Table Of ContentJoël Ouaknine Igor Potapov
James Worrell (Eds.)
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8th International Workshop, RP 2014
Oxford, UK, September 22–24, 2014
Proceedings
123
Lecture Notes in Computer Science 8762
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Joël Ouaknine Igor Potapov
James Worrell (Eds.)
Reachability Problems
8th International Workshop, RP 2014
Oxford, UK, September 22-24, 2014
Proceedings
1 3
VolumeEditors
JoëlOuaknine
UniversityofOxford
DepartmentofComputerScience
Oxford,UK
E-mail:[email protected]
IgorPotapov
UniversityofLiverpool
DepartmentofComputerScience
Liverpool,UK
E-mail:[email protected]
JamesWorrell
UniversityofOxford
DepartmentofComputerScience
Oxford,UK
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-319-11438-5 e-ISBN978-3-319-11439-2
DOI10.1007/978-3-319-11439-2
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Preface
This volume contains the papers presented at the 8th International Workshop
onReachabilityProblems(RP 2014)heldduring September 22–24,2014,atthe
Department of Computer Science, University of Oxford, UK.
RP2014wastheeighthintheseriesofworkshops,followingsuccessfulmeet-
ingsattheUppsalaUniversity,Sweden,in2013,UniversityofBordeaux,France,
in 2012, the University of Genoa, Italy, in 2011, Masaryk University of Brno,
CzechRepublic,in2010,EcolePolytechnique,France,in2009,attheUniversity
of Liverpool, UK, in 2008, and at Turku University, Finland, in 2007.
The aim of the workshop is to bring together scholars from diverse fields
with a shared interested in reachability problems. Reachability is a fundamen-
tal computational problem that appears in many different contexts: concurrent
systems, computational models such as cellular automata and Petri nets, de-
cision procedures for logical theories, program analysis, discrete and continu-
ous systems, time-critical systems, hybrid systems, rewriting systems, algebraic
structures(groups,semigroupsandrings),deterministic ornon-deterministicit-
erative maps, probabilistic and parametric systems, and open systems modelled
as games.
Typically, for a fixed system descriptiongivenin some form (rewriting rules,
transformationsbycomputablefunctions,systemsofequations,logicalformulas,
etc.) a reachability problem consists in checking whether a given set of target
states canbe reachedstartingfroma fixed setof initial states. The setof target
states can be represented explicitly or via some implicit representation (e.g., a
system of equations, a set of minimal elements with respect to some ordering
on the states). Sophisticated quantitative and qualitative properties can often
be reduced to basic reachability questions. Decidability and complexity bound-
aries, algorithmic solutions, and efficient heuristics are all important aspects to
be considered in this context. Algorithmic solutions are often based on differ-
ent combinations of exploration strategies, symbolic manipulations of sets of
states,decompositionproperties,reductiontooptimisationproblemsandlogical
decisionprocedures.Suchalgorithmsalsobenefit fromapproximations,abstrac-
tions, accelerations, and extrapolation heuristics. Ad hoc solutions as well as
solutions basedon general-purposeconstraintsolversand deduction engines are
often combined in order to balance efficiency and flexibility.
The purpose of the conference is to promote the exploration of new ap-
proaches for the modelling and analysis of computational processes by combin-
ingmathematical,algorithmic,andcomputationaltechniques.Topicsofinterest
include (but are not limited to): reachability for infinite state systems; rewrit-
ing systems; reachability analysis in counter/timed/cellular/communicatingau-
tomata; Petri- nets; computational aspects of semigroups, groups, and rings;
reachability in dynamical and hybrid systems; frontiers between decidable and
VI Preface
undecidable reachability problems; complexity and decidability aspects; pre-
dictabilityiniterativemapsandnewcomputationalparadigms.Alltheseaspects
were discussed in the presentations of the eighth edition of the RP workshop.
The proceedings of the previous editions of the workshop appeared in the fol-
lowing volumes:
MikaHirvensalo,VesaHalava,IgorPotapov,JarkkoKari(Eds.):Proceedingsof
the Satellite Workshops of DLT 2007. TUCS General Publication No 45, June
2007. ISBN: 978-952-12-1921-4.
Vesa Halava and Igor Potapov (Eds.): Proceedings of the Second Workshop on
ReachabilityProblemsinComputationalModels(RP2008).ElectronicNotesin
Theoretical Computer Science. Volume 223, Pages 1-264 (26 December 2008).
OlivierBournezandIgorPotapov(Eds.):ReachabilityProblems,ThirdInterna-
tional Workshop, RP 2009, Palaiseau, France, September 23–25, 2009, Lecture
Notes in Computer Science, 5797, Springer 2009.
Antonin Kucera and Igor Potapov (Eds.): Reachability Problems, 4th Interna-
tional Workshop, RP 2010, Brno, Czech Republic, August 28–29,2010, Lecture
Notes in Computer Science, 6227, Springer 2010.
GiorgioDelzanno,IgorPotapov(Eds.):ReachabilityProblems,5thInternational
Workshop, RP 2011, Genoa, Italy, September 28–30, 2011, Lecture Notes in
Computer Science, 6945, Springer 2011.
Alain Finkel, Jerome Leroux, Igor Potapov (Eds.): Reachability Problems, 6th
International Workshop, RP 2012, Bordeaux, France, September 17-19, 2012.
Lecture Notes in Computer Science 7550, Springer 2012.
ParoshAziz Abdulla, Igor Potapov (Eds.): Reachability Problems, 7th Interna-
tional Workshop, RP 2013, Uppsala, Sweden, September 24-26, 2013. Lecture
Notes in Computer Science 8169, Springer 2013.
The four keynote speakers at the 2014 conference were:
– Byron Cook, UCL and Microsoft Research, UK.
