Relations and Kleene Algebra in Computer Science: 11th International Conference on Relational Methods in Computer Science, RelMiCS 2009, and 6th International Conference on Applications of Kleene Algebra, AKA 2009, Doha, Qatar, November 1-5, 2009. Proceed

374 Pages·2009·3.85 MB·English

by  Rohit Parikh (auth.)

Lecture Notes in Computer Science 5827
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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
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IndianInstituteofTechnology,Madras,India
BernhardSteffen
UniversityofDortmund,Germany
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MicrosoftResearch,Cambridge,MA,USA
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UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
Max-PlanckInstituteofComputerScience,Saarbruecken,Germany
Rudolf Berghammer Ali Mohamed Jaoua
Bernhard Möller (Eds.)
Relations
and Kleene Algebra
in Computer Science
11th International Conference on Relational Methods
in Computer Science, RelMiCS 2009
and 6th International Conference onApplications
of KleeneAlgebra,AKA 2009
Doha, Qatar, November 1-5, 2009
Proceedings
1 3
VolumeEditors
RudolfBerghammer
Christian-Albrechts-UniversitätzuKiel
InstitutfürInformatik
Olshausenstraße40
24098Kiel,Germany
E-mail:[email protected]
AliMohamedJaoua
QatarUniversity
CollegeofEngineering
CSE209,P.O.Box2713
Doha,Qatar
E-mail:[email protected]
BernhardMöller
UniversitätAugsburg
InstitutfürInformatik
Universitätsstr.6a
86135Augsburg,Germany
E-mail:[email protected]
LibraryofCongressControlNumber:2009934859
CRSubjectClassification(1998):I.1.1,I.1.3,I.2.4,F.1.1,G.2.1
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
ISSN 0302-9743
ISBN-10 3-642-04638-XSpringerBerlinHeidelbergNewYork
ISBN-13 978-3-642-04638-4SpringerBerlinHeidelbergNewYork
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Preface
This volume contains the proceedings of the 11th International Conference on
RelationalMethodsinComputerScience(RelMiCS11)andthe6thInternational
Conference on Applications of Kleene Algebra (AKA 6). The joint conference
took place in Doha, Quatar, November 1–5, 2009. Its purpose was to bring to-
getherresearchersfromvarioussubdisciplinesofcomputerscience,mathematics
and related fields who use the calculus of relations and/or Kleene algebra as
methodological and conceptual tools in their work.
Thisconferenceisthe jointcontinuationoftwodifferentstrandsofmeetings.
The seminars of the RelMiCS series were held in Schloss Dagstuhl (Germany)
in January 1994, Parati(Brazil) in July 1995,Hammamet (Tunisia) in January
1997, Warsaw (Poland) in September 1998, Qu´ebec (Canada) in January 2000,
and Oisterwijk (The Netherlands) in October 2001.The conference on Applica-
tions of Kleene Algebra started as a workshop,also held in Schloss Dagstuhl, in
February2001.Tojointhesetwothemesinoneconferencewasmainlymotivated
by the substantial common interests and overlap of the two communities. Over
the years this has led to fruitful interactions and openened new and interest-
ing researchdirections. Joint meetings have been held in Malente (Germany) in
May 2003,in St Catherines (Canada) in February 2005, in Manchester (UK) in
August/September 2006 and in Frauenw¨orth (Germany) in April 2008.
Thisvolumecontains24contributionsbyresearchersfromallovertheworld.
In addition to the 22 regular papers there were the invited talks Computational
SocialChoiceUsingRelationAlgebraandRelView byHarriedeSwart(Tilburg
University, Netherlands) and Knowledge and Structure in Social Algorithms by
Rohit Parikh (Brooklyn College and CUNY Grad Center, USA). The papers
show that relational and Kleene algebra methods have wide-ranging diversity
and applicability in theory and practice.
In addition, for the third time, a PhD programme was offered. It included
threeinvitedtutorialsbyMarceloFr´ıas(UniversityofBuenosAires,Argentina),
Ali Jaoua (University of Qatar at Doha) and Gunther Schmidt (University of
the Armed Forces at Munich, Germany).
We are very grateful to the members of the Programme Committee and
the external referees for their care and diligence in reviewing the submitted
papers.We alsowantto thank QatarUniversityforhaving acceptedto hostthe
conference and Aws Al-Taie, Fatma Al-Baker, Zeina Hazem Al-Azmeh, Fatma
Al-Bloushi and Mohamad Hussein for their assistance; they made organizing
this meeting a pleasant experience. We also gratefully appreciate the excellent
facilitiesofferedbythe EasyChairconferenceadministrationsystem.Finally,we
cordiallythankoursponsorsSupremeEducationCouncil(SEC),QatarNational
ResearchFund (QNRF) and Qatar University (QU) for their generous support.
