Machines, Computations, and Universality: 4th International Conference, MCU 2004, Saint Petersburg, Russia, September 21-24, 2004, Revised Selected Papers PDF
Preview Machines, Computations, and Universality: 4th International Conference, MCU 2004, Saint Petersburg, Russia, September 21-24, 2004, Revised Selected Papers
Lecture Notes in Computer Science 3354 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard DavidHutchison LancasterUniversity,UK TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen UniversityofDortmund,Germany MadhuSudan MassachusettsInstituteofTechnology,MA,USA DemetriTerzopoulos NewYorkUniversity,NY,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA MosheY.Vardi RiceUniversity,Houston,TX,USA GerhardWeikum Max-PlanckInstituteofComputerScience,Saarbruecken,Germany Maurice Margenstern (Ed.) Machines, Computations, and Universality 4th International Conference, MCU 2004 Saint Petersburg, Russia, September 21-24, 2004 Revised Selected Papers 1 3 VolumeEditor MauriceMargenstern UniversityofMetz,LITA,EA3097 ÎleduSaulcy,57045Metz,France E-mail:[email protected] LibraryofCongressControlNumber:2005921802 CRSubjectClassification(1998):F.1,F.4,F.3,F.2 ISSN0302-9743 ISBN3-540-25261-4SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springeronline.com ©Springer-VerlagBerlinHeidelberg2005 PrintedinGermany Typesetting:Camera-readybyauthor,dataconversionbyBollerMediendesign Printedonacid-freepaper SPIN:11404262 06/3142 543210 Preface Inthisvolume,thereaderwillfirstfindtheinvitedtalksgivenattheconference. Then, in a second part, he/she will find the contributions which were presented attheconferenceafterselection.Inbothcases,papersaregiveninthealphabetic order of the authors. MCU 2004 was the fourth edition of the conference in theoretical computer science,Machines, Computations andUniversality,formerly,Machines etcalculs universels. The first and the second editions, MCU 1995 and MCU 1998, were organized by Maurice Margenstern, respectively in Paris and in Metz (France). The third edition, MCU 2001, was the first one to be organized outside France and it was held in Chi¸sin˘au (Moldova). Its co-organizerswere Maurice Margen- sternandYuriiRogozhin.TheproceedingsofMCU2001werethefirsttoappear in Lecture Notes in Computer Science, see LNCS 2055. From its very beginning, the MCU conference has been an international sci- entific event. For the fourth edition, Saint Petersburg was chosen to hold the meeting. The success of the meeting confirmed that the choice was appropriate. MCU 2004 also aimed at high scientific standards. We hope that this vol- ume will convince the reader that this tradition of the previous conferences was also upheld by this one. Cellular automata and molecular computing are well representedin this volume.And this is the case for quantum computing, formal languagesandthe theoryofautomatatoo.MCU2004alsodidnotfailits tradi- tionto provideourcommunitywithimportantresultsonTuringmachines.Also a new feature of the Saint Petersburg edition was the contributions on analog models and the presence of unconventional models. Here is an opportunity for me to thank the referees of the submitted papers for their very efficient work. The members of the program committee gave me decisive help on this occasion. Thanks to them, namely Anatoly Beltiukov (co- chair), Erzsebet Csuhaj-Varju´, Nikolai Kossovskii (co-chair), Kenichi Morita, Gheorghe Pa˘un, Yurii Rogozhin and Arto Salomaa, I can offer the reader this issue of LNCS. The local organizing committee included Anatoly Beltiukov, Nikolai Kossovskii, Michail Gerasimov, Igor Soloviov, Sorin Stratulat and, especially, Elena Novikova. MCU 2004 could not have been held without decisive supports. For this reason, I thank the Laboratoire d’Informatique Th´eorique et Appliqu´ee, LITA, the University of Metz, and one of its faculties, UFR MIM. Metz, 29 November 2004 Maurice Margenstern VI Organization Organization MCU 2004 was organized by the Laboratoire d’Informatique Th´eorique et Ap- pliqu´ee (LITA), University of Metz, Metz, France and the Euler International MathematicalInstitute, partofthe SaintPetersburgDepartmentofthe Steklov Institute of Mathematics, Russia. Program Committee Anatoly Beltiukov Co-chair, Udmurt University, Izhevsk, Russia Erzsebet Csuhaj-Varju Hungarian Academy of Sciences, Hungary Nikolai Kossovski Saint Petersburg State University, Russia Maurice Margenstern Co-chair, LITA, University of Metz, France Kenichi Morita Hiroshima University, Japan Yurii Rogozhin InstituteofMathematicsandComputerScience, Chi¸sin˘au, Moldova Arto Salomaa AcademyofFinlandandTurkuCentreforCom- puter Science, Finland Sponsoring Institutions Laboratoired’InformatiqueTh´eoriqueetAppliqu´ee(LITA),UniversityofMetz, Metz, France and the UFR MIM. Table of Contents Invited Lectures Algorithmic Randomness, Quantum Physics, and Incompleteness........ 