– Kousha Etessami, University of Edinburgh, UK.
– Anca Muscholl, LaBRI, University of Bordeaux, France.
– Sylvain Schmitz, LSV and ENS-Cachan, France.
There were 25 submissions. Each submission was reviewed by at least three
Program Committee members. The full list of the members of the Program
Committeeandthelistofexternalreviewerscanbefoundonthenexttwopages.
The ProgramCommittee is grateful for the highly appreciatedand high-quality
workproducedbytheseexternalreviewers.Basedonthesereviews,theProgram
Preface VII
Committee decided to accept 17 papers, in addition to the four invited talks.
The workshop also provided the opportunity to researchers to give informal
presentations that are prepared very shortly before the event and inform the
participants about current researchand work in progress.
Wegratefullyacknowledgetheorganizationteamfortheirhelp.Inparticular
we wish to thank Andrea Pilot, Renate Henison, Jordan Summers-Young and
Elizabeth Walsh.
It is alsoa greatpleasure to acknowledgethe team ofthe EasyChairsystem,
and the fine cooperation with the Lecture Notes in Computer Science team
of Springer, which made the production of this volume possible in time for the
conference.Finally,wethankalltheauthorsfortheirhigh-qualitycontributions,
and the participants for making this edition of RP 2014 a success.
September 2014 Jo¨el Ouaknine
Igor Potapov
James Worrell
Organization
Program Committee
Marius Bozga Verimag/CNRS, France
Thomas Brihaye University of Mons, Belgium
V´eronique Bruy`ere University of Mons, Belgium
Laurent Doyen LSV, ENS Cachan and CNRS, France
John Fearnley University of Liverpool, UK
Gilles Geeraerts Universit´e Libre de Bruxelles, Belgium
Kim Guldstrand Larsen Aalborg University, Denmark
Stefan Go¨ller University of Bremen, Germany
Martin Lange University of Kassel, Germany
Ranko Lazic University of Warwick, UK
Rupak Majumdar MPI-SWS, Germany
Nicolas Markey LSV, CNRS and ENS Cachan, France
Madhavan Mukund Chennai Mathematical Institute, India
Andrzej Murawski University of Warwick, UK
Joel Ouaknine Oxford University, UK
ParitoshPandya TIFR, India
Igor Potapov The University of Liverpool, UK
Alexander Rabinovich Tel Aviv University, Israel
Tayssir Touili LIAFA, CNRS and University Paris Diderot,
France
Thomas Wahl Northeastern University, USA
James Worrell Oxford University, UK
Lijun Zhang DTU, Denmark
Additional Reviewers
Andr´e, E´tienne Fribourg, Laurent
Bertrand, Nathalie Hofman, Piotr
Blondin, Michael Praveen, M.
Boigelot, Bernard Reichert, Julien
Bonnet, Remi Rezine, Ahmed
Chistikov, Dmitry Song, Lei
Devillers, Raymond Steffen, Martin
Donze, Alexandre Turrini, Andrea
Forejt, Vojtech Velner, Yaron
Abstracts of Invited Talks
Algorithms for
Branching Markov Decision Processes
Kousha Etessami
School of Informatics
Universityof Edinburgh
[email protected]
Multi-type branching processes (BPs)are classicstochastic processeswith appli-
cationsinmanyareas,includingbiologyandphysics.ABPmodelsthestochastic
evolution of a population of entities of distinct types. In each generation, every
entity ofeachtype, t, produces a setofentities ofvarioustypes inthe next gen-
eration according to a given probability distribution on offsprings for the type
t. In a Branching Markov Decision Process (BMDP), there is also a controller
whocantakeactionsthataffectthe probabilitydistributionoftheoffspringsfor
each entity of each type. For both BPs and BMDPs, the state space consists of
all possible populations, given by the number of entities of each type, so there
are infinitely many states.
Inrecentyearstherehasbeenabodyofresearchaimedatstudyingthecom-
putationalcomplexityofkeyanalysisproblemsassociatedwithMDPextensions
(and,moregenerallystochastic gameextensions)ofimportantclassesoffinitely-
presentedbut (countably) infinite-state stochastic processes, including BMDPs,
and closely related models, such as stochastic context-free grammars extended
withacontroller.Acentralanalysisproblemforallofthesemodels,whichforms
the key to a number of other analyses, is the problem of computing their op-
timal termination (extinction) probability. In the setting of BMDPs, these are
the maximum (minimum) probabilities, over all control strategies (or policies),
starting from a single entity of a given type, that the process will eventually
reach extinction (i.e., the state where no entities have survived). From these
quantities, one cancompute the optimum probabilityfor anyinitial population,
as well as other quantities of interest.
OnecanwriteBellmanoptimalityequationsfortheoptimalextinctionprob-
abilities of BMDPs, and for a number of related important infinite-state MDP
models. These Bellman equations are multivariate systems of monotone proba-
bilistic max (or min) polynomial equations, which we call max/minPPSs. They
havethe formx =P (x ,...,x ), i=1,...,n,whereeachP (x)≡max q (x)
i i 1 n i j i,j
(respectivelyP (x)≡min q (x))isthemax(min)overafinitenumberofprob-
i j i,j
abilistic polynomials, q (x). A probabilistic polynomial, q(x), is a multi-variate
i,j
polynomial where the monomial coefficients and constant term of q(x) are all
non-negative and sum to ≤1. The least fixed point (LFP) solution of such Bell-
man equations, corresponding to a given BMDP, captures its vector of optimal
extinction probabilities, starting with one object of each type.
This talk will surveyalgorithmsfor, and discuss the complexity of, some key
analysisproblemsforBMDPs.Inparticular,Iwilldiscussrecentjointworkwith
