Table Of ContentAtlantis Studies in Computing
Series Editors: J. Bergstra · M. Mislove
Fabio Mogavero
Logics in Computer
Science
A Study on Extensions of Temporal and
Strategic Logics
Atlantis Studies in Computing
Volume 3
Series Editors
Jan A. Bergstra, University of Amsterdam, Amsterdam, The Netherlands
Michael W. Mislove, Tulane University, New Orleans, USA
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Fabio Mogavero
Logics in Computer Science
A Study on Extensions of Temporal
and Strategic Logics
FabioMogavero
Università degli StudidiNapoliFederico II
Napoli
Italy
ISSN 2212-8557 ISSN 2212-8565 (electronic)
ISBN 978-94-91216-94-7 ISBN 978-94-91216-95-4 (eBook)
DOI 10.2991/978-94-91216-95-4
LibraryofCongressControlNumber:2013938748
(cid:2)AtlantisPressandtheauthors2013
Thisbook,oranypartsthereof,maynotbereproducedforcommercialpurposesinanyformorbyany
means, electronic or mechanical, including photocopying, recording or any information storage and
retrievalsystemknownortobeinvented,withoutpriorpermissionfromthePublisher.
Printedonacid-freepaper
To Antonella,
my gentle love
To my parents and grandparents
‘‘Thought is only a flash between two long
nights, but this flash is everything.’’
Henri Poincare
Foreword
TheItalianchapteroftheEuropeanAssociationforTheoreticalComputerScience
(EATCS)wasfoundedin1988,andaimsatfacilitatingtheexchangeofideasand
resultsamongItaliantheoreticalcomputerscientists,andatstimulatingcooperation
betweenthe theoretical andthe applied communities inItaly.
One of the major activities of this chapter isto promoteresearch in theoretical
computerscience,stimulatingscientificexcellencebysupportingandencouraging
the very best and creative young Italian theoretical computer scientists. This is
done also by sponsoring a prize for the best Ph.D. thesis. This award has been
usually presented every two years and an interdisciplinary committee selects the
besttwoPh.D.theses,amongthosedefendedintheprevioustwo-yearperiod,one
on the themes of Algorithms, Automata, Complexity and Game Theory, and the
other on the themes of Logics, Semantics and Programming Theory.
In 2012 we started a cooperation with Atlantis Press so that the selected Ph.D.
theses would be published as volumes in the Atlantis Studies in Computing. The
present volume contains one of the two theses selected for publication in 2012:
Logics in Computer Science by Fabio Mogavero (supervisor: Prof. Aniello
Murano, University of Napoli Federico II, Napoli, Italy)
and
On Searching and Extracting Strings from Compressed Textual Data by Ros-
sano Venturini (supervisor: Prof. Paolo Ferragina, University of Pisa, Italy).
The scientific committee which selected these theses was composed of Pro-
fessorsMarcellaAnselmo(UniversityofSalerno),PierluigiCrescenzi(University
of Florence) and Gianluigi Zavattaro (University of Bologna).
They gave the following reasons to justify the assignment of the award to the
thesis by Fabio Mogavero
‘‘The thesis by Fabio Mogavero addresses problems related to property spec-
ification and verification by means of temporal logics and model checking.
Inparticular,thisworksignificantlycontributestotwospecificfields:temporal
logics with graded modalities, as far as closed systems are concerned, and logics
for strategies, as far as concurrent and multi-agent systems are concerned.
Gradedmodalitiesareparticularlyusefultoexpresspropertieslike:‘‘thereare
atleastndifferentcomputationsallowingthesystemtoreachapredefinedstate’’.
vii
viii Foreword
Concerningthissubject,themaincontributionofthethesisisGCTL:anextension
of the Computation Tree Logic (CTL) with such operators. The study of suc-
cinctness and complexity of satisfiability for GCTL is particularly valuable: sat-
isfiabilityturnsouttobeanEXPTIME-COMPLETEproblem,asitisthecaseforother
logics with graded modalities in the literature, while GCTL is proved to be
exponentially more succinct with respect to those logics.
The logics for strategies have been proposed in the literature as tools to deal
withinteractionsinopensystems.Aboutthissubject,themaincontributionofthis
thesis is SL, a logic particularly useful to reason about multi-agent concurrent
systems. SL strictly includes other similar logics such as the strategy logic in the
literature, like the strategy logic by Chatterjee-Henzinger-Piterman. The model
checking problem is proved to be 2EXPTIME-COMPLETE for SL, a result that sig-
nificantly improves the complexity boundaries already known for the logic by
Chatterjee-Henzinger-Piterman.
Theaboveresultshavebeenpresentedatconferencesofexcellentinternational
level like the Symposium on Logic in Computer Science (LICS) and the
Conference on Foundations of Software Technology and Theoretical Computer
Science (FSTTCS).’’
ThisyeartheItalianchapterofEATCSdecidedtodedicatethetwoprizestothe
memoryofProf.StefanoVarricchio(theoneonthemesofAlgorithms,Automata,
Complexity and Game Theory), and Prof. Nadia Busi (the one on themes on
Logics, Semantics and Programming Theory), both excellent researchers who
prematurely passed away.
I hope that this initiative will further contribute to strengthen the sense of
belongingtothesamecommunityofalltheyoungresearcherswhohaveaccepted
the challenges posed by any branch of theoretical computer science.