1 C.S. Calude On the Complexity of Universal Programs ........................... 18 A. Colmerauer Finite Sets of Words and Computing ................................ 36 J. Karhuma¨ki Universality and Cellular Automata ................................. 50 K. Sutner Leaf Language Classes............................................. 60 K.W. Wagner Selected Contributions Computational Completeness of P Systems with Active Membranes and Two Polarizations............................................. 82 A. Alhazov, R. Freund, G. Pa˘un Computing with a Distributed Reaction-Diffusion Model............... 93 S. Bandini, G. Mauri, G. Pavesi, C. Simone Computational Universality in Symbolic Dynamical Systems ........... 104 J.-C. Delvenne, P. K˚urka, V.D. Blondel Real Recursive Functions and Real Extensions of Recursive Functions ... 116 O. Bournez, E. Hainry Ordering and Convex Polyominoes .................................. 128 G. Castiglione, A. Restivo Subshifts Behavior of Cellular Automata. Topological Properties and Related Languages ................................................ 140 G. Cattaneo, A. Dennunzio Evolution and Observation: A Non-standard Way to Accept Formal Languages ....................................................... 153 M. Cavaliere, P. Leupold The Computational Power of Continuous Dynamic Systems ............ 164 J. Mycka, J.F. Costa VIII Table of Contents Abstract Geometrical Computation for Black Hole Computation ........ 176 J. Durand-Lose Is Bosco’s Rule Universal? ......................................... 188 K.M. Evans Sequential P Systems with Unit Rules and Energy Assigned to Membranes ...................................................... 200 R. Freund, A. Leporati, M. Oswald, C. Zandron Hierarchies of DLOGTIME-Uniform Circuits ......................... 211 C. Iwamoto, N. Hatayama, K. Morita, K. Imai, D. Wakamatsu Several New Generalized Linear- and Optimum-Time Synchronization Algorithms for Two-Dimensional Rectangular Arrays .................. 223 H. Umeo, M. Hisaoka, M. Teraoka, M. Maeda Register Complexity of LOOP-, WHILE-,and GOTO-Programs ............. 233 M. Holzer, M. Kutrib Classification and Universality of Reversible Logic Elements with One-Bit Memory.................................................. 245 K. Morita, T. Ogiro, K. Tanaka, H. Kato Universal Families of Reversible P Systems........................... 257 A. Leporati, C. Zandron, G. Mauri Solving 3CNF-SAT and HPP in Linear Time Using WWW............. 269 F. Manea, C. Mart´ın-Vide, V. Mitrana Completing a Code in a Regular Submonoid of the Free Monoid ........ 281 J. N´eraud On Computational Universality in Language Equations ................ 292 A. Okhotin Attacking the Common Algorithmic Problem by Recognizer P Systems .. 304 M.J. P´erez Jim´enez, F.J. Romero Campero On the Minimal Automaton of the Shuffle of Words and Araucarias ..... 316 R. Schott, J.-C. Spehner Author Index ................................................ 329 When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is almost certainly wrong. ArthurC. Clarke Algorithmic Randomness, Quantum Physics, and Incompleteness Cristian S. Calude Department of ComputerScience University of Auckland,New Zealand [email protected] Abstract. Is randomness in quantum mechanics “algorithmically ran- dom”? Is there any relation between Heisenberg’s uncertainty relation and G¨odel’s incompleteness? Can quantumrandomness beusedto tres- pass the Turing’s barrier? Can complexity shed more light on incom- pleteness? In this paper we use variants of “algorithmic complexity” to discuss theabovequestions. 