November 2009 Rudolf Berghammer
Ali Jaoua
Bernhard M¨oller
Organization
Programme Committee
J. Al’Jaam Doha, Qatar
R. Berghammer Kiel, Germany
H. de Swart Tilburg, Netherlands
J. Desharnais Laval, Canada
R. Duwairi Doha, Qatar
M. Fr´ıas Buenos Aires, Argentina
H. Furusawa Kagoshima,Japan
P. H¨ofner Augsburg, Germany
A. Jaoua Doha, Qatar
P. Jipsen Chapman, USA
W. Kahl McMaster, Canada
Y. Kawahara Kyushu, Japan
L. Meinicke Sydney, Australia
A. Mili Tunis, Tunisia; New York, USA
B. M¨oller Augsburg, Germany
C. Morgan Sydney, Australia
E. Orl(cid:2)owska Warsaw, Poland
S. Saminger-Platz Linz, Austria
G. Schmidt Munich, Germany
R. Schmidt Manchester, UK
G. Struth Sheffield, UK
M. Winter Brock, Canada
External Referees
Bernd Braßel Koki Nishizawa
Jean-Lou De Carufel Viorel Preoteasa
Jan Christiansen Ingrid Rewitzky
Han-Hing Dang Pawel Sobocinski
Ernst-ErichDoberkat Kim Solin
Roland Glu¨ck Sam Staton
Table of Contents
Knowledge and Structure in Social Algorithms....................... 1
Rohit Parikh
Computational Social Choice Using Relation Algebra and RelView.... 13
Harrie de Swart, Rudolf Berghammer, and Agnieszka Rusinowska
A Model of Internet Routing Using Semi-modules.................... 29
John N. Billings and Timothy G. Griffin
Visibly Pushdown Kleene Algebra and Its Use in Interprocedural
Analysis of (Mutually) Recursive Programs.......................... 44
Claude Bolduc and B´echir Ktari
Towards Algebraic Separation Logic................................ 59
Han-Hing Dang, Peter H¨ofner, and Bernhard Mo¨ller
Domain and Antidomain Semigroups ............................... 73
Jules Desharnais, Peter Jipsen, and Georg Struth
Composing Partially Ordered Monads .............................. 88
Patrik Eklund and Robert Helgesson
A Relation-Algebraic Approach to Liveness of Place/TransitionNets ... 103
Alexander Fronk and Rudolf Berghammer
∗-Continuous Idempotent Left Semirings and Their Ideal Completion... 119
Hitoshi Furusawa and Fumiya Sanda
A Semiring Approach to Equivalences, Bisimulations and Control ...... 134
Roland Glu¨ck, Bernhard Mo¨ller, and Michel Sintzoff
General Correctness Algebra ...................................... 150
Walter Guttmann
Foundations of Concurrent Kleene Algebra .......................... 166
C.A.R. Hoare, Bernhard Mo¨ller, Georg Struth, and Ian Wehrman
Armstrong’s Inference Rules in Dedekind Categories.................. 187
Toshikazu Ishida, Kazumasa Honda, and Yasuo Kawahara
Data Mining, Reasoning and Incremental Information Retrieval
through Non Enlargeable Rectangular Relation Coverage.............. 199
Ali Jaoua, Rehab Duwairi, Samir Elloumi, and Sadok Ben Yahia
Collagories for Relational Adhesive Rewriting ....................... 211
Wolfram Kahl
VIII Table of Contents
Cardinal Addition in Distributive Allegories ......................... 227
Yasuo Kawahara and Michael Winter
Relational Methods in the Analysis of While Loops: Observations of
Versatility ...................................................... 242
Asma Louhichi, Olfa Mraihi, Lamia Labed Jilani,
Khaled Bsaies, and Ali Mili
Modalities, Relations, and Learning: A Relational Interpretation of
Learning Approaches ............................................. 260
Martin Eric Mu¨ller
The Cube of Kleene Algebras and the Triangular Prism of
Multirelations ................................................... 276
Koki Nishizawa, Norihiro Tsumagari, and Hitoshi Furusawa
Discrete Duality for Relation Algebras and Cylindric Algebras......... 291
Ewa Orl(cid:3)owska and Ingrid Rewitzky
Contact Relations with Applications................................ 306
Gunther Schmidt and Rudolf Berghammer
A While ProgramNormal Form Theorem in Total Correctness......... 322
Kim Solin
Complements in Distributive Allegories ............................. 337
Michael Winter
On the Skeleton of Stonian p-Ortholattices.......................... 351
Michael Winter, Torsten Hahmann, and Michael Gruninger
Author Index.................................................. 367
Knowledge and Structure in Social Algorithms
Rohit Parikh
Brooklyn College and CUNY Graduate Center
City University of New York
365 Fifth Avenue
New York,NY 10016
http://sci.brooklyn.cuny.edu/cis/parikh/
Abstract. While contemporary Game Theory has concentrated much
on strategy, there is somewhat less attention paid to the role of knowl-
edgeandinformationtransfer.Thereareexceptionstothisruleofcourse,
especially starting with the work of Aumann [2], and with contribu-
tions made by ourselves with coauthors Cogan, Krasucki and Pacuit
[17,13]. But we have still only scratched the surface and there is still
a lot more that can be done. In this paper we point to the important
role which knowledge plays in social procedures (colorfully called Social
Software [15]).
