Unconventional Computing: 7th International Conference, UC 2008 Vienna, Austria, August 25-28, 2008. Proceedings

266 Pages·2008·10.349 MB·English

by  Časlav Brukner (auth.), Cristian S. Calude, José Félix Costa, Rudolf Freund, Marion Oswald, Grzegorz Rozenberg (eds.)

Lecture Notes in Computer Science 5204
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
AlfredKobsa
UniversityofCalifornia,Irvine,CA,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
UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
Max-PlanckInstituteofComputerScience,Saarbruecken,Germany
Cristian S. Calude José Félix Costa
Rudolf Freund Marion Oswald
Grzegorz Rozenberg (Eds.)
Unconventional
Computation
7th International Conference, UC 2008
Vienna, Austria, August 25-28, 2008
Proceedings
1 3
VolumeEditors
CristianS.Calude
UniversityofAuckland,DepartmentofComputerScience
92019Auckland,NewZealand
E-mail:[email protected]
JoséFélixCosta
UniversidadeTécnicadeLisboa,DepartmentofMathematics
1049-001Lisboa,Portugal
E-mail:[email protected]
RudolfFreund
MarionOswald
ViennaUniversityofTechnology,FacultyofInformatics
1040Vienna,Austria
E-mail:{rudi,marion}@emcc.at
GrzegorzRozenberg
LeidenUniversity,LeidenInstituteofAdvancedComputerScience
2333CALeiden,TheNetherlands
and
UniversityofColorado,DepartmentofComputerScience
Boulder,CO80309-0430,USA
E-mail:[email protected]
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CRSubjectClassification(1998):F.1,F.2
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ISBN-10 3-540-85193-3SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-85193-6SpringerBerlinHeidelbergNewYork
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Preface
The 7th International Conference on Unconventional Computation, UC 2008,
organized under the auspices of the EATCS, by the Vienna University of Tech-
nology (Vienna, Austria) and the Centre for Discrete Mathematics and Theo-
retical Computer Science (Auckland, New Zealand) was held in Vienna during
August 25–28,2008.
ThevenuefortheconferencewastheParkhotelSch¨onbrunnintheimmediate
vicinity of Scho¨nbrunn Palace, which, together with its ancillary buildings and
extensive park, is by virtue of its long and colorful history one of the most
importantculturalmonumentsinAustria.Vienna,locatedintheheartofcentral
Europe, is an old city whose historical role as the capital of a great empire and
the residence of the Habsburgs is reflected in its architectural monuments, its
famousartcollectionsanditsrichculturallife,inwhichmusichasalwaysplayed
an important part.
The International Conference on Unconventional Computation (UC) series,
https://www.cs.auckland.ac.nz/CDMTCS/conferences/uc/,isdevotedtoall
aspectsofunconventionalcomputation–theoryaswellasexperimentsandappli-
cations.Typical,butnotexclusive,topicsare:naturalcomputingincludingquan-
tum,cellular,molecular,neuralandevolutionarycomputing,chaosanddynamical
system-basedcomputing,andvariousproposalsforcomputationsthatgobeyond
theTuringmodel.
The first venue of the Unconventional Computation Conference (formerly
called Unconventional Models of Computation) was Auckland, New Zealand in
1998; subsequent sites of the conference were Brussels, Belgium in 2000, Kobe,
Japanin 2002,Seville, Spain in 2005,York, UK in 2006,and Kingston, Canada
in 2007.
The titles of volumes of previous UC conferences are as follows:
1. Calude,C.S.,Casti,J.,Dinneen,M.J.(eds.):UnconventionalModelsofCom-
putation. Springer, Singapore (1998)
2. Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.): Unconventional Models of
Computation,UMC2K:ProceedingsoftheSecondInternationalConference.
Springer, London (2001)
3. Calude, C.S., Dinneen, M.J., Peper,F. (eds.): UMC 2002.LNCS, vol. 2509.
Springer, Heidelberg (2002)
4. Calude,C.S.,Dinneen,M.J.,Pa˘un,G.,Jesu´sP´erez-J´ımenez,M.,Rozenberg,
G. (eds.): UC 2005. LNCS, vol. 3699.Springer, Heidelberg (2005)
5. Calude, C.S., Dinneen, M.J., Pa˘un, G., Rozenberg, G., Stepney, S. (eds.):
UC 2006. LNCS, vol. 4135. Springer, Heidelberg (2006)
6. Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T.