1 Introduction Whether a U nucleus will emit an alpha particle in a given interval of time 238 is “random”.If we collapse a wave function, what it ends of being is “random”. Which slit the electron went through in the double slit experiment, again, is “random”. Isthereanysenseto saythat“random”inthe abovesentencesmeans “truly random”? When we flip a coin, whether it’s heads or tails looks random, but it’s not truly random. It’s determined by the way we flip the coin, the force on the coin, the way force is applied, the weight of the coin, air currents acting on it, and many other factors. This means that if we calculated all these values, we would know if it was heads or tails without looking. Without knowing this information—and this is what happens in practice—the result looks as if it’s random, but it’s not truly random. Is quantum randomness “truly random”? Our working model of “truly ran- dom”is“algorithmicrandomness”inthesenseofAlgorithmicInformationThe- ory (see, for example, [5]). In this paper we compare quantum randomnesswith algorithmicrandomnessinanattempttoobtainpartialanswerstothefollowing questions: Is randomness in quantum mechanics “algorithmically random”? Is thereanyrelationbetweenHeisenberg’suncertaintyrelationandGo¨del’sincom- pleteness? Can quantum randomness be used to trespass the Turing’s barrier? Cancomplexitycastmorelightonincompleteness?Ouranalysisistentativeand raises more questions than offers answers. M.Margenstern(Ed.):MCU2004,LNCS3354,pp.1–17,2005. (cid:2)c Springer-VerlagBerlinHeidelberg2005 2 C.S. Calude 2 Algorithmic Randomness The main idea of Algorithmic Information Theory (shortly, AIT) was traced back in time (see [15,16]) to Leibniz, 1686 ([36], 40–41). If we have a finite set of points (e.g. say, observations of an experiment), then one can find many mathematical formulae each of which produces a curve passing through them all, in the order that they were given. Can we say that the given set of points satisfy the “law” described by such a mathematical formula? If the set is very large and complex, and the formula is comparatively simpler, then, indeed, we have a law. In Chaitin’s words [15], “a scientific theory is a computer program thatcalculatesthe observations,andthatthe smallerthe programis,the better the theory.”1 If the mathematical formula is not substantially simpler than the data itself, then we don’t have a law; still, there may be another mathematical formula qualifying as “law” for the given set. If no mathematical formula is substantially simpler than the set itself, the set is unstructured, law-less. Using thecomputerparadigm,ifnoprogram is substantially simpler than the set itself, then the set is “algorithmically random”. Ofcourse,tomakeideaspreciseweneedtodefinethebasicnotions,complex finite set, (substantially) smaller program, etc. A convenient way is to code all objects as binary strings and use Turing machines as a model of computation. For technical reasons (see [5,23]), our model is a self-delimiting Turing ma- chine, that is a Turing machine C which processes binary strings into binary strings and has a prefix-free domain: if C(x) is defined and y is either a proper prefix or an extension of x, then C(y) is not defined. The self-delimiting Turing machineU isuniversalif foreveryself-delimiting TuringmachineC thereexists afixedbinarystringp(thesimulator)suchthatforeveryinputx,U(px)=C(x): eitherbothcomputationsU(px)andC(x)stopand,inthiscasetheyproducethe same output or both computations never stop. Universal self-delimiting Turing machinescanbe effectivelyconstructed.The relationwithcomputability theory is given by the following theorem: A set is computably enumerable (shortly, c.e.) iff can be generated by some self-delimiting Turing machine. The Omega number introduced in [13] (cid:2) Ω = 2−|x| =0.ω ω ...ω ... (1) U 1 2 n U(x) stops is the halting probability of U; |x| denotes the length of the (binary) string x. Omegais one ofthe mostimportantconcepts in algorithmicinformationtheory (see [5]). 1 Themodernapproach,equatingamathematical formulawithacomputerprogram, would probably not surprise Leibniz, who designed a succession of mechanical cal- culators, wrote on the binary notation (in 1679) and proposed the famous “let us calculate” dictum; see more in Davis [20], chapterone.
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