Keywords: Knowledge, Society, Algorithms.
The peculiar character of the problem of a rational economic order is
determined precisely by the fact that the knowledge of the circumstances
of which we must make use never exists in concentrated or integrated
form, but solely as the dispersed bits of incomplete and frequently con-
tradictory knowledge which all the separate individuals possess. The eco-
nomic problem of society is thus not merely a problem of how to allocate
“given” resources – if “given” is taken to mean given to a single mind
which deliberately solves the problem set by these “data.” It is rather
a problem of how to secure the best use of resources known to any of
the members of society, for ends whose relative importance only these
individuals know.
F. Hayek
Individualism and Economic Order
1 Introduction
The first third of the XXth century saw two important developments. One of
these was Ramsey’s tracing of personal probabilities to an agent’s choices [22].
This was a precursorto the workof de Finetti, vonNeumann andMorgenstern,
R.Berghammeretal.(Eds.):RelMiCS/AKA2009,LNCS5827,pp.1–12,2009.
(cid:2)c Springer-VerlagBerlinHeidelberg2009
2 R. Parikh
andSavage[6,10,23].TheotheronewasTuring’sinventionoftheTuringmachine
[26] and the formulation of the Church-Turing thesis according to which all
computablefunctionsonnaturalnumberswererecursiveorTuringcomputable.1
Gametheoryhasdependedheavilyonthefirstofthesedevelopments,sinceof
course von Neumann and Morgenstern can be regarded as the fathers of Game
theory.Buttheotherdevelopmenthasreceivedlessattention.Thatdevelopment
led to the development and design of computers and also to fields like Logic of
Programs, Complexity Theory and Analysis of Algorithms. It also resulted in
much deeper understanding of algorithms, but only of computer algorithms.
Social algorithms have remained largely unanalyzed mathematically except in
special subfields like Social Choice Theory [1] or Fair Division [3]. These fields,
however, do not tend to analyze complex social algorithms (even algorithms of
modestcomplexitylikethe twothousandyearoldEuclid’salgorithm)asisdone
in computer science.2 The typical game theoretic example tends to be either a
one shot game, or else such a game repeated.
A later development, going back to the work of Hintikka, Lewis and a little
later Aumann [8,9,2], brought in the issue of knowledge. The notion of common
knowledge is of course very important for Aumann as common knowledge of
rationality can be seen as a justification for backward induction arguments.
But knowledge too has received less attention than it might. We all know
that the Valerie Plame affair [21] had something to do with someone knowing
something which they should not have,andsomeone revealingsomething which
they should not have. But why should they not? Clearly because of certain
possibleconsequences.Knowledgeandknowledgetransferareubiquitousinhow
social algorithms work. Note that the fact that the FBI bugged Burris’s phone
conversationswith Blagojevich’sbrother played an important role, and the fact
thatwedonotwanttheFBItohaveunlimitedrighttolisteninonconversations
are extremely important knowledge considerations.
We will try in this paper to bring attention to the importance of the two
issues of knowledge and logical structure of algorithms, and show the way to a
broader arena in which game theorists might want to play. Hopefully, in fact
almost certainly, there is a rich general theory to be developed.
1 TheresearchreportedherewassupportedinpartbyaresearchgrantfromthePSC-
CUNY program. Previous versions of this paper were presented at a workshop on
knowledgeat theUniversityof Quebecin Montreal(2007), andat theWorld Game
Theory meeting at Northwestern University (2008).
2 But society itself is replete with extremely complex algorithms. Just consider the
complexityinvolvedin Obama’s election tothepresidency,theconsequentvacating
of his senate seat, Blagojevich’s acquiring the right to name Obama’s successor,
Blagojevich namingBurristoObama’svacantseat,Blagojevich’s impeachmentand
removal from office, demands, so far unsuccessful, for Burris to step down, and, no
doubt,quietsatisfaction onthepartoftheRepublicans.AndevenObama’selection
to the presidency is hardly a simple event since it involved factors like Hillary’s
association with her husband, a former president, an initital feeling on the part of
African-AmericansthatObama,havingnoancestryintheinstitutionofslaverywas
not “one of us,” etc. etc.