(eds.): UC 2007. LNCS, vol. 4618.Springer, Heidelberg (2007)
VI Preface
The Steering Committee of the International Conference on Unconventional
Computation series includes Thomas Ba¨ck (Leiden, The Netherlands), Cristian
S.Calude (Auckland,New Zealand,Co-chair),LovK.Grover(MurrayHill, NJ,
USA), Jan van Leeuwen (Utrecht, The Netherlands), Seth Lloyd (Cambridge,
MA, USA), Gheorghe Pa˘un (Bucharest, Romania), Tommaso Toffoli (Boston,
MA,USA),CarmeTorras(Barcelona,Spain),GrzegorzRozenberg(Leiden,The
Netherlands,andBoulder,Colorado,USA,Co-chair),andArtoSalomaa(Turku,
Finland).
The four keynote speakers of the conference for 2008 were:
– CˇaslavBrukner(AustrianAcademyofSciences,Austria):“QuantumExperi-
mentsCanTestMathematicalUndecidability”
– Anne Condon (University of British Columbia, Canada): “Computational
Challenges and Opportunities in the Design of Unconventional Machines
from Nucleic Acids”
– David Corne (Heriot-Watt University, UK): “Predictions for the Future of
Optimization Research”
– JonTimmis (UniversityofYork,UK):“ImmuneSystemsandComputation:
An Interdisciplinary Adventure”
In addition, UC 2008 hosted three workshops – one on “Computing with
Biomolecules,”organizedbyErzs´ebetCsuhaj-Varju´(HungarianAcademyofSci-
ences,Hungary)andRudolfFreund(ViennaUniversityofTechnology,Austria),
oneon“OpticalSupercomputing,”organizedbyShlomiDolev(Ben-GurionUni-
versity,Israel),MihaiOltean(Babes-BolyaiUniversity,Romania)andWolfgang
Osten(StuttgartUniversity,Germany)andoneon“PhysicsandComputation,”
organizedbyCristianS.Calude(UniversityofAuckland,NewZealand)andJos´e
F´elix Costa (Technical University of Lisbon, Portugal).
The ProgrammeCommittee is gratefulfor the highly appreciatedworkdone
by the referees for the conference. These experts were:
SelimG.Akl,CristianS.Calude,AlbertoCastellini,BarryS.Cooper,David
Corne, Jos´e F´elix Costa, Erzs´ebet Csuhaj-Varju´, Michael J. Dinneen, Gerard
Dreyfus,RudolfFreund,DanielGrac¸a,MikaHirvensalo,NatashaJonoska,Jarkko
Kari, Yun-Bum Kim, Manuel Lameiras Campagnolo, Vincenzo Manca, Marius
Nagy, Turlough Neary, Marion Oswald, Roberto Pagliarini, Gheorghe Pa˘un,
Ferdinand Peper,Petrus H. Potgieter,KaiSalomaa,KarlSvozil,Carme Torras,
HiroshiUmeoandDamienWoods.
TheProgrammeCommitteeconsistingofSelimG.Akl(Kingston,ON,Cana-
da),CristianS.Calude(Auckland,NewZealand),BarryS.Cooper(Leeds,UK),
David Corne (Edinburgh, UK), Jos´e F´elix Costa (Lisbon, Portugal, Co-chair),
Erzs´ebetCsuhaj-Varju´(Budapest,Hungary),MichaelJ.Dinneen(Auckland,New
Zealand), Gerard Dreyfus (Paris, France), Rudolf Freund (Vienna, Austria,
Co-chair), Eric Goles (Santiago, Chile), Natasha Jonoska (Tampa, FL, USA),
JarkkoKari(Turku,Finland),Vincenzo Manca(Verona,Italy),GheorghePa˘un
(Bucharest,Romania),FerdinandPeper(Kobe,Japan),PetrusH.Potgieter(Pre-
toria,SouthAfrica),KaiSalomaa(Kingston,Canada),KarlSvozil(Vienna,Aus-
tria),CarmeTorras(Barcelona,Spain),HiroshiUmeo(Osaka,Japan),HaroldT.
Preface VII
Wareham(St.John’s,NL,Canada),DamienWoods(Cork,Ireland)andXinYao
(Birmingham,UK)selected16papers(outof22)tobepresentedasregularcon-
tributions.
