matician now at Simon Fraser University in British Columbia, is another collector of numbers and sequences, who volunteered a few years ago to help revise and expand the Handbook. Sloane and Plouffe are coauthors of the new edition, published last year as the Encyclopedia of Integer Sequences. It is a muchenlarged and enriched work, with more than 5,400 entries. Sloane's sequence database is also accessible by electronic mail. If you send a message to the In ternet address
Effectiveness ∗
, 2011
"... We describe axiomatizations of several aspects of effectiveness: effectiveness of transitions; effectiveness relative to oracles; and absolute effectiveness, as posited by the ChurchTuring Thesis. Efficiency is doing things right; effectiveness is doing the right things. —Peter F. Drucker ..."
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We describe axiomatizations of several aspects of effectiveness: effectiveness of transitions; effectiveness relative to oracles; and absolute effectiveness, as posited by the ChurchTuring Thesis. Efficiency is doing things right; effectiveness is doing the right things. —Peter F. Drucker
Beyond Turing Machines ∗
, 907
"... www.cstruct.org This paper discusses ”computational ” systems capable of ”computing” functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite descriptions by interacting with their environme ..."
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www.cstruct.org This paper discusses ”computational ” systems capable of ”computing” functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite descriptions by interacting with their environment. 1