Napoli, January 2013 Tiziana Calamoneri
Preface
For a supervisor, it is always a pleasure and an honor to write a foreword for the
thesis of his Ph.D. student. For an excellent student like Fabio, this becomes
enormously great.
Rather than talking about the remarkable results obtained by Fabio, which are
absolutely well introduced and described in this thesis, I would like to talk about
passion, tenacity, perseverance, and above all the difficulty that Fabio had to
overcome in obtaining them. Also, I would love to report how everything began
and some anecdotes, which I am sure, one day, by reading them here again, will
give a remembrance of the good time we spent all together during the Ph.D.
period. Moreover, I would like to mention some of the people who had a signif-
icant role along Fabio’s scientific training.
IstillrememberthefirsttimeImetFabio.Itwastheendof2006.Fabiotoldme
ofhispassionfortheformalmethods,inparticularmodalandtemporallogics,the
several booksandarticleshehadread,and hiswilltodoaMaster thesis onthese
topics. I must admit that I was surprised and a little bit puzzled to see an engi-
neeringstudentinterestedinsuchtopicsandaskingacomputerscienceresearcher
to be his thesis advisor. At the same time I was happy, because during the years
spent at the computer science course, I had never seen a student of mine with the
same true interests.
At that time, I had just finished a tough work on mu-calculus enriched with
graded and backwards modalities. I spoke to Fabio and mentioned to him the
possibility of extending the same work to branching-time temporal logics. For a
week, Fabio came back to me with a series of comments on my work and a first
clearformalizationofGradedComputationTreeLogicwithbackwardsmodalities.
It was at that moment that I got fully convinced that Fabio could easily attend a
Ph.D.programandachievehighlevelresults.ThefirstaimwastofinishhisMaster
thesis in time for the Ph.D. call, that is, within October 2007, but without letting
the Master thesis to suffer in quality. We achieved the time target by a whisker!
FabiodiscussedhisMasterthesisattheendofOctoberand,mostimportant,hegot
a special encomium from the board that led me to be very proud of all the work
done. Then, Fabio participated in the Ph.D. examination and got the best score.
Thus, we immediately started the doctoral program. We decided together local
ix
x Preface
coursesandsummerschoolstoattend.Mainly,weimmediatelywentbacktowork
on the topics of research undertaken during the Master’s thesis and thanks to
important new results, we wrote two articles, one on Graded Computation Tree
Logic (GCTL, for short) and the other on Minimal Model Quantifiers. Both have
requiredalotofeffortthathasoftenledustoworkwithoutinterruptionforweeks
(Sundaysincluded).Theresultshavebeenverysatisfactoryandafteraboutayear
both works have been published in conference proceedings. In particular the
resultsonGCTLwerepresentedattheoutstandingconferenceLICS2009byFabio,
in the United States of America.
Meanwhile, I have to mention that, at the same Ph.D. competition that Fabio
took, another engineering student participated and won: Alessandro Bianco.
Immediately after the competition, Alessandro joined our group, working under
mysupervisionaswell.ItwasFabiowhoencouragedandpersuadedAlessandroto
participateinthePh.D.competitionandwithpleasureIcansaythathispresencein
the laboratory has been a great enrichment for the entire group. In this, Fabio has
proved to be an excellent talent scout. Fabio has been a sincere friend toward
Alessandroandalwaysspurredhimontheresearchactivity.Itwasagreatpleasure
togetinthelabandseethemdiscussdeeplyonresearchtopicsofanysort.Inthree
years, we achieved many important results together with Alessandro but, unfor-
tunately, many of them did not find space in this thesis. I think that period would
not have been the same without having Alessandro with us.
I promised at the beginning some anecdotes. Well, here they are. Mostly, they
are related with Fabio’s traveling. Let me say that every trip Fabio has taken
duringhisPh.D.,beitaschool,aconference,oravisitingresearcherperiod,there
has always been something disastrous: a flood, a train trip canceled, an airplane
that would have changed the landing airport at the very last moment, to mention
justafew.Forexample,thefirstschoolFabioattendedwasinGermany.Whilehe
was moving from the school location to the hotel, a deluge fell on Fabio, without
giving him any opportunity of covering. The second school was in Italy, at Ber-
tinoro, the return home was an odyssey because of a train crash. But, my favorite
stories are related to the four months spent by Fabio as a visiting scholar in
Houston tovisitMoshe Vardiat RiceUniversity,inthe Autumnof2008.Well,it
wasmewhopushedFabiotovisitMoshe.Overall,IvisitedMosheformorethana
year during my Ph.D. and I enjoyed very much my stay there. On the contrary,
Fabio’svisitingstayhasbeenfullofadventure,startingwiththeoutgoingjourney:
duetoaviolentstorminHouston,theairplanehadtofinallylandinDallas.After
about a month of permanence in Houston, a violent hurricane came and swept
away half of the city. Most of the population remained without electricity for
almost a month with all the difficulties that could arise, and so it happened for
Fabio. You can imagine my apprehension being in Italy! Well, at the end Fabio
returned to Italy 17 pounds lighter, but with a formidable research idea: a new
Strategy Logic (SL, for short)! At least the research goal was achieved.
At Rice, Moshe first introduced Fabio to the logics for strategic reasoning
throughATL*,thenhesuggestedhimtoinvestigatethislogicalongwithsomesort
ofextensions,includingthepastmodalitiesandtheconceptofrelentfulness.Then,