WeextendourthankstoallmembersofthelocalConferenceCommittee,par-
ticularly to Aneta Binder, Rudolf Freund (Chair), Franziska Gusel, and Marion
Oswald of the Vienna University of Technology for their invaluable organiza-
tional work.
The conference was partially supported by the Institute of Computer Lan-
guagesof the Vienna University of Technology,the KurtGo¨del Society, andthe
OCG (Austrian Computer Society); we extend to all our gratitude.
It is a great pleasure to acknowledge the fine co-operation with the Lecture
Notes in Computer Science team of Springer for producing this volume in time
for the conference.
June 2008 Cristian S. Calude
Jos´e F´elix Costa
Rudolf Freund
Marion Oswald
Grzegorz Rozenberg
Table of Contents
Invited Papers
Quantum Experiments Can Test Mathematical Undecidability......... 1
Cˇaslav Brukner
Computational Challenges and Opportunities in the Design of
Unconventional Machines from Nucleic Acids ........................ 6
Anne Condon
Predictions for the Future of Optimisation Research.................. 7
David Corne
Immune Systems and Computation: An Interdisciplinary Adventure .... 8
Jon Timmis, Paul Andrews, Nick Owens, and Ed Clark
Regular Contributions
Distributed Learning of Wardrop Equilibria ......................... 19
Dominique Barth, Olivier Bournez, Octave Boussaton, and
Johanne Cohen
Oracles and Advice as Measurements............................... 33
Edwin Beggs, Jos´e F´elix Costa, Bruno Loff, and John V. Tucker
From Gene Regulation to Stochastic Fusion ......................... 51
Gabriel Ciobanu
A Biologically Inspired Model with Fusion and Clonation of
Membranes ..................................................... 64
Giorgio Delzanno and Laurent Van Begin
Computing Omega-Limit Sets in Linear Dynamical Systems ........... 83
Emmanuel Hainry
The Expressiveness of Concentration Controlled P Systems............ 96
Shankara Narayanan Krishna
On Faster Integer Calculations Using Non-arithmetic Primitives ....... 111
Katharina Lu¨rwer-Bru¨ggemeier and Martin Ziegler
A Framework for Designing Novel Magnetic Tiles Capable of Complex
Self-assemblies................................................... 129
Urmi Majumder and John H. Reif
X Table of Contents
The Role of Conceptual Structure in Designing Cellular Automata to
Perform Collective Computation ................................... 146
Manuel Marques-Pita, Melanie Mitchell, and Luis M. Rocha
A Characterisation of NL Using Membrane Systems without Charges
and Dissolution.................................................. 164
Niall Murphy and Damien Woods
Quantum Wireless Sensor Networks ................................ 177
Naya Nagy, Marius Nagy, and Selim G. Akl
On the Computational Complexity of Spiking Neural P Systems ....... 189
Turlough Neary
Self-assembly of Decidable Sets .................................... 206
Matthew J. Patitz and Scott M. Summers
Ultrafilter and Non-standard Turing Machines ....................... 220
Petrus H. Potgieter and Elem´er E. Rosinger
Parallel Optimization of a Reversible (Quantum) Ripple-Carry
Adder .......................................................... 228
Michael Kirkedal Thomsen and Holger Bock Axelsen
Automata on Multisets of Communicating Objects ................... 242
Linmin Yang, Yong Wang, and Zhe Dang
Author Index.................................................. 259
Quantum Experiments Can Test Mathematical
Undecidability
Cˇaslav Brukner
Institutefor QuantumOptics and QuantumInformation,
Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
Faculty of Physics, University of Vienna,
Boltzmanngasse 5, A-1090 Vienna, Austria
Abstract. Wheneveramathematicalpropositiontobeprovedrequires
more information than it is contained in an axiomatic system, it can
neither be proved nor disproved, i.e. it is undecidable, within this ax-
iomatic system. I will show that certain mathematical propositions can
be encoded in quantum states and truth values of the propositions can
be tested in quantum measurements. I will then show that whenever a
proposition is undecidable within the system of axioms encoded in the
state, the measurement associated with the proposition gives random
outcomes.Thissuggestsaviewaccordingtowhichrandomnessinquan-
tum mechanics is of irreducible nature.
Inhisseminalworkfrom1931,G¨odelprovedthattheHilbertprogrammeonax-
iomatizationofmathematicscannotbefulfilledinprinciple,becauseanysystem
of axioms that is capable of expressing elementary arithmetic would necessarily
have to be either incomplete or inconsistent. It would always be the case that
either some proposition would be at once both provably true and false, or that
some propositions would never be derivable from the axioms.
One may wonder what G¨odel’s incompleteness theorem implies for physics.
For example, is there any connection between the incompleteness theorems and
quantum mechanics as both fundamentally limit our knowledge? Opinions on
the impact of the incompleteness theorem on physics vary considerably, from
the conclusion that, ”just because physics makes use of mathematics, it is by
no means requiredthat G¨odelplacesany limit upon the overallscope of physics
to understand the laws of Nature” [1], via demonstration that algorithmic ran-
domness is implied by a ”formal uncertainty principle” similar to Heisenberg’s
one [2], to a derivation of non-computability of sequences of quantum outcomes
from the quantum value indefiniteness [3,4].
In 1982, Chaitin gave an information theoretical formulation of the incom-
pleteness theorem suggesting that it arises whenever a propositionto be proven
and the axioms contain together more information than the set of axioms alone
[5,6]. In this work, when relating mathematical undecidability to quantum ran-
domness,IwillexclusivelyrefertotheincompletenessinChaitin’ssenseandnot
to the original work of G¨odel.
C.S.Caludeetal.(Eds.):UC2008,LNCS5204,pp.1–5,2008.
(cid:2)c Springer-VerlagBerlinHeidelberg2008
2 Cˇ. Brukner
Considerad-valentfunctionf(x)∈0,...,d−1ofasinglebinaryargumentx∈
{0,1},withdaprimenumber1.Thereared2suchfunctions.Wewillpartitionthe
functions into d+1 different waysfollowing the procedureofRef. [7]. In a given
partition,thed2 functionswillbedividedintoddifferentgroupseachcontaining
dfunctions.Enumeratingthefirstdpartitionsbythe integera=0,...,d−1and
the groups by b = 0,...,d−1, the groups of functions are generated from the
formula:
f(1)=af(0)⊕b, (1)
where the sum is modulo d. In the last partition, enumerated by a = d, the
functionsaredividedintogroupsb=0,...,d−1accordingtothefunctionalvalue
f(0)=b.Thefunctions canbe representedina tableinwhicha enumeratesthe
rows of the table, while b enumerates different columns. For all but the last row
the table is built in the following way : (i) choose the row, a, and the column,
b; (ii) vary f(0)=0,...,d−1 and compute f(1) according to Eq. (1); (iii) write
pairsf(0)f(1)inthe cell.The lastrow(a=d) is built asfollows:(i)choosethe
columnb;(ii)varyf(1)=0,...,d−1andputf(0)=b;(iii)writepairsf(0)f(1)
in the cell. For example, for d=3, one has
b=0 b=1 b=2
001020011121021222 “f(1)=b”
001122011220021021 “f(1)=f(0)⊕b”
001221011022021120 “f(1)=2f(0)⊕b”
000102101112202122 “f(0)=b”
(2)
The groups(cells in the table)of functions thatdo notbelong to the lastrow
are specified by the proposition:
{a,b}:“The function values f(0) and f(1) satisfy f(1)=af(0)⊕b”, (3)
while those from the last row by
{d,b}:“The function value f(0)=b”. (4)
The propositions corresponding to different partitions a are independent from
eachother.Forexample,ifonepostulatestheproposition(A)“f(1)=af(0)⊕b”
to be true, i.e. if we choose it as an “axiom”, then it is possible to prove that
“theorem” (T1) “f(1) = af(0)⊕ b(cid:3)” is false for all b(cid:3) (cid:4)= b. Proposition (T1)
is decidable within the axiom (A). Within the same axiom (A) it is, however,
impossibletoproveordisprove“theorem”(T2)“f(1)=mf(0)⊕n”withm(cid:4)=a.
Having only axiom (A), i.e. only one dit of information, there is not enough
information to know also the truth value of (T2). Ascribing truth values to two
1 The considerations here can be generalized to all dimensions that are powers of
primes. This is related to the fact that in these cases a complete set of mutually
unbiasedbasesisknowntoexit.Inall othercasesthisisanopenquestionandgoes
beyond thescope of thispaper (see, for example, Ref. [7]).